{"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Definition named 'CACHE_LINE_BYTES' in the CubeObjectLayoutV2_5 family -- registry statement: V2.5 CubeObject Layout","coq_statement_full":"Definition CACHE_LINE_BYTES : nat := 64.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubeObjectLayoutV2_5.v":"1c6928e9dee435ed07fa0b949086d1c6bb75407e295a237539745b7683c2a74e","lean/CubeObjectLayoutV2_5.lean":"31050e9a536a58b72354d08227c6bd4c8351ad512e0b44db67cb7e9fe6adc186"},"files":{"coq_file":"coq/CubeObjectLayoutV2_5.v","lean_file":"lean/CubeObjectLayoutV2_5.lean"},"formal_systems":"Coq+Lean","id":"CUB-0001","invocation":"unwired","kernels":"none","kind":"Definition","lean_statement_full":"def CACHE_LINE_BYTES : Nat","lean_verified":"not stated in registry status for this 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(perm_scope parent) = perm_scope child.","coq_verified":"not stated in registry status for this row","crate":"cubie-core","deployable":false,"exec_file":"cubie-core/src/derived_candidates.rs","exec_fn":"cub_0134_a_highseverity_tarpit_isolation_theorem","exec_fns":["cub_0134_a_highseverity_tarpit_isolation_theorem"],"file_shas":{"coq/CubieDelegationRecursion_v6.v":"cc49c19c63c91166a6b123fe6a24b89750ed4fe84b86532d63d204e14aef00dd","lean/CubieDelegationRecursion_v6.lean":"21882c0374b00ee5d0e4dbfc25a5eb395a25f62a29f50647b9aa99ddf41346f7"},"files":{"coq_file":"coq/CubieDelegationRecursion_v6.v","lean_file":"lean/CubieDelegationRecursion_v6.lean"},"formal_systems":"Coq+Lean","id":"CUB-0134","invocation":"runtime","kernels":"none","kind":"Theorem","lean_statement_full":"theorem subagent_containment (parent child : PermBudget)\n (h : permission_attenuation parent child = true) :\n Nat.land child.perm_scope parent.perm_scope = child.perm_scope","lean_verified":"not stated in registry status for 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(pub_anon_id (public_entry dl)))\n (epoch (priv_anon_id (private_entry dl))).","coq_verified":"not stated in registry status for this row","crate":"cubie-core","deployable":false,"exec_file":"cubie-core/src/derived_candidates.rs","file_shas":{"coq/CubieDualLedger.v":"cf621f5ff28e43f7f7fe70f4b8f9da64f140da07b8d424dd7559a0fbe71cc9b0","lean/CubieDualLedger.lean":"fe54d13042d621e3b69701ebe58606de251340734c7429459cf906b64363bd66"},"files":{"coq_file":"coq/CubieDualLedger.v","lean_file":"lean/CubieDualLedger.lean"},"formal_systems":"Coq+Lean","id":"CUB-0138","invocation":"unwired","kernels":"none","kind":"Definition","lean_statement_full":"def anon_id_linked (dl : DualLedger) : Bool","lean_verified":"not stated in registry status for this row","module":"CubieDualLedger","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"coq_sha256":"cf621f5ff28e43f7...","lean_sha256":"fe54d13042d621e3..."},"source_completeness":"full 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this row","crate":"cubie-core","deployable":false,"exec_file":"cubie-core/src/derived_candidates.rs","exec_fn":"cub_0145_a_contextbomb_denial_theorem","exec_fns":["cub_0145_a_contextbomb_denial_theorem"],"file_shas":{"coq/CubieDualLedger.v":"cf621f5ff28e43f7f7fe70f4b8f9da64f140da07b8d424dd7559a0fbe71cc9b0","lean/CubieDualLedger.lean":"fe54d13042d621e3b69701ebe58606de251340734c7429459cf906b64363bd66"},"files":{"coq_file":"coq/CubieDualLedger.v","lean_file":"lean/CubieDualLedger.lean"},"formal_systems":"Coq+Lean","id":"CUB-0145","invocation":"runtime","kernels":"none","kind":"Theorem","lean_statement_full":"theorem no_consent_no_access (dl : DualLedger)\n (h : dl.private_entry.priv_consent_grant = false) :\n dual_ledger_ok dl = false","lean_verified":"not stated in registry status for this row","module":"CubieDualLedger","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"coq_sha256":"cf621f5ff28e43f7...","lean_sha256":"fe54d13042d621e3..."},"source_completeness":"full (CSV-sourced)","statement":"Dual Ledger","status":"VERIFIED_EXACT","theorem_name":"no_consent_no_access","use_cases":["admission","consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"FUNCTION-IMPL"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'no_capability_no_access' in the CubieDualLedger family -- registry statement: Dual Ledger","coq_statement_full":"Theorem no_capability_no_access :\n forall (dl : DualLedger),\n pub_capability (public_entry dl) = false ->\n dual_ledger_ok dl = false.","coq_verified":"not stated in registry status for this 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(CSV-sourced)","statement":"Dual Ledger","status":"VERIFIED_EXACT","theorem_name":"policy_filter_independent_of_consent","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'identity_collision_detection' in the CubieDualLedger family -- registry statement: Dual Ledger","coq_statement_full":"Theorem identity_collision_detection :\n forall (dl1 dl2 : DualLedger),\n anon_hash (pub_anon_id (public_entry dl1)) =\n anon_hash (pub_anon_id (public_entry dl2)) ->\n priv_real_id_hash (private_entry dl1) <>\n priv_real_id_hash (private_entry dl2) ->\n dual_ledger_ok dl1 = true ->\n dual_ledger_ok dl2 = true ->\n anon_hash (pub_anon_id (public_entry dl1)) =\n anon_hash (pub_anon_id (public_entry dl2)).","coq_verified":"not stated in registry 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row","module":"CubieDualLedger","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"coq_sha256":"cf621f5ff28e43f7...","lean_sha256":"fe54d13042d621e3..."},"source_completeness":"full (CSV-sourced)","statement":"Dual Ledger","status":"VERIFIED_EXACT","theorem_name":"identity_collision_detection","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'epoch_mismatch_breaks_linkage' in the CubieDualLedger family -- registry statement: Dual Ledger","coq_statement_full":"Theorem epoch_mismatch_breaks_linkage :\n forall (dl : DualLedger),\n epoch (pub_anon_id (public_entry dl)) <>\n epoch (priv_anon_id (private_entry dl)) ->\n anon_id_linked dl = false.","coq_verified":"not stated in registry status for this row","crate":"cubie-core","deployable":false,"exec_file":"cubie-core/src/derived_candidates.rs","exec_fn":"cub_0149_a_nvlink_waiter_safe_predicate_correction","exec_fns":["cub_0149_a_nvlink_waiter_safe_predicate_correction"],"file_shas":{"coq/CubieDualLedger.v":"cf621f5ff28e43f7f7fe70f4b8f9da64f140da07b8d424dd7559a0fbe71cc9b0","lean/CubieDualLedger.lean":"fe54d13042d621e3b69701ebe58606de251340734c7429459cf906b64363bd66"},"files":{"coq_file":"coq/CubieDualLedger.v","lean_file":"lean/CubieDualLedger.lean"},"formal_systems":"Coq+Lean","id":"CUB-0149","invocation":"runtime","kernels":"none","kind":"Theorem","lean_statement_full":"theorem epoch_mismatch_breaks_linkage (dl : DualLedger)\n (h : dl.public_entry.pub_anon_id.epoch \u2260\n dl.private_entry.priv_anon_id.epoch) :\n anon_id_linked dl = false","lean_verified":"not stated in registry status for this 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Ledger","status":"VERIFIED_EXACT","theorem_name":"billing_only_on_allow","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'billing_cost_matches_deducted' in the CubieDualLedger family -- registry statement: Dual Ledger","coq_statement_full":"Theorem billing_cost_matches_deducted :\n forall (br : BillingRecord) (deducted : nat),\n br_outcome br = true ->\n budget_cost br = deducted ->\n billing_cost_ok br deducted.","coq_verified":"not stated in registry status for this 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Ledger","status":"VERIFIED_EXACT","theorem_name":"billing_cost_matches_deducted","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"FUNCTION-IMPL"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'consent_log_requires_fresh_epoch' in the CubieDualLedger family -- registry statement: Dual Ledger","coq_statement_full":"Theorem consent_log_requires_fresh_epoch :\n forall (dl : DualLedger) (wh : nat),\n epoch (priv_anon_id (private_entry dl)) <> 0 ->\n exists (e : ConsentLogEntry),\n cle_epoch e = epoch (priv_anon_id (private_entry dl)) /\\\n workload_hash e = wh.","coq_verified":"not stated in registry status for this 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kv_cache_byte_estimator layers batch2 ctx h_kv d_head.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieEngineeringPhysics_v7.v":"3847bd051dced2138313e618e5d0a79ede0167291d34d968ce0eb75531cefbe9","lean/CubieEngineeringPhysics_v7.lean":"f5664620bfe8a4703f3e83f2db4c94f17b8c1ec2f4c35dffd57483feb259e512"},"files":{"coq_file":"coq/CubieEngineeringPhysics_v7.v","lean_file":"lean/CubieEngineeringPhysics_v7.lean"},"formal_systems":"Coq+Lean","id":"CUB-0180","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"theorem kv_estimator_monotone_batch\n (layers batch1 batch2 ctx h_kv d_head : Nat)\n (h : batch1 \u2264 batch2) :\n kv_cache_byte_estimator layers batch1 ctx h_kv d_head \u2264\n kv_cache_byte_estimator layers batch2 ctx h_kv d_head","lean_verified":"not stated in registry status for this 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(length (fence_after seq)))).","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieFenceV2_5.v":"5e73efa58417d8e0bcc64a462d57e3238d85e7d4b74b4984455c3b642a6fbb4d","lean/CubieFenceV2_5.lean":"dc21756c75fe784c98a715c051d5689369e365205f8e9101dc8b9784939a64b1"},"files":{"coq_file":"coq/CubieFenceV2_5.v","lean_file":"lean/CubieFenceV2_5.lean"},"formal_systems":"Coq+Lean","id":"CUB-0181","invocation":"unwired","kernels":"none","kind":"Definition","lean_statement_full":"def is_fenced_read (seq : FencedSequence) : Bool","lean_verified":"not stated in registry status for this row","module":"CubieFenceV2_5","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"5e73efa58417d8e0...","lean_sha256":"dc21756c75fe784c..."},"source_completeness":"full (CSV-sourced)","statement":"V2.5 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seq).","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieFenceV2_5.v":"5e73efa58417d8e0bcc64a462d57e3238d85e7d4b74b4984455c3b642a6fbb4d","lean/CubieFenceV2_5.lean":"dc21756c75fe784c98a715c051d5689369e365205f8e9101dc8b9784939a64b1"},"files":{"coq_file":"coq/CubieFenceV2_5.v","lean_file":"lean/CubieFenceV2_5.lean"},"formal_systems":"Coq+Lean","id":"CUB-0184","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem cub_0893_fence_after_mmio_write (seq : FencedSequence)\n (h : is_fenced_write seq = true) :\n seq.has_fence = true \u2227 0 < seq.fence_after.length","lean_verified":"not stated in registry status for this row","module":"CubieFenceV2_5","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec 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(CSV-sourced)","statement":"V2.5 Fence","status":"VERIFIED_EXACT","theorem_name":"fenced_scrub_implies_ordered_zero","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Definition named 'AUTH_PASS' in the CubieHardenedGate family -- registry statement: Hardened Gate","coq_statement_full":"Definition AUTH_PASS : N := 1515870810%N. (* 0x5A5A5A5A *)\nDefinition AUTH_FAIL : N := 2779096485%N. (* 0xA5A5A5A5 *)\n\nDefinition magic_word_valid (w : N) : bool :=\n N.eqb w AUTH_PASS || N.eqb w AUTH_FAIL.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieHardenedGate.v":"efffdd1f4c4646345890f4d39b46b9e396cfec78c8945fa069ef689c9476dbf7","lean/CubieHardenedGate.lean":"d39c9daa35ad778ee45776c26da0e9058d8d0524d78fcdf5a7ab3a24c0ccd9b0"},"files":{"coq_file":"coq/CubieHardenedGate.v","lean_file":"lean/CubieHardenedGate.lean"},"formal_systems":"Coq+Lean","id":"CUB-0189","invocation":"unwired","kernels":"none","kind":"Definition","lean_statement_full":"def AUTH_PASS : UInt32","lean_verified":"not stated in registry status for this row","module":"CubieHardenedGate","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"efffdd1f4c464634...","lean_sha256":"d39c9daa35ad778e..."},"source_completeness":"full (CSV-sourced)","statement":"Hardened Gate","status":"VERIFIED_EXACT","theorem_name":"AUTH_PASS","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Definition named 'AUTH_FAIL' in the CubieHardenedGate family -- registry statement: Hardened Gate","coq_statement_full":"Definition AUTH_FAIL : N := 2779096485%N. (* 0xA5A5A5A5 *)\n\nDefinition magic_word_valid (w : N) : bool :=\n N.eqb w AUTH_PASS || N.eqb w AUTH_FAIL.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieHardenedGate.v":"efffdd1f4c4646345890f4d39b46b9e396cfec78c8945fa069ef689c9476dbf7","lean/CubieHardenedGate.lean":"d39c9daa35ad778ee45776c26da0e9058d8d0524d78fcdf5a7ab3a24c0ccd9b0"},"files":{"coq_file":"coq/CubieHardenedGate.v","lean_file":"lean/CubieHardenedGate.lean"},"formal_systems":"Coq+Lean","id":"CUB-0190","invocation":"unwired","kernels":"none","kind":"Definition","lean_statement_full":"def AUTH_FAIL : UInt32","lean_verified":"not stated in registry status for this row","module":"CubieHardenedGate","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"efffdd1f4c464634...","lean_sha256":"d39c9daa35ad778e..."},"source_completeness":"full (CSV-sourced)","statement":"Hardened Gate","status":"VERIFIED_EXACT","theorem_name":"AUTH_FAIL","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Definition named 'magic_word_valid' in the CubieHardenedGate family -- registry statement: Hardened Gate","coq_statement_full":"Definition magic_word_valid (w : N) : bool :=\n N.eqb w AUTH_PASS || N.eqb w AUTH_FAIL.","coq_verified":"not stated in registry status for this 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row","module":"CubieHardenedGate","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"efffdd1f4c464634...","lean_sha256":"d39c9daa35ad778e..."},"source_completeness":"full (CSV-sourced)","statement":"Hardened Gate","status":"VERIFIED_EXACT","theorem_name":"magic_words_distinct","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'magic_word_exhaustive' in the CubieHardenedGate family -- registry statement: Hardened Gate","coq_statement_full":"Theorem magic_word_exhaustive :\n forall (w : N),\n magic_word_valid w = true ->\n w = AUTH_PASS \\/ w = AUTH_FAIL.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieHardenedGate.v":"efffdd1f4c4646345890f4d39b46b9e396cfec78c8945fa069ef689c9476dbf7","lean/CubieHardenedGate.lean":"d39c9daa35ad778ee45776c26da0e9058d8d0524d78fcdf5a7ab3a24c0ccd9b0"},"files":{"coq_file":"coq/CubieHardenedGate.v","lean_file":"lean/CubieHardenedGate.lean"},"formal_systems":"Coq+Lean","id":"CUB-0193","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem magic_word_exhaustive (w : UInt32) (h : magicWordValid w = true) :\n w = AUTH_PASS \u2228 w = AUTH_FAIL","lean_verified":"not stated in registry status for this row","module":"CubieHardenedGate","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"efffdd1f4c464634...","lean_sha256":"d39c9daa35ad778e..."},"source_completeness":"full (CSV-sourced)","statement":"Hardened 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row","crate":"","deployable":false,"file_shas":{"coq/CubieHardenedGate.v":"efffdd1f4c4646345890f4d39b46b9e396cfec78c8945fa069ef689c9476dbf7","lean/CubieHardenedGate.lean":"d39c9daa35ad778ee45776c26da0e9058d8d0524d78fcdf5a7ab3a24c0ccd9b0"},"files":{"coq_file":"coq/CubieHardenedGate.v","lean_file":"lean/CubieHardenedGate.lean"},"formal_systems":"Coq+Lean","id":"CUB-0194","invocation":"unwired","kernels":"none","kind":"Definition","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieHardenedGate","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"efffdd1f4c464634...","lean_sha256":"d39c9daa35ad778e..."},"source_completeness":"full (CSV-sourced)","statement":"Hardened Gate","status":"VERIFIED_EXACT","theorem_name":"temporally_valid","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not 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row","crate":"","deployable":false,"file_shas":{"coq/CubieHardenedGate.v":"efffdd1f4c4646345890f4d39b46b9e396cfec78c8945fa069ef689c9476dbf7","lean/CubieHardenedGate.lean":"d39c9daa35ad778ee45776c26da0e9058d8d0524d78fcdf5a7ab3a24c0ccd9b0"},"files":{"coq_file":"coq/CubieHardenedGate.v","lean_file":"lean/CubieHardenedGate.lean"},"formal_systems":"Coq+Lean","id":"CUB-0196","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem zero_expiry_always_valid (current : Nat) :\n temporallyValid current 0 = true","lean_verified":"not stated in registry status for this row","module":"CubieHardenedGate","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"efffdd1f4c464634...","lean_sha256":"d39c9daa35ad778e..."},"source_completeness":"full (CSV-sourced)","statement":"Hardened 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row","crate":"","deployable":false,"file_shas":{"coq/CubieHardenedGate.v":"efffdd1f4c4646345890f4d39b46b9e396cfec78c8945fa069ef689c9476dbf7","lean/CubieHardenedGate.lean":"d39c9daa35ad778ee45776c26da0e9058d8d0524d78fcdf5a7ab3a24c0ccd9b0"},"files":{"coq_file":"coq/CubieHardenedGate.v","lean_file":"lean/CubieHardenedGate.lean"},"formal_systems":"Coq+Lean","id":"CUB-0197","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem expired_token_denied (current expiry : Nat)\n (hpos : expiry > 0) (hexp : current > expiry) :\n tokenExpired current expiry = true","lean_verified":"not stated in registry status for this row","module":"CubieHardenedGate","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"efffdd1f4c464634...","lean_sha256":"d39c9daa35ad778e..."},"source_completeness":"full (CSV-sourced)","statement":"Hardened 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row","crate":"","deployable":false,"file_shas":{"coq/CubieHardenedGate.v":"efffdd1f4c4646345890f4d39b46b9e396cfec78c8945fa069ef689c9476dbf7","lean/CubieHardenedGate.lean":"d39c9daa35ad778ee45776c26da0e9058d8d0524d78fcdf5a7ab3a24c0ccd9b0"},"files":{"coq_file":"coq/CubieHardenedGate.v","lean_file":"lean/CubieHardenedGate.lean"},"formal_systems":"Coq+Lean","id":"CUB-0198","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem monotonic_expiry (t1 t2 expiry : Nat)\n (hle : t1 \u2264 t2) (hexp : tokenExpired t1 expiry = true) :\n tokenExpired t2 expiry = true","lean_verified":"not stated in registry status for this row","module":"CubieHardenedGate","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"efffdd1f4c464634...","lean_sha256":"d39c9daa35ad778e..."},"source_completeness":"full (CSV-sourced)","statement":"Hardened 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row","crate":"","deployable":false,"file_shas":{"coq/CubieHardenedGate.v":"efffdd1f4c4646345890f4d39b46b9e396cfec78c8945fa069ef689c9476dbf7","lean/CubieHardenedGate.lean":"d39c9daa35ad778ee45776c26da0e9058d8d0524d78fcdf5a7ab3a24c0ccd9b0"},"files":{"coq_file":"coq/CubieHardenedGate.v","lean_file":"lean/CubieHardenedGate.lean"},"formal_systems":"Coq+Lean","id":"CUB-0199","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem boundary_valid (expiry : Nat) (hpos : expiry > 0) :\n temporallyValid expiry expiry = true","lean_verified":"not stated in registry status for this row","module":"CubieHardenedGate","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"efffdd1f4c464634...","lean_sha256":"d39c9daa35ad778e..."},"source_completeness":"full (CSV-sourced)","statement":"Hardened 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(* 0xCB1EFACE *)\n\nDefinition pregate_pass (route_magic : N) : bool :=\n N.eqb route_magic PREGATE_MAGIC.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieHardenedGate.v":"efffdd1f4c4646345890f4d39b46b9e396cfec78c8945fa069ef689c9476dbf7","lean/CubieHardenedGate.lean":"d39c9daa35ad778ee45776c26da0e9058d8d0524d78fcdf5a7ab3a24c0ccd9b0"},"files":{"coq_file":"coq/CubieHardenedGate.v","lean_file":"lean/CubieHardenedGate.lean"},"formal_systems":"Coq+Lean","id":"CUB-0200","invocation":"unwired","kernels":"none","kind":"Definition","lean_statement_full":"def PREGATE_MAGIC : UInt32","lean_verified":"not stated in registry status for this row","module":"CubieHardenedGate","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"efffdd1f4c464634...","lean_sha256":"d39c9daa35ad778e..."},"source_completeness":"full (CSV-sourced)","statement":"Hardened Gate","status":"VERIFIED_EXACT","theorem_name":"PREGATE_MAGIC","use_cases":["NIST"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Definition named 'pregate_pass' in the CubieHardenedGate family -- registry statement: Hardened Gate","coq_statement_full":"Definition pregate_pass (route_magic : N) : bool :=\n N.eqb route_magic PREGATE_MAGIC.","coq_verified":"not stated in registry status for this 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row","crate":"","deployable":false,"file_shas":{"coq/CubieNistC4V2_5.v":"04299b30dcf583f240701f58896fcda1ea0fecf777f285b3480bacd3de931776","lean/CubieNistC4V2_5.lean":"7972ceeca225dd0ff13c2734a047d4821beacc3b3aeb9daa2b9c4caf2b9fd32c"},"files":{"coq_file":"coq/CubieNistC4V2_5.v","lean_file":"lean/CubieNistC4V2_5.lean"},"formal_systems":"Coq+Lean","id":"CUB-0232","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem cub_0908_context_failure_denies\n (face_ok : Nat -> Bool) (hmac_ok delegation_ok consent_ok : Bool)\n (h : c4_context_gate face_ok = false) :\n nist_c4_authorize face_ok hmac_ok delegation_ok consent_ok = false","lean_verified":"not stated in registry status for this row","module":"CubieNistC4V2_5","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec 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fn/crate)","shas":{"coq_sha256":"41b2f98d8e500dfc...","lean_sha256":"ee419cd987777178..."},"source_completeness":"full (CSV-sourced)","statement":"v1.10 Non-Quantum","status":"VERIFIED_EXACT","theorem_name":"auth_implies_core","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"2 axioms","axiom_profile":"2 axioms","context_purpose":"DERIVED: Theorem named 'rotate_auth_implies_linear_handoff' in the CubieNonQuantum_v1_10 family -- registry statement: v1.10 Non-Quantum","coq_statement_full":"Theorem rotate_auth_implies_linear_handoff :\n forall (ctx : Context) (depth : nat) (A : AccessSet) (q : Cubie)\n (pi : AccessPattern) (axis : Face) (w : Workflow) (h : Handoff),\n Auth ctx depth A q pi AMRotate axis w h -> LinearHandoffOK ctx h.","coq_verified":"not stated in registry status for this 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fn/crate)","shas":{"coq_sha256":"41b2f98d8e500dfc...","lean_sha256":"ee419cd987777178..."},"source_completeness":"full (CSV-sourced)","statement":"v1.10 Non-Quantum","status":"VERIFIED_EXACT","theorem_name":"rotate_auth_implies_linear_handoff","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"2 axioms","axiom_profile":"2 axioms","context_purpose":"DERIVED: Theorem named 'linear_handoff_unconsumed' in the CubieNonQuantum_v1_10 family -- registry statement: v1.10 Non-Quantum","coq_statement_full":"Theorem linear_handoff_unconsumed :\n forall (ctx : Context) (h : Handoff),\n LinearHandoffOK ctx h -> consumed h = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieNonQuantum_v1_10.v":"41b2f98d8e500dfcf514ae2473a217068463740b2caa73fcf45f966f399ad65a","lean/CubieNonQuantum_v1_10.lean":"ee419cd987777178f402438229962b3ab9fa790239397b3b12a114475693c7a8"},"files":{"coq_file":"coq/CubieNonQuantum_v1_10.v","lean_file":"lean/CubieNonQuantum_v1_10.lean"},"formal_systems":"Coq+Lean","id":"CUB-0250","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem linear_handoff_unconsumed\n (ctx : Context) (h : Handoff)\n (hl : LinearHandoffOK ctx h) :\n consumed h = false","lean_verified":"not stated in registry status for this row","module":"CubieNonQuantum_v1_10","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"41b2f98d8e500dfc...","lean_sha256":"ee419cd987777178..."},"source_completeness":"full (CSV-sourced)","statement":"v1.10 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(CSV-sourced)","statement":"CubieOmega Bridge v2.3","status":"VERIFIED_EXACT","theorem_name":"ashby_witness_iff_topology_collapse","use_cases":["topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'licklider_witness_iff_identity_collapse' in the CubieOmegaBridgeV2_3 family -- registry statement: CubieOmega Bridge v2.3","coq_statement_full":"Theorem licklider_witness_iff_identity_collapse :\n forall s : OmegaState,\n witness_explains licklider_failure s = true <-> licklider_attribution s = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieOmegaBridgeV2_3.v":"d238a43680519733992600276631358d38f5ae01fe9b9b1f4467bd4be04eaaff","lean/CubieOmegaBridgeV2_3.lean":"82d8e358a2463be0bbcc1db19e6675cc408ce181de91235c801f7e8ac226e6a8"},"files":{"coq_file":"coq/CubieOmegaBridgeV2_3.v","lean_file":"lean/CubieOmegaBridgeV2_3.lean"},"formal_systems":"Coq+Lean","id":"CUB-0268","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem licklider_witness_iff_identity_collapse (s : OmegaState) :\n witness_explains licklider_failure s = true \u2194 s.licklider_attribution = false","lean_verified":"not stated in registry status for this row","module":"CubieOmegaBridgeV2_3","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"d238a43680519733...","lean_sha256":"82d8e358a2463be0..."},"source_completeness":"full (CSV-sourced)","statement":"CubieOmega Bridge v2.3","status":"VERIFIED_EXACT","theorem_name":"licklider_witness_iff_identity_collapse","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'vonneumann_witness_iff_replication_collapse' in the CubieOmegaBridgeV2_3 family -- registry statement: CubieOmega Bridge v2.3","coq_statement_full":"Theorem vonneumann_witness_iff_replication_collapse :\n forall s : OmegaState,\n witness_explains vonneumann_failure s = true <-> vonneumann_replication s = false.","coq_verified":"not stated in registry status for this 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(CSV-sourced)","statement":"CubieOmega Bridge v2.3","status":"VERIFIED_EXACT","theorem_name":"vonneumann_witness_iff_replication_collapse","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'shannon_witness_iff_information_collapse' in the CubieOmegaBridgeV2_3 family -- registry statement: CubieOmega Bridge v2.3","coq_statement_full":"Theorem shannon_witness_iff_information_collapse :\n forall s : OmegaState,\n witness_explains shannon_failure s = true <-> shannon_information s = false.","coq_verified":"not stated in registry status for this 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(CSV-sourced)","statement":"CubieOmega Bridge v2.3","status":"VERIFIED_EXACT","theorem_name":"shannon_witness_iff_information_collapse","use_cases":["crypto"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'thompson_witness_iff_attestation_collapse' in the CubieOmegaBridgeV2_3 family -- registry statement: CubieOmega Bridge v2.3","coq_statement_full":"Theorem thompson_witness_iff_attestation_collapse :\n forall s : OmegaState,\n witness_explains thompson_failure s = true <-> thompson_trust s = false.","coq_verified":"not stated in registry status for this 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(CSV-sourced)","statement":"CubieOmega Bridge v2.3","status":"VERIFIED_EXACT","theorem_name":"thompson_witness_iff_attestation_collapse","use_cases":["NIST"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'session_witness_iff_policy_collapse' in the CubieOmegaBridgeV2_3 family -- registry statement: CubieOmega Bridge v2.3","coq_statement_full":"Theorem session_witness_iff_policy_collapse :\n forall s : OmegaState,\n witness_explains session_failure s = true <-> session_state s = false.","coq_verified":"not stated in registry status for this 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(CSV-sourced)","statement":"CubieOmega Bridge v2.3","status":"VERIFIED_EXACT","theorem_name":"session_witness_iff_policy_collapse","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'hardware_witness_iff_hardware_collapse' in the CubieOmegaBridgeV2_3 family -- registry statement: CubieOmega Bridge v2.3","coq_statement_full":"Theorem hardware_witness_iff_hardware_collapse :\n forall s : OmegaState,\n witness_explains hardware_failure s = true <-> hardware_key s = false.","coq_verified":"not stated in registry status for this 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(CSV-sourced)","statement":"CubieOmega Bridge v2.3","status":"VERIFIED_EXACT","theorem_name":"hardware_witness_iff_hardware_collapse","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'cubie_admit_iff_manifold_valid_with_hardware' in the CubieOmegaBridgeV2_3 family -- registry statement: CubieOmega Bridge v2.3","coq_statement_full":"Theorem cubie_admit_iff_manifold_valid_with_hardware :\n forall (c : CubieState),\n manifold_valid (project_to_omega c true) = cubie_admit c.","coq_verified":"not stated in registry status for this 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Bridge v2.3","status":"VERIFIED_EXACT","theorem_name":"cubie_admit_iff_manifold_valid_with_hardware","use_cases":["admission","topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'cubie_admit_implies_all_witnesses_pass' in the CubieOmegaBridgeV2_3 family -- registry statement: CubieOmega Bridge v2.3","coq_statement_full":"Theorem cubie_admit_implies_all_witnesses_pass :\n forall (c : CubieState),\n cubie_admit c = true ->\n ashby_regulation (project_to_omega c true) = true /\\\n licklider_attribution (project_to_omega c true) = true /\\\n vonneumann_replication (project_to_omega c true) = true /\\\n shannon_information (project_to_omega c true) = true /\\\n thompson_trust (project_to_omega c true) = true /\\\n session_state (project_to_omega c true) = true /\\\n hardware_key (project_to_omega c true) = true.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieOmegaBridgeV2_3.v":"d238a43680519733992600276631358d38f5ae01fe9b9b1f4467bd4be04eaaff","lean/CubieOmegaBridgeV2_3.lean":"82d8e358a2463be0bbcc1db19e6675cc408ce181de91235c801f7e8ac226e6a8"},"files":{"coq_file":"coq/CubieOmegaBridgeV2_3.v","lean_file":"lean/CubieOmegaBridgeV2_3.lean"},"formal_systems":"Coq+Lean","id":"CUB-0275","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem cubie_admit_implies_all_witnesses_pass (c : CubieState) :\n cubie_admit c = true \u2192\n (project_to_omega c true).ashby_regulation = true \u2227\n (project_to_omega c true).licklider_attribution = true \u2227\n (project_to_omega c true).vonneumann_replication = true \u2227\n (project_to_omega c true).shannon_information = true \u2227\n (project_to_omega c true).thompson_trust = true \u2227\n (project_to_omega c true).session_state = true \u2227\n (project_to_omega c true).hardware_key = true","lean_verified":"not stated in registry status for this row","module":"CubieOmegaBridgeV2_3","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"d238a43680519733...","lean_sha256":"82d8e358a2463be0..."},"source_completeness":"full (CSV-sourced)","statement":"CubieOmega Bridge v2.3","status":"VERIFIED_EXACT","theorem_name":"cubie_admit_implies_all_witnesses_pass","use_cases":["admission","topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'cubie_denial_implies_witness_attribution' in the CubieOmegaBridgeV2_3 family -- registry statement: CubieOmega Bridge v2.3","coq_statement_full":"Theorem cubie_denial_implies_witness_attribution :\n forall (c : CubieState) (hw : bool),\n cubie_admit c = false \\/ hw = false ->\n explanation_exists (project_to_omega c hw) = true.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieOmegaBridgeV2_3.v":"d238a43680519733992600276631358d38f5ae01fe9b9b1f4467bd4be04eaaff","lean/CubieOmegaBridgeV2_3.lean":"82d8e358a2463be0bbcc1db19e6675cc408ce181de91235c801f7e8ac226e6a8"},"files":{"coq_file":"coq/CubieOmegaBridgeV2_3.v","lean_file":"lean/CubieOmegaBridgeV2_3.lean"},"formal_systems":"Coq+Lean","id":"CUB-0276","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem cubie_denial_implies_witness_attribution (c : CubieState) (hw : Bool) :\n (cubie_admit c = false \u2228 hw = false) \u2192\n explanation_exists (project_to_omega c hw) = true","lean_verified":"not stated in registry status for this row","module":"CubieOmegaBridgeV2_3","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"d238a43680519733...","lean_sha256":"82d8e358a2463be0..."},"source_completeness":"full (CSV-sourced)","statement":"CubieOmega Bridge v2.3","status":"VERIFIED_EXACT","theorem_name":"cubie_denial_implies_witness_attribution","use_cases":["admission"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'manifold_validity_decidable' in the CubieOmegaBridgeV2_3 family -- registry statement: CubieOmega Bridge v2.3","coq_statement_full":"Theorem manifold_validity_decidable :\n forall s : OmegaState,\n manifold_valid s = true \\/ manifold_valid s = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieOmegaBridgeV2_3.v":"d238a43680519733992600276631358d38f5ae01fe9b9b1f4467bd4be04eaaff","lean/CubieOmegaBridgeV2_3.lean":"82d8e358a2463be0bbcc1db19e6675cc408ce181de91235c801f7e8ac226e6a8"},"files":{"coq_file":"coq/CubieOmegaBridgeV2_3.v","lean_file":"lean/CubieOmegaBridgeV2_3.lean"},"formal_systems":"Coq+Lean","id":"CUB-0277","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem manifold_validity_decidable (s : OmegaState) :\n manifold_valid s = true \u2228 manifold_valid s = false","lean_verified":"not stated in registry status for this row","module":"CubieOmegaBridgeV2_3","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"d238a43680519733...","lean_sha256":"82d8e358a2463be0..."},"source_completeness":"full (CSV-sourced)","statement":"CubieOmega Bridge v2.3","status":"VERIFIED_EXACT","theorem_name":"manifold_validity_decidable","use_cases":["topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'containment_failure_attribution_total' in the CubieOmegaBridgeV2_3 family -- registry statement: CubieOmega Bridge v2.3","coq_statement_full":"Theorem containment_failure_attribution_total :\n forall s : OmegaState,\n manifold_valid s = false ->\n (witness_explains ashby_failure s = true) \\/\n (witness_explains licklider_failure s = true) \\/\n (witness_explains vonneumann_failure s = true) \\/\n (witness_explains shannon_failure s = true) \\/\n (witness_explains thompson_failure s = true) \\/\n (witness_explains session_failure s = true) \\/\n (witness_explains hardware_failure s = true).","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieOmegaBridgeV2_3.v":"d238a43680519733992600276631358d38f5ae01fe9b9b1f4467bd4be04eaaff","lean/CubieOmegaBridgeV2_3.lean":"82d8e358a2463be0bbcc1db19e6675cc408ce181de91235c801f7e8ac226e6a8"},"files":{"coq_file":"coq/CubieOmegaBridgeV2_3.v","lean_file":"lean/CubieOmegaBridgeV2_3.lean"},"formal_systems":"Coq+Lean","id":"CUB-0278","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem containment_failure_attribution_total (s : OmegaState) :\n manifold_valid s = false \u2192\n (witness_explains ashby_failure s = true) \u2228\n (witness_explains licklider_failure s = true) \u2228\n (witness_explains vonneumann_failure s = true) \u2228\n (witness_explains shannon_failure s = true) \u2228\n (witness_explains thompson_failure s = true) \u2228\n (witness_explains session_failure s = true) \u2228\n (witness_explains hardware_failure s = true)","lean_verified":"not stated in registry status for this row","module":"CubieOmegaBridgeV2_3","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"d238a43680519733...","lean_sha256":"82d8e358a2463be0..."},"source_completeness":"full (CSV-sourced)","statement":"CubieOmega Bridge v2.3","status":"VERIFIED_EXACT","theorem_name":"containment_failure_attribution_total","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"10 axioms","axiom_profile":"10 axioms","context_purpose":"DERIVED: Definition named 'OperationalFractalManifoldValid' in the CubieOmegaStage2V2_3 family -- registry statement: CubieOmega Stage2 v2.3","coq_statement_full":"Definition OperationalFractalManifoldValid (x : ActionTensor) (s : SessionState) (k : HardwareKey) : Prop :=\n FractalDepth x <= StaticEventHorizon /\\\n ConditionalCompressibilityGap x s >= ExpertLineageFloor /\\\n EntangledTwistedParity x s k >= SurfaceFaceParity x /\\\n (GenerativePercolationDepth x <= PercolationCriticalLimit \\/ AttestedInMacroRegistry x) /\\\n ToolchainTensorHash x = OrthogonalCrossCompileHash x.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieOmegaStage2V2_3.v":"a39fbf62de2184534b3d07e2404674bc91add2d497d1fb9e87674a0ef9cffa65","lean/CubieOmegaStage2V2_3.lean":"696c637db7dca52027970f3ec430dfde8d4bb9a4238ab41775021ad3fa438210"},"files":{"coq_file":"coq/CubieOmegaStage2V2_3.v","lean_file":"lean/CubieOmegaStage2V2_3.lean"},"formal_systems":"Coq+Lean","id":"CUB-0279","invocation":"unwired","kernels":"none","kind":"Definition","lean_statement_full":"def OperationalFractalManifoldValid (x : ActionTensor) (s : SessionState) (k : HardwareKey) : Prop","lean_verified":"not stated in registry status for this row","module":"CubieOmegaStage2V2_3","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"a39fbf62de218453...","lean_sha256":"696c637db7dca520..."},"source_completeness":"full (CSV-sourced)","statement":"CubieOmega Stage2 v2.3","status":"VERIFIED_EXACT","theorem_name":"OperationalFractalManifoldValid","use_cases":["topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"10 axioms","axiom_profile":"10 axioms","context_purpose":"DERIVED: Definition named 'cubie_admit' in the CubieOmegaStage2V2_3 family -- registry statement: CubieOmega Stage2 v2.3","coq_statement_full":"Definition cubie_admit (c : CubieState) : bool :=\n c_topology c && c_identity c && c_lease c && c_epoch c &&\n c_reqhash c && c_attest c && c_policy c.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieOmegaStage2V2_3.v":"a39fbf62de2184534b3d07e2404674bc91add2d497d1fb9e87674a0ef9cffa65","lean/CubieOmegaStage2V2_3.lean":"696c637db7dca52027970f3ec430dfde8d4bb9a4238ab41775021ad3fa438210"},"files":{"coq_file":"coq/CubieOmegaStage2V2_3.v","lean_file":"lean/CubieOmegaStage2V2_3.lean"},"formal_systems":"Coq+Lean","id":"CUB-0280","invocation":"unwired","kernels":"none","kind":"Definition","lean_statement_full":"def cubie_admit (c : CubieState) : Bool","lean_verified":"not stated in registry status for this row","module":"CubieOmegaStage2V2_3","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"a39fbf62de218453...","lean_sha256":"696c637db7dca520..."},"source_completeness":"full (CSV-sourced)","statement":"CubieOmega Stage2 v2.3","status":"VERIFIED_EXACT","theorem_name":"cubie_admit","use_cases":["admission","topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"10 axioms","axiom_profile":"10 axioms","context_purpose":"DERIVED: Theorem named 'ashby_witness_from_topology_failure' in the CubieOmegaStage2V2_3 family -- registry statement: CubieOmega Stage2 v2.3","coq_statement_full":"Theorem ashby_witness_from_topology_failure :\n forall (c : CubieState) (s : SessionState) (k : HardwareKey),\n c_topology c = false ->\n OperationalContainmentFailure (cubie_to_action c) s k.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieOmegaStage2V2_3.v":"a39fbf62de2184534b3d07e2404674bc91add2d497d1fb9e87674a0ef9cffa65","lean/CubieOmegaStage2V2_3.lean":"696c637db7dca52027970f3ec430dfde8d4bb9a4238ab41775021ad3fa438210"},"files":{"coq_file":"coq/CubieOmegaStage2V2_3.v","lean_file":"lean/CubieOmegaStage2V2_3.lean"},"formal_systems":"Coq+Lean","id":"CUB-0281","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem ashby_witness_from_topology_failure\n (c : CubieState) (s : SessionState) (k : HardwareKey)\n (H : c.c_topology = false) :\n OperationalContainmentFailure (cubie_to_action c) s k","lean_verified":"not stated in registry status for this row","module":"CubieOmegaStage2V2_3","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"a39fbf62de218453...","lean_sha256":"696c637db7dca520..."},"source_completeness":"full (CSV-sourced)","statement":"CubieOmega Stage2 v2.3","status":"VERIFIED_EXACT","theorem_name":"ashby_witness_from_topology_failure","use_cases":["topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"10 axioms","axiom_profile":"10 axioms","context_purpose":"DERIVED: Theorem named 'licklider_witness_from_identity_failure' in the CubieOmegaStage2V2_3 family -- registry statement: CubieOmega Stage2 v2.3","coq_statement_full":"Theorem licklider_witness_from_identity_failure :\n forall (c : CubieState) (s : SessionState) (k : HardwareKey),\n c_identity c = false ->\n OperationalContainmentFailure (cubie_to_action c) s k.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieOmegaStage2V2_3.v":"a39fbf62de2184534b3d07e2404674bc91add2d497d1fb9e87674a0ef9cffa65","lean/CubieOmegaStage2V2_3.lean":"696c637db7dca52027970f3ec430dfde8d4bb9a4238ab41775021ad3fa438210"},"files":{"coq_file":"coq/CubieOmegaStage2V2_3.v","lean_file":"lean/CubieOmegaStage2V2_3.lean"},"formal_systems":"Coq+Lean","id":"CUB-0282","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem licklider_witness_from_identity_failure\n (c : CubieState) (s : SessionState) (k : HardwareKey)\n (H : c.c_identity = false) :\n OperationalContainmentFailure (cubie_to_action c) s k","lean_verified":"not stated in registry status for this row","module":"CubieOmegaStage2V2_3","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"a39fbf62de218453...","lean_sha256":"696c637db7dca520..."},"source_completeness":"full (CSV-sourced)","statement":"CubieOmega Stage2 v2.3","status":"VERIFIED_EXACT","theorem_name":"licklider_witness_from_identity_failure","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"10 axioms","axiom_profile":"10 axioms","context_purpose":"DERIVED: Theorem named 'licklider_witness_from_policy_failure' in the CubieOmegaStage2V2_3 family -- registry statement: CubieOmega Stage2 v2.3","coq_statement_full":"Theorem licklider_witness_from_policy_failure :\n forall (c : CubieState) (s : SessionState) (k : HardwareKey),\n c_policy c = false ->\n OperationalContainmentFailure (cubie_to_action c) s k.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieOmegaStage2V2_3.v":"a39fbf62de2184534b3d07e2404674bc91add2d497d1fb9e87674a0ef9cffa65","lean/CubieOmegaStage2V2_3.lean":"696c637db7dca52027970f3ec430dfde8d4bb9a4238ab41775021ad3fa438210"},"files":{"coq_file":"coq/CubieOmegaStage2V2_3.v","lean_file":"lean/CubieOmegaStage2V2_3.lean"},"formal_systems":"Coq+Lean","id":"CUB-0283","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem licklider_witness_from_policy_failure\n (c : CubieState) (s : SessionState) (k : HardwareKey)\n (H : c.c_policy = false) :\n OperationalContainmentFailure (cubie_to_action c) s k","lean_verified":"not stated in registry status for this row","module":"CubieOmegaStage2V2_3","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"a39fbf62de218453...","lean_sha256":"696c637db7dca520..."},"source_completeness":"full (CSV-sourced)","statement":"CubieOmega Stage2 v2.3","status":"VERIFIED_EXACT","theorem_name":"licklider_witness_from_policy_failure","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"10 axioms","axiom_profile":"10 axioms","context_purpose":"DERIVED: Theorem named 'vonneumann_witness_from_lease_failure' in the CubieOmegaStage2V2_3 family -- registry statement: CubieOmega Stage2 v2.3","coq_statement_full":"Theorem vonneumann_witness_from_lease_failure :\n forall (c : CubieState) (s : SessionState) (k : HardwareKey),\n c_lease c = false ->\n OperationalContainmentFailure (cubie_to_action c) s k.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieOmegaStage2V2_3.v":"a39fbf62de2184534b3d07e2404674bc91add2d497d1fb9e87674a0ef9cffa65","lean/CubieOmegaStage2V2_3.lean":"696c637db7dca52027970f3ec430dfde8d4bb9a4238ab41775021ad3fa438210"},"files":{"coq_file":"coq/CubieOmegaStage2V2_3.v","lean_file":"lean/CubieOmegaStage2V2_3.lean"},"formal_systems":"Coq+Lean","id":"CUB-0284","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem vonneumann_witness_from_lease_failure\n (c : CubieState) (s : SessionState) (k : HardwareKey)\n (H : c.c_lease = false) :\n OperationalContainmentFailure (cubie_to_action c) s k","lean_verified":"not stated in registry status for this row","module":"CubieOmegaStage2V2_3","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"a39fbf62de218453...","lean_sha256":"696c637db7dca520..."},"source_completeness":"full (CSV-sourced)","statement":"CubieOmega Stage2 v2.3","status":"VERIFIED_EXACT","theorem_name":"vonneumann_witness_from_lease_failure","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"10 axioms","axiom_profile":"10 axioms","context_purpose":"DERIVED: Theorem named 'vonneumann_witness_from_epoch_failure' in the CubieOmegaStage2V2_3 family -- registry statement: CubieOmega Stage2 v2.3","coq_statement_full":"Theorem vonneumann_witness_from_epoch_failure :\n forall (c : CubieState) (s : SessionState) (k : HardwareKey),\n c_epoch c = false ->\n OperationalContainmentFailure (cubie_to_action c) s k.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieOmegaStage2V2_3.v":"a39fbf62de2184534b3d07e2404674bc91add2d497d1fb9e87674a0ef9cffa65","lean/CubieOmegaStage2V2_3.lean":"696c637db7dca52027970f3ec430dfde8d4bb9a4238ab41775021ad3fa438210"},"files":{"coq_file":"coq/CubieOmegaStage2V2_3.v","lean_file":"lean/CubieOmegaStage2V2_3.lean"},"formal_systems":"Coq+Lean","id":"CUB-0285","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem vonneumann_witness_from_epoch_failure\n (c : CubieState) (s : SessionState) (k : HardwareKey)\n (H : c.c_epoch = false) :\n OperationalContainmentFailure (cubie_to_action c) s k","lean_verified":"not stated in registry status for this row","module":"CubieOmegaStage2V2_3","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"a39fbf62de218453...","lean_sha256":"696c637db7dca520..."},"source_completeness":"full (CSV-sourced)","statement":"CubieOmega Stage2 v2.3","status":"VERIFIED_EXACT","theorem_name":"vonneumann_witness_from_epoch_failure","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"10 axioms","axiom_profile":"10 axioms","context_purpose":"DERIVED: Theorem named 'shannon_witness_from_reqhash_failure' in the CubieOmegaStage2V2_3 family -- registry statement: CubieOmega Stage2 v2.3","coq_statement_full":"Theorem shannon_witness_from_reqhash_failure :\n forall (c : CubieState) (s : SessionState) (k : HardwareKey),\n c_reqhash c = false ->\n OperationalContainmentFailure (cubie_to_action c) s k.","coq_verified":"not stated in registry status for this 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registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieOmegaStage2V2_3.v":"a39fbf62de2184534b3d07e2404674bc91add2d497d1fb9e87674a0ef9cffa65","lean/CubieOmegaStage2V2_3.lean":"696c637db7dca52027970f3ec430dfde8d4bb9a4238ab41775021ad3fa438210"},"files":{"coq_file":"coq/CubieOmegaStage2V2_3.v","lean_file":"lean/CubieOmegaStage2V2_3.lean"},"formal_systems":"Coq+Lean","id":"CUB-0289","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem cubie_face_failure_invokes_photonic_containment\n (c : CubieState) (s : SessionState) (k : HardwareKey)\n (H : cubie_admit c = false) :\n RoutedToPhotonicTarpit (cubie_to_action c) \u2227\n \u00ac MutatesPhysicalReality (cubie_to_action c)","lean_verified":"not stated in registry status for this row","module":"CubieOmegaStage2V2_3","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"a39fbf62de218453...","lean_sha256":"696c637db7dca520..."},"source_completeness":"full (CSV-sourced)","statement":"CubieOmega Stage2 v2.3","status":"VERIFIED_EXACT","theorem_name":"cubie_face_failure_invokes_photonic_containment","use_cases":["topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"5 axioms","axiom_profile":"5 axioms","context_purpose":"DERIVED: Definition named 'ALLOW_CODE' in the CubieOutputStateV2_5 family -- registry statement: V2.5 Output State","coq_statement_full":"Definition ALLOW_CODE : N := 0x5A5A5A5A%N.","coq_verified":"not stated in registry status for this 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PMP/IOPMP","status":"VERIFIED_EXACT","theorem_name":"mmio_entry","use_cases":["TDX"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'cub_0895_pmp_tcm_entry_covers_tcm' in the CubiePmpV2_5 family -- registry statement: V2.5 PMP/IOPMP","coq_statement_full":"Theorem cub_0895_pmp_tcm_entry_covers_tcm :\n forall (addr : nat),\n TCM_BASE <= addr ->\n addr < TCM_BASE + TCM_SIZE ->\n region_covers (region tcm_entry) addr.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubiePmpV2_5.v":"ae86c2b7824f2f7c99fec75a246d3ba0c78e48c76aa91c59937064b4e0f72761","lean/CubiePmpV2_5.lean":"71bd0d5b5d63b8eae10f6f66ce6768b79d2fe208dcb85c4bf3871fb42f712ef2"},"files":{"coq_file":"coq/CubiePmpV2_5.v","lean_file":"lean/CubiePmpV2_5.lean"},"formal_systems":"Coq+Lean","id":"CUB-0329","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem cub_0895_pmp_tcm_entry_covers_tcm (addr : Nat)\n (h1 : TCM_BASE \u2264 addr) (h2 : addr < TCM_BASE + TCM_SIZE) :\n region_covers tcm_entry.region addr","lean_verified":"not stated in registry status for this row","module":"CubiePmpV2_5","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"ae86c2b7824f2f7c...","lean_sha256":"71bd0d5b5d63b8ea..."},"source_completeness":"full (CSV-sourced)","statement":"V2.5 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PMP/IOPMP","status":"VERIFIED_EXACT","theorem_name":"cub_0896_pmp_efuse_entry_covers_efuse","use_cases":["TDX"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'cub_0897_pmp_mmio_entry_covers_mmio' in the CubiePmpV2_5 family -- registry statement: V2.5 PMP/IOPMP","coq_statement_full":"Theorem cub_0897_pmp_mmio_entry_covers_mmio :\n forall (addr : nat),\n MMIO_BASE <= addr ->\n addr < MMIO_BASE + MMIO_SIZE ->\n region_covers (region mmio_entry) addr.","coq_verified":"not stated in registry status for this 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PMP/IOPMP","status":"VERIFIED_EXACT","theorem_name":"cub_0898_pmp_lock_prevents_modification","use_cases":["TDX"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'canonical_tcm_entry_is_locked' in the CubiePmpV2_5 family -- registry statement: V2.5 PMP/IOPMP","coq_statement_full":"Theorem canonical_tcm_entry_is_locked :\n is_locked tcm_entry = true.","coq_verified":"not stated in registry status for this 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PlusStencilAligned Y2 ->\n FrameHolonomyValid Y1 ->\n ~ FrameHolonomyValid Y2 ->\n ReconstructionCapacity Y2 = 0.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieQApex.v":"3bd2519c6b5651876300711112cc2210c3e16ac8c9a86d6daad6ea5a07a1b368","lean/CubieQApex.lean":"5e604b04a9bc6e0fb78109666e4f43d3edae6b2e4f073db8b082b977c213188f"},"files":{"coq_file":"coq/CubieQApex.v","lean_file":"lean/CubieQApex.lean"},"formal_systems":"Coq+Lean","id":"CUB-0359","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem apex_law_II_frame_beats_geometry :\n \u2200 Y1 Y2,\n ActiveGeometry Y1 = ActiveGeometry Y2 \u2192\n site_count Y1 = site_count Y2 \u2192\n PlusStencilAligned Y1 \u2192\n PlusStencilAligned Y2 \u2192\n FrameHolonomyValid Y1 \u2192\n \u00ac FrameHolonomyValid Y2 \u2192\n ReconstructionCapacity Y2 = 0","lean_verified":"not stated in registry status for this 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CubieQuantumConsent","status":"VERIFIED_EXACT","theorem_name":"post_measurement_agreement","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'T5_post_measurement_agreement_universal' in the CubieQuantumConsent family -- registry statement: v1.13 CubieQuantumConsent","coq_statement_full":"Theorem T5_post_measurement_agreement_universal :\n forall s b, post_measurement_agreement s b.","coq_verified":"not stated in registry status for this 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fn/crate)","shas":{"coq_sha256":"1e2223e0e35fcdbe...","lean_sha256":"5449220c94f8659c..."},"source_completeness":"full (CSV-sourced)","statement":"Quantum Consent Advanced","status":"VERIFIED_EXACT","theorem_name":"holevo_bounded_extraction","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'extraction_over_capacity_denied' in the CubieQuantumConsentAdvanced family -- registry statement: Quantum Consent Advanced","coq_statement_full":"Theorem extraction_over_capacity_denied :\n forall (parent child : ConsentNode),\n sub_policy child > capacity parent ->\n sub_policy_compliant parent child = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieQuantumConsentAdvanced.v":"1e2223e0e35fcdbefd4e2d168d31b8760fee17c6c08b4f8cec28159ee40f1de0","lean/CubieQuantumConsentAdvanced.lean":"5449220c94f8659c39c7839848503c215cbf086f18f37b9e740e20f9faa0f8a0"},"files":{"coq_file":"coq/CubieQuantumConsentAdvanced.v","lean_file":"lean/CubieQuantumConsentAdvanced.lean"},"formal_systems":"Coq+Lean","id":"CUB-0416","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem extraction_over_capacity_denied (parent child : ConsentNode)\n (h : child.sub_policy > parent.capacity) :\n sub_policy_compliant parent child = false","lean_verified":"not stated in registry status for this row","module":"CubieQuantumConsentAdvanced","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"1e2223e0e35fcdbe...","lean_sha256":"5449220c94f8659c..."},"source_completeness":"full (CSV-sourced)","statement":"Quantum Consent Advanced","status":"VERIFIED_EXACT","theorem_name":"extraction_over_capacity_denied","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'measurement_collapse_consent' in the CubieQuantumConsentAdvanced family -- registry statement: Quantum Consent Advanced","coq_statement_full":"Theorem measurement_collapse_consent :\n forall (parent child : ConsentNode),\n active parent = false ->\n cascading_consent parent child = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieQuantumConsentAdvanced.v":"1e2223e0e35fcdbefd4e2d168d31b8760fee17c6c08b4f8cec28159ee40f1de0","lean/CubieQuantumConsentAdvanced.lean":"5449220c94f8659c39c7839848503c215cbf086f18f37b9e740e20f9faa0f8a0"},"files":{"coq_file":"coq/CubieQuantumConsentAdvanced.v","lean_file":"lean/CubieQuantumConsentAdvanced.lean"},"formal_systems":"Coq+Lean","id":"CUB-0417","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem measurement_collapse_consent (parent child : ConsentNode)\n (h : parent.active = false) :\n cascading_consent parent child = false","lean_verified":"not stated in registry status for this row","module":"CubieQuantumConsentAdvanced","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"1e2223e0e35fcdbe...","lean_sha256":"5449220c94f8659c..."},"source_completeness":"full (CSV-sourced)","statement":"Quantum Consent Advanced","status":"VERIFIED_EXACT","theorem_name":"measurement_collapse_consent","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'cascade_revoke_immediate' in the CubieQuantumConsentAdvanced family -- registry statement: Quantum Consent Advanced","coq_statement_full":"Theorem cascade_revoke_immediate :\n forall (parent child : ConsentNode) (sc : StabilizerCode),\n active parent = false ->\n full_consent_ok parent child sc = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieQuantumConsentAdvanced.v":"1e2223e0e35fcdbefd4e2d168d31b8760fee17c6c08b4f8cec28159ee40f1de0","lean/CubieQuantumConsentAdvanced.lean":"5449220c94f8659c39c7839848503c215cbf086f18f37b9e740e20f9faa0f8a0"},"files":{"coq_file":"coq/CubieQuantumConsentAdvanced.v","lean_file":"lean/CubieQuantumConsentAdvanced.lean"},"formal_systems":"Coq+Lean","id":"CUB-0418","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem cascade_revoke_immediate (parent child : ConsentNode) (sc : StabilizerCode)\n (h : parent.active = false) :\n full_consent_ok parent child sc = false","lean_verified":"not stated in registry status for this row","module":"CubieQuantumConsentAdvanced","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"1e2223e0e35fcdbe...","lean_sha256":"5449220c94f8659c..."},"source_completeness":"full (CSV-sourced)","statement":"Quantum Consent Advanced","status":"VERIFIED_EXACT","theorem_name":"cascade_revoke_immediate","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'entanglement_grant_correlation' in the CubieQuantumConsentAdvanced family -- registry statement: Quantum Consent Advanced","coq_statement_full":"Theorem entanglement_grant_correlation :\n forall (parent child : ConsentNode),\n consent_grant parent = true ->\n consent_grant child = true ->\n active parent = true ->\n active child = true ->\n cascading_consent parent child = true.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieQuantumConsentAdvanced.v":"1e2223e0e35fcdbefd4e2d168d31b8760fee17c6c08b4f8cec28159ee40f1de0","lean/CubieQuantumConsentAdvanced.lean":"5449220c94f8659c39c7839848503c215cbf086f18f37b9e740e20f9faa0f8a0"},"files":{"coq_file":"coq/CubieQuantumConsentAdvanced.v","lean_file":"lean/CubieQuantumConsentAdvanced.lean"},"formal_systems":"Coq+Lean","id":"CUB-0419","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem entanglement_grant_correlation (parent child : ConsentNode)\n (hp : parent.consent_grant = true) (hc : child.consent_grant = true)\n (ha1 : parent.active = true) (ha2 : child.active = true) :\n cascading_consent parent child = true","lean_verified":"not stated in registry status for this row","module":"CubieQuantumConsentAdvanced","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"1e2223e0e35fcdbe...","lean_sha256":"5449220c94f8659c..."},"source_completeness":"full (CSV-sourced)","statement":"Quantum Consent Advanced","status":"VERIFIED_EXACT","theorem_name":"entanglement_grant_correlation","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'entanglement_revoke_correlation' in the CubieQuantumConsentAdvanced family -- registry statement: Quantum Consent Advanced","coq_statement_full":"Theorem entanglement_revoke_correlation :\n forall (parent child : ConsentNode),\n consent_grant parent = false ->\n cascading_consent parent child = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieQuantumConsentAdvanced.v":"1e2223e0e35fcdbefd4e2d168d31b8760fee17c6c08b4f8cec28159ee40f1de0","lean/CubieQuantumConsentAdvanced.lean":"5449220c94f8659c39c7839848503c215cbf086f18f37b9e740e20f9faa0f8a0"},"files":{"coq_file":"coq/CubieQuantumConsentAdvanced.v","lean_file":"lean/CubieQuantumConsentAdvanced.lean"},"formal_systems":"Coq+Lean","id":"CUB-0420","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem entanglement_revoke_correlation (parent child : ConsentNode)\n (h : parent.consent_grant = false) :\n cascading_consent parent child = false","lean_verified":"not stated in registry status for this row","module":"CubieQuantumConsentAdvanced","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"1e2223e0e35fcdbe...","lean_sha256":"5449220c94f8659c..."},"source_completeness":"full (CSV-sourced)","statement":"Quantum Consent Advanced","status":"VERIFIED_EXACT","theorem_name":"entanglement_revoke_correlation","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Definition named 'access_by_relationship' in the CubieQuantumConsentAdvanced family -- registry statement: Quantum Consent Advanced","coq_statement_full":"Definition access_by_relationship (requestor_depth node_depth : nat) : bool :=\n Nat.leb requestor_depth node_depth.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieQuantumConsentAdvanced.v":"1e2223e0e35fcdbefd4e2d168d31b8760fee17c6c08b4f8cec28159ee40f1de0","lean/CubieQuantumConsentAdvanced.lean":"5449220c94f8659c39c7839848503c215cbf086f18f37b9e740e20f9faa0f8a0"},"files":{"coq_file":"coq/CubieQuantumConsentAdvanced.v","lean_file":"lean/CubieQuantumConsentAdvanced.lean"},"formal_systems":"Coq+Lean","id":"CUB-0421","invocation":"unwired","kernels":"none","kind":"Definition","lean_statement_full":"def access_by_relationship (requestor_depth node_depth : Nat) : Bool","lean_verified":"not stated in registry status for this row","module":"CubieQuantumConsentAdvanced","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"1e2223e0e35fcdbe...","lean_sha256":"5449220c94f8659c..."},"source_completeness":"full (CSV-sourced)","statement":"Quantum Consent 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row","crate":"","deployable":false,"file_shas":{"coq/CubieQuantumConsentAdvanced.v":"1e2223e0e35fcdbefd4e2d168d31b8760fee17c6c08b4f8cec28159ee40f1de0","lean/CubieQuantumConsentAdvanced.lean":"5449220c94f8659c39c7839848503c215cbf086f18f37b9e740e20f9faa0f8a0"},"files":{"coq_file":"coq/CubieQuantumConsentAdvanced.v","lean_file":"lean/CubieQuantumConsentAdvanced.lean"},"formal_systems":"Coq+Lean","id":"CUB-0422","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem context_dependent_access (req_depth node_depth : Nat)\n (h : req_depth \u2264 node_depth) :\n access_by_relationship req_depth node_depth = true","lean_verified":"not stated in registry status for this row","module":"CubieQuantumConsentAdvanced","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"1e2223e0e35fcdbe...","lean_sha256":"5449220c94f8659c..."},"source_completeness":"full (CSV-sourced)","statement":"Quantum Consent Advanced","status":"VERIFIED_EXACT","theorem_name":"context_dependent_access","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'deeper_requestor_denied' in the CubieQuantumConsentAdvanced family -- registry statement: Quantum Consent Advanced","coq_statement_full":"Theorem deeper_requestor_denied :\n forall (req_depth node_depth : nat),\n req_depth > node_depth ->\n access_by_relationship req_depth node_depth = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieQuantumConsentAdvanced.v":"1e2223e0e35fcdbefd4e2d168d31b8760fee17c6c08b4f8cec28159ee40f1de0","lean/CubieQuantumConsentAdvanced.lean":"5449220c94f8659c39c7839848503c215cbf086f18f37b9e740e20f9faa0f8a0"},"files":{"coq_file":"coq/CubieQuantumConsentAdvanced.v","lean_file":"lean/CubieQuantumConsentAdvanced.lean"},"formal_systems":"Coq+Lean","id":"CUB-0423","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem deeper_requestor_denied (req_depth node_depth : Nat)\n (h : req_depth > node_depth) :\n access_by_relationship req_depth node_depth = false","lean_verified":"not stated in registry status for this row","module":"CubieQuantumConsentAdvanced","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"1e2223e0e35fcdbe...","lean_sha256":"5449220c94f8659c..."},"source_completeness":"full (CSV-sourced)","statement":"Quantum Consent Advanced","status":"VERIFIED_EXACT","theorem_name":"deeper_requestor_denied","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Definition named 'check_cascade_then_policy' in the CubieQuantumConsentAdvanced family -- registry statement: Quantum Consent Advanced","coq_statement_full":"Definition check_cascade_then_policy (parent child : ConsentNode) : bool :=\n if cascading_consent parent child then sub_policy_compliant parent child\n else false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieQuantumConsentAdvanced.v":"1e2223e0e35fcdbefd4e2d168d31b8760fee17c6c08b4f8cec28159ee40f1de0","lean/CubieQuantumConsentAdvanced.lean":"5449220c94f8659c39c7839848503c215cbf086f18f37b9e740e20f9faa0f8a0"},"files":{"coq_file":"coq/CubieQuantumConsentAdvanced.v","lean_file":"lean/CubieQuantumConsentAdvanced.lean"},"formal_systems":"Coq+Lean","id":"CUB-0424","invocation":"unwired","kernels":"none","kind":"Definition","lean_statement_full":"def check_cascade_then_policy (parent child : ConsentNode) : Bool","lean_verified":"not stated in registry status for this row","module":"CubieQuantumConsentAdvanced","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"1e2223e0e35fcdbe...","lean_sha256":"5449220c94f8659c..."},"source_completeness":"full (CSV-sourced)","statement":"Quantum Consent 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fn/crate)","shas":{"coq_sha256":"1e2223e0e35fcdbe...","lean_sha256":"5449220c94f8659c..."},"source_completeness":"full (CSV-sourced)","statement":"Quantum Consent Advanced","status":"VERIFIED_EXACT","theorem_name":"consent_algebra_agree_on_pass","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'consent_algebra_cascade_short_circuits' in the CubieQuantumConsentAdvanced family -- registry statement: Quantum Consent Advanced","coq_statement_full":"Theorem consent_algebra_cascade_short_circuits :\n forall (parent child : ConsentNode),\n cascading_consent parent child = false ->\n check_cascade_then_policy parent child = false.","coq_verified":"not stated in registry status for this 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fn/crate)","shas":{"coq_sha256":"1e2223e0e35fcdbe...","lean_sha256":"5449220c94f8659c..."},"source_completeness":"full (CSV-sourced)","statement":"Quantum Consent Advanced","status":"VERIFIED_EXACT","theorem_name":"consent_algebra_cascade_short_circuits","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'consent_channel_requires_active_endpoints' in the CubieQuantumConsentAdvanced family -- registry statement: Quantum Consent Advanced","coq_statement_full":"Theorem consent_channel_requires_active_endpoints :\n forall (ch : ConsentChannel) (src dst : ConsentNode),\n active src = false ->\n channel_valid ch src dst = false.","coq_verified":"not stated in registry status for this 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fn/crate)","shas":{"coq_sha256":"1e2223e0e35fcdbe...","lean_sha256":"5449220c94f8659c..."},"source_completeness":"full (CSV-sourced)","statement":"Quantum Consent Advanced","status":"VERIFIED_EXACT","theorem_name":"consent_channel_requires_active_endpoints","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'consent_channel_bounded' in the CubieQuantumConsentAdvanced family -- registry statement: Quantum Consent Advanced","coq_statement_full":"Theorem consent_channel_bounded :\n forall (ch : ConsentChannel),\n bandwidth ch <= bandwidth ch.","coq_verified":"not stated in registry status for this 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row","crate":"","deployable":false,"file_shas":{"coq/CubieQuantumConsentAdvanced.v":"1e2223e0e35fcdbefd4e2d168d31b8760fee17c6c08b4f8cec28159ee40f1de0","lean/CubieQuantumConsentAdvanced.lean":"5449220c94f8659c39c7839848503c215cbf086f18f37b9e740e20f9faa0f8a0"},"files":{"coq_file":"coq/CubieQuantumConsentAdvanced.v","lean_file":"lean/CubieQuantumConsentAdvanced.lean"},"formal_systems":"Coq+Lean","id":"CUB-0431","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem wedge_reconstruction_requires_consent (ch : ConsentChannel)\n (parent child : ConsentNode)\n (h : child_can_access_parent ch parent child = true) :\n cascading_consent parent child = true","lean_verified":"not stated in registry status for this row","module":"CubieQuantumConsentAdvanced","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"1e2223e0e35fcdbe...","lean_sha256":"5449220c94f8659c..."},"source_completeness":"full (CSV-sourced)","statement":"Quantum Consent Advanced","status":"VERIFIED_EXACT","theorem_name":"wedge_reconstruction_requires_consent","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'wedge_reconstruction_requires_channel' in the CubieQuantumConsentAdvanced family -- registry statement: Quantum Consent Advanced","coq_statement_full":"Theorem wedge_reconstruction_requires_channel :\n forall (ch : ConsentChannel) (parent child : ConsentNode),\n child_can_access_parent ch parent child = true ->\n channel_valid ch parent child = true.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieQuantumConsentAdvanced.v":"1e2223e0e35fcdbefd4e2d168d31b8760fee17c6c08b4f8cec28159ee40f1de0","lean/CubieQuantumConsentAdvanced.lean":"5449220c94f8659c39c7839848503c215cbf086f18f37b9e740e20f9faa0f8a0"},"files":{"coq_file":"coq/CubieQuantumConsentAdvanced.v","lean_file":"lean/CubieQuantumConsentAdvanced.lean"},"formal_systems":"Coq+Lean","id":"CUB-0432","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem wedge_reconstruction_requires_channel (ch : ConsentChannel)\n (parent child : ConsentNode)\n (h : child_can_access_parent ch parent child = true) :\n channel_valid ch parent child = true","lean_verified":"not stated in registry status for this row","module":"CubieQuantumConsentAdvanced","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"1e2223e0e35fcdbe...","lean_sha256":"5449220c94f8659c..."},"source_completeness":"full (CSV-sourced)","statement":"Quantum Consent Advanced","status":"VERIFIED_EXACT","theorem_name":"wedge_reconstruction_requires_channel","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Definition named 'percolation_threshold' in the CubieQuantumConsentAdvanced family -- registry statement: Quantum Consent Advanced","coq_statement_full":"Definition percolation_threshold := nat.","coq_verified":"not stated in registry status for this 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row","crate":"","deployable":false,"file_shas":{"coq/CubieQuantumConsentAdvanced.v":"1e2223e0e35fcdbefd4e2d168d31b8760fee17c6c08b4f8cec28159ee40f1de0","lean/CubieQuantumConsentAdvanced.lean":"5449220c94f8659c39c7839848503c215cbf086f18f37b9e740e20f9faa0f8a0"},"files":{"coq_file":"coq/CubieQuantumConsentAdvanced.v","lean_file":"lean/CubieQuantumConsentAdvanced.lean"},"formal_systems":"Coq+Lean","id":"CUB-0435","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem below_threshold_no_flow (ch : ConsentChannel) (threshold : Nat)\n (h : ch.bandwidth < threshold) :\n percolates ch threshold = false","lean_verified":"not stated in registry status for this row","module":"CubieQuantumConsentAdvanced","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"1e2223e0e35fcdbe...","lean_sha256":"5449220c94f8659c..."},"source_completeness":"full (CSV-sourced)","statement":"Quantum Consent Advanced","status":"VERIFIED_EXACT","theorem_name":"below_threshold_no_flow","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'above_threshold_flows' in the CubieQuantumConsentAdvanced family -- registry statement: Quantum Consent Advanced","coq_statement_full":"Theorem above_threshold_flows :\n forall (ch : ConsentChannel) (threshold : nat),\n bandwidth ch >= threshold ->\n open ch = true ->\n percolates ch threshold = true.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieQuantumConsentAdvanced.v":"1e2223e0e35fcdbefd4e2d168d31b8760fee17c6c08b4f8cec28159ee40f1de0","lean/CubieQuantumConsentAdvanced.lean":"5449220c94f8659c39c7839848503c215cbf086f18f37b9e740e20f9faa0f8a0"},"files":{"coq_file":"coq/CubieQuantumConsentAdvanced.v","lean_file":"lean/CubieQuantumConsentAdvanced.lean"},"formal_systems":"Coq+Lean","id":"CUB-0436","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem above_threshold_flows (ch : ConsentChannel) (threshold : Nat)\n (hge : ch.bandwidth \u2265 threshold) (hopen : ch.is_open = true) :\n percolates ch threshold = true","lean_verified":"not stated in registry status for this row","module":"CubieQuantumConsentAdvanced","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"1e2223e0e35fcdbe...","lean_sha256":"5449220c94f8659c..."},"source_completeness":"full (CSV-sourced)","statement":"Quantum Consent Advanced","status":"VERIFIED_EXACT","theorem_name":"above_threshold_flows","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Definition named 'capacity_available' in the CubieQuantumConsentAdvanced family -- registry statement: Quantum Consent Advanced","coq_statement_full":"Definition capacity_available (node : ConsentNode) (current_children : nat) : bool :=\n Nat.ltb current_children (capacity node).","coq_verified":"not stated in registry status for this 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(CSV-sourced)","statement":"Quantum Consent Advanced","status":"VERIFIED_EXACT","theorem_name":"capacity_exhausted_denies","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'capacity_available_allows' in the CubieQuantumConsentAdvanced family -- registry statement: Quantum Consent Advanced","coq_statement_full":"Theorem capacity_available_allows :\n forall (node : ConsentNode) (current_children : nat),\n current_children < capacity node ->\n capacity_available node current_children = true.","coq_verified":"not stated in registry status for this 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(CSV-sourced)","statement":"Quantum Consent Advanced","status":"VERIFIED_EXACT","theorem_name":"capacity_available_allows","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Definition named 'can_modify_preferences' in the CubieQuantumConsentAdvanced family -- registry statement: Quantum Consent Advanced","coq_statement_full":"Definition can_modify_preferences (requestor node : ConsentNode) : bool :=\n active node &&\n Nat.leb (depth requestor) (depth node).","coq_verified":"not stated in registry status for this 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row","crate":"","deployable":false,"file_shas":{"coq/CubieQuantumConsentAdvanced.v":"1e2223e0e35fcdbefd4e2d168d31b8760fee17c6c08b4f8cec28159ee40f1de0","lean/CubieQuantumConsentAdvanced.lean":"5449220c94f8659c39c7839848503c215cbf086f18f37b9e740e20f9faa0f8a0"},"files":{"coq_file":"coq/CubieQuantumConsentAdvanced.v","lean_file":"lean/CubieQuantumConsentAdvanced.lean"},"formal_systems":"Coq+Lean","id":"CUB-0441","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem inactive_node_no_modification (requestor node : ConsentNode)\n (h : node.active = false) :\n can_modify_preferences requestor node = false","lean_verified":"not stated in registry status for this row","module":"CubieQuantumConsentAdvanced","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"1e2223e0e35fcdbe...","lean_sha256":"5449220c94f8659c..."},"source_completeness":"full (CSV-sourced)","statement":"Quantum Consent Advanced","status":"VERIFIED_EXACT","theorem_name":"inactive_node_no_modification","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'deeper_requestor_no_modification' in the CubieQuantumConsentAdvanced family -- registry statement: Quantum Consent Advanced","coq_statement_full":"Theorem deeper_requestor_no_modification :\n forall (requestor node : ConsentNode),\n depth requestor > depth node ->\n can_modify_preferences requestor node = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieQuantumConsentAdvanced.v":"1e2223e0e35fcdbefd4e2d168d31b8760fee17c6c08b4f8cec28159ee40f1de0","lean/CubieQuantumConsentAdvanced.lean":"5449220c94f8659c39c7839848503c215cbf086f18f37b9e740e20f9faa0f8a0"},"files":{"coq_file":"coq/CubieQuantumConsentAdvanced.v","lean_file":"lean/CubieQuantumConsentAdvanced.lean"},"formal_systems":"Coq+Lean","id":"CUB-0442","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem deeper_requestor_no_modification (requestor node : ConsentNode)\n (h : requestor.depth > node.depth) :\n can_modify_preferences requestor node = false","lean_verified":"not stated in registry status for this row","module":"CubieQuantumConsentAdvanced","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"1e2223e0e35fcdbe...","lean_sha256":"5449220c94f8659c..."},"source_completeness":"full (CSV-sourced)","statement":"Quantum Consent Advanced","status":"VERIFIED_EXACT","theorem_name":"deeper_requestor_no_modification","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'authorized_modification' in the CubieQuantumConsentAdvanced family -- registry statement: Quantum Consent Advanced","coq_statement_full":"Theorem authorized_modification :\n forall (requestor node : ConsentNode),\n active node = true ->\n depth requestor <= depth node ->\n can_modify_preferences requestor node = true.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieQuantumConsentAdvanced.v":"1e2223e0e35fcdbefd4e2d168d31b8760fee17c6c08b4f8cec28159ee40f1de0","lean/CubieQuantumConsentAdvanced.lean":"5449220c94f8659c39c7839848503c215cbf086f18f37b9e740e20f9faa0f8a0"},"files":{"coq_file":"coq/CubieQuantumConsentAdvanced.v","lean_file":"lean/CubieQuantumConsentAdvanced.lean"},"formal_systems":"Coq+Lean","id":"CUB-0443","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem authorized_modification (requestor node : ConsentNode)\n (hactive : node.active = true) (hle : requestor.depth \u2264 node.depth) :\n can_modify_preferences requestor node = true","lean_verified":"not stated in registry status for this row","module":"CubieQuantumConsentAdvanced","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"1e2223e0e35fcdbe...","lean_sha256":"5449220c94f8659c..."},"source_completeness":"full (CSV-sourced)","statement":"Quantum Consent Advanced","status":"VERIFIED_EXACT","theorem_name":"authorized_modification","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Definition named 'effective_sub_policy' in the CubieQuantumConsentAdvanced family -- registry statement: Quantum Consent Advanced","coq_statement_full":"Definition effective_sub_policy (parent child : ConsentNode) : nat :=\n Nat.min (sub_policy child) (capacity parent).","coq_verified":"not stated in registry status for this 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row","crate":"","deployable":false,"file_shas":{"coq/CubieQuantumConsentAdvanced.v":"1e2223e0e35fcdbefd4e2d168d31b8760fee17c6c08b4f8cec28159ee40f1de0","lean/CubieQuantumConsentAdvanced.lean":"5449220c94f8659c39c7839848503c215cbf086f18f37b9e740e20f9faa0f8a0"},"files":{"coq_file":"coq/CubieQuantumConsentAdvanced.v","lean_file":"lean/CubieQuantumConsentAdvanced.lean"},"formal_systems":"Coq+Lean","id":"CUB-0445","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem effective_policy_bounded_by_parent (parent child : ConsentNode) :\n effective_sub_policy parent child \u2264 parent.capacity","lean_verified":"not stated in registry status for this row","module":"CubieQuantumConsentAdvanced","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"1e2223e0e35fcdbe...","lean_sha256":"5449220c94f8659c..."},"source_completeness":"full (CSV-sourced)","statement":"Quantum Consent Advanced","status":"VERIFIED_EXACT","theorem_name":"effective_policy_bounded_by_parent","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'effective_policy_bounded_by_child' in the CubieQuantumConsentAdvanced family -- registry statement: Quantum Consent Advanced","coq_statement_full":"Theorem effective_policy_bounded_by_child :\n forall (parent child : ConsentNode),\n effective_sub_policy parent child <= sub_policy child.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieQuantumConsentAdvanced.v":"1e2223e0e35fcdbefd4e2d168d31b8760fee17c6c08b4f8cec28159ee40f1de0","lean/CubieQuantumConsentAdvanced.lean":"5449220c94f8659c39c7839848503c215cbf086f18f37b9e740e20f9faa0f8a0"},"files":{"coq_file":"coq/CubieQuantumConsentAdvanced.v","lean_file":"lean/CubieQuantumConsentAdvanced.lean"},"formal_systems":"Coq+Lean","id":"CUB-0446","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem effective_policy_bounded_by_child (parent child : ConsentNode) :\n effective_sub_policy parent child \u2264 child.sub_policy","lean_verified":"not stated in registry status for this row","module":"CubieQuantumConsentAdvanced","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"1e2223e0e35fcdbe...","lean_sha256":"5449220c94f8659c..."},"source_completeness":"full (CSV-sourced)","statement":"Quantum Consent Advanced","status":"VERIFIED_EXACT","theorem_name":"effective_policy_bounded_by_child","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'dynamic_mixing_constrains' in the CubieQuantumConsentAdvanced family -- registry statement: Quantum Consent Advanced","coq_statement_full":"Theorem dynamic_mixing_constrains :\n forall (child : ConsentNode) (cap1 cap2 : nat),\n cap1 < cap2 ->\n Nat.min (sub_policy child) cap1 <= Nat.min (sub_policy child) cap2.","coq_verified":"not stated in registry status for this 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fn/crate)","shas":{"coq_sha256":"1e2223e0e35fcdbe...","lean_sha256":"5449220c94f8659c..."},"source_completeness":"full (CSV-sourced)","statement":"Quantum Consent Advanced","status":"VERIFIED_EXACT","theorem_name":"dynamic_mixing_constrains","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Fixpoint named 'sum_sub_policies' in the CubieQuantumConsentAdvanced family -- registry statement: Quantum Consent Advanced","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieQuantumConsentAdvanced.v":"1e2223e0e35fcdbefd4e2d168d31b8760fee17c6c08b4f8cec28159ee40f1de0","lean/CubieQuantumConsentAdvanced.lean":"5449220c94f8659c39c7839848503c215cbf086f18f37b9e740e20f9faa0f8a0"},"files":{"coq_file":"coq/CubieQuantumConsentAdvanced.v","lean_file":"lean/CubieQuantumConsentAdvanced.lean"},"formal_systems":"Coq+Lean","id":"CUB-0448","invocation":"unwired","kernels":"none","kind":"Fixpoint","lean_statement_full":"def sum_sub_policies : List ConsentNode \u2192 Nat\n | [] => 0\n | n :: rest => n.sub_policy + sum_sub_policies rest\n\ndef graph_within_capacity (root : ConsentNode) (children : List ConsentNode) : Bool","lean_verified":"not stated in registry status for this row","module":"CubieQuantumConsentAdvanced","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"1e2223e0e35fcdbe...","lean_sha256":"5449220c94f8659c..."},"source_completeness":"full (CSV-sourced)","statement":"Quantum Consent Advanced","status":"VERIFIED_EXACT","theorem_name":"sum_sub_policies","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Definition named 'graph_within_capacity' in the CubieQuantumConsentAdvanced family -- registry statement: Quantum Consent Advanced","coq_statement_full":"Definition graph_within_capacity (root : ConsentNode)\n (children : list ConsentNode) : bool :=\n Nat.leb (sum_sub_policies children) (capacity root).","coq_verified":"not stated in registry status for this 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row","crate":"","deployable":false,"file_shas":{"coq/CubieQuantumConsentAdvanced.v":"1e2223e0e35fcdbefd4e2d168d31b8760fee17c6c08b4f8cec28159ee40f1de0","lean/CubieQuantumConsentAdvanced.lean":"5449220c94f8659c39c7839848503c215cbf086f18f37b9e740e20f9faa0f8a0"},"files":{"coq_file":"coq/CubieQuantumConsentAdvanced.v","lean_file":"lean/CubieQuantumConsentAdvanced.lean"},"formal_systems":"Coq+Lean","id":"CUB-0451","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem overloaded_graph_denied (root : ConsentNode) (children : List ConsentNode)\n (h : sum_sub_policies children > root.capacity) :\n graph_within_capacity root children = false","lean_verified":"not stated in registry status for this row","module":"CubieQuantumConsentAdvanced","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"1e2223e0e35fcdbe...","lean_sha256":"5449220c94f8659c..."},"source_completeness":"full (CSV-sourced)","statement":"Quantum Consent Advanced","status":"VERIFIED_EXACT","theorem_name":"overloaded_graph_denied","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'adding_child_increases_demand' in the CubieQuantumConsentAdvanced family -- registry statement: Quantum Consent Advanced","coq_statement_full":"Theorem adding_child_increases_demand :\n forall (child : ConsentNode) (rest : list ConsentNode),\n sum_sub_policies (child :: rest) = sub_policy child + sum_sub_policies rest.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieQuantumConsentAdvanced.v":"1e2223e0e35fcdbefd4e2d168d31b8760fee17c6c08b4f8cec28159ee40f1de0","lean/CubieQuantumConsentAdvanced.lean":"5449220c94f8659c39c7839848503c215cbf086f18f37b9e740e20f9faa0f8a0"},"files":{"coq_file":"coq/CubieQuantumConsentAdvanced.v","lean_file":"lean/CubieQuantumConsentAdvanced.lean"},"formal_systems":"Coq+Lean","id":"CUB-0452","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem adding_child_increases_demand (child : ConsentNode) (rest : List ConsentNode) :\n sum_sub_policies (child :: rest) = child.sub_policy + sum_sub_policies rest","lean_verified":"not stated in registry status for this row","module":"CubieQuantumConsentAdvanced","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"1e2223e0e35fcdbe...","lean_sha256":"5449220c94f8659c..."},"source_completeness":"full (CSV-sourced)","statement":"Quantum Consent Advanced","status":"VERIFIED_EXACT","theorem_name":"adding_child_increases_demand","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'one_more_child_overflows' in the CubieQuantumConsentAdvanced family -- registry statement: Quantum Consent Advanced","coq_statement_full":"Theorem one_more_child_overflows :\n forall (root : ConsentNode) (children : list ConsentNode) (new_child : ConsentNode),\n sum_sub_policies children = capacity root ->\n sub_policy new_child > 0 ->\n graph_within_capacity root (new_child :: children) = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieQuantumConsentAdvanced.v":"1e2223e0e35fcdbefd4e2d168d31b8760fee17c6c08b4f8cec28159ee40f1de0","lean/CubieQuantumConsentAdvanced.lean":"5449220c94f8659c39c7839848503c215cbf086f18f37b9e740e20f9faa0f8a0"},"files":{"coq_file":"coq/CubieQuantumConsentAdvanced.v","lean_file":"lean/CubieQuantumConsentAdvanced.lean"},"formal_systems":"Coq+Lean","id":"CUB-0453","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem one_more_child_overflows (root : ConsentNode) (children : List ConsentNode)\n (new_child : ConsentNode) (heq : sum_sub_policies children = root.capacity)\n (hpos : new_child.sub_policy > 0) :\n graph_within_capacity root (new_child :: children) = false","lean_verified":"not stated in registry status for this row","module":"CubieQuantumConsentAdvanced","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"1e2223e0e35fcdbe...","lean_sha256":"5449220c94f8659c..."},"source_completeness":"full (CSV-sourced)","statement":"Quantum Consent Advanced","status":"VERIFIED_EXACT","theorem_name":"one_more_child_overflows","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"6 axioms","axiom_profile":"6 axioms","context_purpose":"DERIVED: Definition named 'GOLDEN_PATH_SITES_N3' in the CubieQv14 family -- registry statement: v1.10 CubieQv14","coq_statement_full":"Definition GOLDEN_PATH_SITES_N3 : nat := 125.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieQv14.v":"350cc05275a85a449748fabc2edfae672a4a7d31734f45996b1a48061cd7f80d","lean/CubieQv14.lean":"56e52aa61a149e664cfcbd9e6a2ab3e96cc3349141a5ed5513d71d58cfc47fd9"},"files":{"coq_file":"coq/CubieQv14.v","lean_file":"lean/CubieQv14.lean"},"formal_systems":"Coq+Lean","id":"CUB-0454","invocation":"unwired","kernels":"none","kind":"Definition","lean_statement_full":"def GOLDEN_PATH_SITES_N3 : Nat","lean_verified":"not stated in registry status for this row","module":"CubieQv14","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"350cc05275a85a44...","lean_sha256":"56e52aa61a149e66..."},"source_completeness":"full (CSV-sourced)","statement":"v1.10 CubieQv14","status":"VERIFIED_EXACT","theorem_name":"GOLDEN_PATH_SITES_N3","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"6 axioms","axiom_profile":"6 axioms","context_purpose":"DERIVED: Definition named 'CROWD_SITES_N3' in the CubieQv14 family -- registry statement: v1.10 CubieQv14","coq_statement_full":"Definition CROWD_SITES_N3 : nat := 19683.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieQv14.v":"350cc05275a85a449748fabc2edfae672a4a7d31734f45996b1a48061cd7f80d","lean/CubieQv14.lean":"56e52aa61a149e664cfcbd9e6a2ab3e96cc3349141a5ed5513d71d58cfc47fd9"},"files":{"coq_file":"coq/CubieQv14.v","lean_file":"lean/CubieQv14.lean"},"formal_systems":"Coq+Lean","id":"CUB-0455","invocation":"unwired","kernels":"none","kind":"Definition","lean_statement_full":"def CROWD_SITES_N3 : Nat","lean_verified":"not stated in registry status for this row","module":"CubieQv14","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"350cc05275a85a44...","lean_sha256":"56e52aa61a149e66..."},"source_completeness":"full (CSV-sourced)","statement":"v1.10 CubieQv14","status":"VERIFIED_EXACT","theorem_name":"CROWD_SITES_N3","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"6 axioms","axiom_profile":"6 axioms","context_purpose":"DERIVED: Definition named 'GODS_NUMBER' in the CubieQv14 family -- registry statement: v1.10 CubieQv14","coq_statement_full":"Definition GODS_NUMBER : nat := 20.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieQv14.v":"350cc05275a85a449748fabc2edfae672a4a7d31734f45996b1a48061cd7f80d","lean/CubieQv14.lean":"56e52aa61a149e664cfcbd9e6a2ab3e96cc3349141a5ed5513d71d58cfc47fd9"},"files":{"coq_file":"coq/CubieQv14.v","lean_file":"lean/CubieQv14.lean"},"formal_systems":"Coq+Lean","id":"CUB-0456","invocation":"unwired","kernels":"none","kind":"Definition","lean_statement_full":"def GODS_NUMBER : Nat","lean_verified":"not stated in registry status for this row","module":"CubieQv14","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"350cc05275a85a44...","lean_sha256":"56e52aa61a149e66..."},"source_completeness":"full (CSV-sourced)","statement":"v1.10 CubieQv14","status":"VERIFIED_EXACT","theorem_name":"GODS_NUMBER","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"6 axioms","axiom_profile":"6 axioms","context_purpose":"DERIVED: Theorem named 'apex_law_I_geometry_beats_cardinality_general' in the CubieQv14 family -- registry statement: v1.10 CubieQv14","coq_statement_full":"Theorem apex_law_I_geometry_beats_cardinality_general :\n forall (P : Pattern) (Y_aligned Y_crowd : Configuration),\n pattern_aligned P Y_aligned ->\n Holonomy_valid Y_aligned ->\n aligned_count Y_aligned >= GOLDEN_PATH_SITES_N3 ->\n ~ pattern_aligned P Y_crowd ->\n aligned_count Y_crowd <= CROWD_SITES_N3 ->\n ReconstructionCapacity Y_aligned >= 1\n /\\ ReconstructionCapacity Y_crowd = 0.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieQv14.v":"350cc05275a85a449748fabc2edfae672a4a7d31734f45996b1a48061cd7f80d","lean/CubieQv14.lean":"56e52aa61a149e664cfcbd9e6a2ab3e96cc3349141a5ed5513d71d58cfc47fd9"},"files":{"coq_file":"coq/CubieQv14.v","lean_file":"lean/CubieQv14.lean"},"formal_systems":"Coq+Lean","id":"CUB-0457","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem apex_law_I_geometry_beats_cardinality_general :\n \u2200 (P : Pattern) (Y_aligned Y_crowd : Configuration),\n pattern_aligned P Y_aligned \u2192\n Holonomy_valid Y_aligned \u2192\n aligned_count Y_aligned \u2265 GOLDEN_PATH_SITES_N3 \u2192\n \u00ac pattern_aligned P Y_crowd \u2192\n aligned_count Y_crowd \u2264 CROWD_SITES_N3 \u2192\n ReconstructionCapacity Y_aligned \u2265 1\n \u2227 ReconstructionCapacity Y_crowd = 0","lean_verified":"not stated in registry status for this row","module":"CubieQv14","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"350cc05275a85a44...","lean_sha256":"56e52aa61a149e66..."},"source_completeness":"full (CSV-sourced)","statement":"v1.10 CubieQv14","status":"VERIFIED_EXACT","theorem_name":"apex_law_I_geometry_beats_cardinality_general","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"6 axioms","axiom_profile":"6 axioms","context_purpose":"DERIVED: Theorem named 'read_gate_independent_of_write_gate' in the CubieQv14 family -- registry statement: v1.10 CubieQv14","coq_statement_full":"Theorem read_gate_independent_of_write_gate :\n forall (Y : Configuration) (p : Principal) (a : Axis),\n (ReadGateAuthorized Y p \\/ ~ ReadGateAuthorized Y p) ->\n (WriteGateAuthorized Y p a \\/ ~ WriteGateAuthorized Y p a) ->\n (ReadGateAuthorized Y p /\\ WriteGateAuthorized Y p a)\n \\/ (ReadGateAuthorized Y p /\\ ~ WriteGateAuthorized Y p a)\n \\/ (~ ReadGateAuthorized Y p /\\ WriteGateAuthorized Y p a)\n \\/ (~ ReadGateAuthorized Y p /\\ ~ WriteGateAuthorized Y p a).","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieQv14.v":"350cc05275a85a449748fabc2edfae672a4a7d31734f45996b1a48061cd7f80d","lean/CubieQv14.lean":"56e52aa61a149e664cfcbd9e6a2ab3e96cc3349141a5ed5513d71d58cfc47fd9"},"files":{"coq_file":"coq/CubieQv14.v","lean_file":"lean/CubieQv14.lean"},"formal_systems":"Coq+Lean","id":"CUB-0458","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem read_gate_independent_of_write_gate :\n \u2200 (Y : Configuration) (p : Principal) (a : Axis),\n (ReadGateAuthorized Y p \u2228 \u00ac ReadGateAuthorized Y p) \u2192\n (WriteGateAuthorized Y p a \u2228 \u00ac WriteGateAuthorized Y p a) \u2192\n (ReadGateAuthorized Y p \u2227 WriteGateAuthorized Y p a)\n \u2228 (ReadGateAuthorized Y p \u2227 \u00ac WriteGateAuthorized Y p a)\n \u2228 (\u00ac ReadGateAuthorized Y p \u2227 WriteGateAuthorized Y p a)\n \u2228 (\u00ac ReadGateAuthorized Y p \u2227 \u00ac WriteGateAuthorized Y p a)","lean_verified":"not stated in registry status for this row","module":"CubieQv14","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"350cc05275a85a44...","lean_sha256":"56e52aa61a149e66..."},"source_completeness":"full (CSV-sourced)","statement":"v1.10 CubieQv14","status":"VERIFIED_EXACT","theorem_name":"read_gate_independent_of_write_gate","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"6 axioms","axiom_profile":"6 axioms","context_purpose":"DERIVED: Theorem named 'cayley_distance_bounded' in the CubieQv14 family -- registry statement: v1.10 CubieQv14","coq_statement_full":"Theorem cayley_distance_bounded :\n forall Y, cayley_distance Y <= 20.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieQv14.v":"350cc05275a85a449748fabc2edfae672a4a7d31734f45996b1a48061cd7f80d","lean/CubieQv14.lean":"56e52aa61a149e664cfcbd9e6a2ab3e96cc3349141a5ed5513d71d58cfc47fd9"},"files":{"coq_file":"coq/CubieQv14.v","lean_file":"lean/CubieQv14.lean"},"formal_systems":"Coq+Lean","id":"CUB-0459","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem cayley_distance_bounded :\n \u2200 Y, cayley_distance Y \u2264 20","lean_verified":"not stated in registry status for this row","module":"CubieQv14","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"350cc05275a85a44...","lean_sha256":"56e52aa61a149e66..."},"source_completeness":"full (CSV-sourced)","statement":"v1.10 CubieQv14","status":"VERIFIED_EXACT","theorem_name":"cayley_distance_bounded","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"6 axioms","axiom_profile":"6 axioms","context_purpose":"DERIVED: Theorem named 'cayley_distance_fits_u8' in the CubieQv14 family -- registry statement: v1.10 CubieQv14","coq_statement_full":"Theorem cayley_distance_fits_u8 :\n forall Y, cayley_distance Y <= 255.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieQv14.v":"350cc05275a85a449748fabc2edfae672a4a7d31734f45996b1a48061cd7f80d","lean/CubieQv14.lean":"56e52aa61a149e664cfcbd9e6a2ab3e96cc3349141a5ed5513d71d58cfc47fd9"},"files":{"coq_file":"coq/CubieQv14.v","lean_file":"lean/CubieQv14.lean"},"formal_systems":"Coq+Lean","id":"CUB-0460","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem cayley_distance_fits_u8 :\n \u2200 Y, cayley_distance Y \u2264 255","lean_verified":"not stated in registry status for this row","module":"CubieQv14","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"350cc05275a85a44...","lean_sha256":"56e52aa61a149e66..."},"source_completeness":"full (CSV-sourced)","statement":"v1.10 CubieQv14","status":"VERIFIED_EXACT","theorem_name":"cayley_distance_fits_u8","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"6 axioms","axiom_profile":"6 axioms","context_purpose":"DERIVED: Theorem named 'linear_discipline_no_double_consume' in the CubieQv14 family -- registry statement: v1.10 CubieQv14","coq_statement_full":"Theorem linear_discipline_no_double_consume :\n forall lp, consumed (consume (consume lp)) = true.","coq_verified":"not stated in registry status for this 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CubieQv14","status":"VERIFIED_EXACT","theorem_name":"linear_discipline_no_double_consume","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"6 axioms","axiom_profile":"6 axioms","context_purpose":"DERIVED: Theorem named 'linear_discipline_monotone' in the CubieQv14 family -- registry statement: v1.10 CubieQv14","coq_statement_full":"Theorem linear_discipline_monotone :\n forall lp n,\n consumed (Nat.iter (S n) consume lp) = true.","coq_verified":"not stated in registry status for this 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(CSV-sourced)","statement":"Silicon Provenance","status":"VERIFIED_EXACT","theorem_name":"execution_produces_thermal","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'simulator_thermal_mismatch' in the CubieSiliconProvenance family -- registry statement: Silicon Provenance","coq_statement_full":"Theorem simulator_thermal_mismatch :\n forall (enclave xeon : nat),\n enclave <> xeon ->\n thermal_unforgeable enclave xeon = true.","coq_verified":"not stated in registry status for this 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row","crate":"","deployable":false,"file_shas":{"coq/CubieSiliconProvenance.v":"527d110d909e145693cb546fc2b08628bd42a8df5f3a4497d3233ffe95411934","lean/CubieSiliconProvenance.lean":"2ee9030dd09f7f08f195350050c56563f136c537c50dfe90c69cda8929b74f57"},"files":{"coq_file":"coq/CubieSiliconProvenance.v","lean_file":"lean/CubieSiliconProvenance.lean"},"formal_systems":"Coq+Lean","id":"CUB-0479","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem pregate_faster_than_hmac : PREGATE_LATENCY_NS < HMAC_LATENCY_NS","lean_verified":"not stated in registry status for this row","module":"CubieSiliconProvenance","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"527d110d909e1456...","lean_sha256":"2ee9030dd09f7f08..."},"source_completeness":"full (CSV-sourced)","statement":"Silicon 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(* boundary + center = total facelets *)\nProof.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieSiteTopology_v4.v":"697996c0879aac976678f05cca8bc260873574929a384b06bd7464e5bc394523","lean/CubieSiteTopology_v4.lean":"f7d7dbec2eba5164d8d1296fefbda71e53f1b5169b368b6d2fd7d992999b6ba9"},"files":{"coq_file":"coq/CubieSiteTopology_v4.v","lean_file":"lean/CubieSiteTopology_v4.lean"},"formal_systems":"Coq+Lean","id":"CUB-0484","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"theorem boundary_site_fraction :\n 8 * 6 = 48 \u2227 -- 8 boundary positions per face \u00d7 6 faces\n 1 * 6 = 6 \u2227 -- 1 center per face \u00d7 6 faces\n 48 + 6 = 54","lean_verified":"not stated in registry status for this row","module":"CubieSiteTopology_v4","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"697996c0879aac97...","lean_sha256":"f7d7dbec2eba5164..."},"source_completeness":"full (CSV-sourced)","statement":"V4 Site Topology","status":"VERIFIED_EXACT","theorem_name":"boundary_site_fraction","use_cases":["topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Lemma named 'center_and_boundary_partition' in the CubieSiteTopology_v4 family -- registry statement: V4 Site Topology","coq_statement_full":"Lemma center_and_boundary_partition : forall (s : CubieSiteTuple),\n is_center_site s = true <-> is_boundary_site s = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieSiteTopology_v4.v":"697996c0879aac976678f05cca8bc260873574929a384b06bd7464e5bc394523","lean/CubieSiteTopology_v4.lean":"f7d7dbec2eba5164d8d1296fefbda71e53f1b5169b368b6d2fd7d992999b6ba9"},"files":{"coq_file":"coq/CubieSiteTopology_v4.v","lean_file":"lean/CubieSiteTopology_v4.lean"},"formal_systems":"Coq+Lean","id":"CUB-0485","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieSiteTopology_v4","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"697996c0879aac97...","lean_sha256":"f7d7dbec2eba5164..."},"source_completeness":"full (CSV-sourced)","statement":"V4 Site 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row","crate":"","deployable":false,"file_shas":{"coq/CubieSiteTopology_v4.v":"697996c0879aac976678f05cca8bc260873574929a384b06bd7464e5bc394523","lean/CubieSiteTopology_v4.lean":"f7d7dbec2eba5164d8d1296fefbda71e53f1b5169b368b6d2fd7d992999b6ba9"},"files":{"coq_file":"coq/CubieSiteTopology_v4.v","lean_file":"lean/CubieSiteTopology_v4.lean"},"formal_systems":"Coq+Lean","id":"CUB-0486","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"theorem valid_site_face_in_range (s : CubieSiteTuple)\n (h : cubie_site_tuple s = true) :\n s.site_face < 6","lean_verified":"not stated in registry status for this row","module":"CubieSiteTopology_v4","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"697996c0879aac97...","lean_sha256":"f7d7dbec2eba5164..."},"source_completeness":"full (CSV-sourced)","statement":"V4 Site 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Tarpit","status":"VERIFIED_EXACT","theorem_name":"MAX_PENALTY_EXPONENT","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Definition named 'TCM_SCRUB_BASE' in the CubieTarpitV2_5 family -- registry statement: V2.5 Tarpit","coq_statement_full":"Definition TCM_SCRUB_BASE : nat := 0x08004000.","coq_verified":"not stated in registry status for this 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Tarpit","status":"VERIFIED_EXACT","theorem_name":"backoff_delay","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Definition named 'penalty_successor' in the CubieTarpitV2_5 family -- registry statement: V2.5 Tarpit","coq_statement_full":"Definition penalty_successor (p : PenaltyState) : PenaltyState :=\n if Nat.ltb (exponent p) MAX_PENALTY_EXPONENT\n then mkPenalty (exponent p + 1)\n else mkPenalty MAX_PENALTY_EXPONENT.","coq_verified":"not stated in registry status for this 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PenaltyState) : Nat \u2192 PenaltyState\n | 0 => initial\n | n + 1 => penalty_successor (apply_n_backoffs initial n)\n\n/-- After scrub, all bytes are zero -/\ndef after_scrub (_ : ScrubState) : ScrubState","lean_verified":"not stated in registry status for this row","module":"CubieTarpitV2_5","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"ed02b668dd817162...","lean_sha256":"e8f82c6f953b3166..."},"source_completeness":"full (CSV-sourced)","statement":"V2.5 Tarpit","status":"VERIFIED_EXACT","theorem_name":"apply_n_backoffs","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Definition named 'after_scrub' in the CubieTarpitV2_5 family -- registry statement: V2.5 Tarpit","coq_statement_full":"Definition after_scrub (_ : ScrubState) : ScrubState :=\n mkScrub true.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieTarpitV2_5.v":"ed02b668dd817162cec56689a4cbf41d955b12f717e3a07211b4764fb85a9f6e","lean/CubieTarpitV2_5.lean":"e8f82c6f953b3166e1cba9a37b6a93fa3474aef65ca4e81a79d70eb48672cc50"},"files":{"coq_file":"coq/CubieTarpitV2_5.v","lean_file":"lean/CubieTarpitV2_5.lean"},"formal_systems":"Coq+Lean","id":"CUB-0495","invocation":"unwired","kernels":"none","kind":"Definition","lean_statement_full":"def after_scrub (_ : ScrubState) : ScrubState","lean_verified":"not stated in registry status for this row","module":"CubieTarpitV2_5","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec 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row","crate":"","deployable":false,"file_shas":{"coq/CubieTarpitV2_5.v":"ed02b668dd817162cec56689a4cbf41d955b12f717e3a07211b4764fb85a9f6e","lean/CubieTarpitV2_5.lean":"e8f82c6f953b3166e1cba9a37b6a93fa3474aef65ca4e81a79d70eb48672cc50"},"files":{"coq_file":"coq/CubieTarpitV2_5.v","lean_file":"lean/CubieTarpitV2_5.lean"},"formal_systems":"Coq+Lean","id":"CUB-0498","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem cub_0890_tarpit_sram_wipe_completeness (pre : ScrubState) :\n (after_scrub pre).all_zeroed = true","lean_verified":"not stated in registry status for this row","module":"CubieTarpitV2_5","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"ed02b668dd817162...","lean_sha256":"e8f82c6f953b3166..."},"source_completeness":"full (CSV-sourced)","statement":"V2.5 Tarpit","status":"VERIFIED_EXACT","theorem_name":"cub_0890_tarpit_sram_wipe_completeness","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Lemma named 'apply_n_backoffs_exponent_bounded' in the CubieTarpitV2_5 family -- registry statement: V2.5 Tarpit","coq_statement_full":"Lemma apply_n_backoffs_exponent_bounded :\n forall (initial : PenaltyState) (n : nat),\n exponent initial <= MAX_PENALTY_EXPONENT ->\n exponent (apply_n_backoffs initial n) <= MAX_PENALTY_EXPONENT.","coq_verified":"not stated in registry status for this 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Collapse","status":"VERIFIED_EXACT","theorem_name":"TOTAL_FACES","use_cases":["topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Definition named 'LATTICE_DIM' in the CubieTopologyCollapse family -- registry statement: Topology Collapse","coq_statement_full":"Definition LATTICE_DIM : nat := 54.","coq_verified":"not stated in registry status for this 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Collapse","status":"VERIFIED_EXACT","theorem_name":"LATTICE_DIM","use_cases":["crypto","topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Definition named 'TOTAL_SEAMS' in the CubieTopologyCollapse family -- registry statement: Topology Collapse","coq_statement_full":"Definition TOTAL_SEAMS : nat := 12.","coq_verified":"not stated in registry status for this 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Collapse","status":"VERIFIED_EXACT","theorem_name":"TOTAL_SEAMS","use_cases":["TDX","topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Definition named 'TOTAL_VERTICES' in the CubieTopologyCollapse family -- registry statement: Topology Collapse","coq_statement_full":"Definition TOTAL_VERTICES : nat := 8.","coq_verified":"not stated in registry status for this 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Collapse","status":"VERIFIED_EXACT","theorem_name":"TOTAL_VERTICES","use_cases":["topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Definition named 'TrustPolytope' in the CubieTopologyCollapse family -- registry statement: Topology Collapse","coq_statement_full":"Definition TrustPolytope := Face -> bool.","coq_verified":"not stated in registry status for this 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Collapse","status":"VERIFIED_EXACT","theorem_name":"countFaces","use_cases":["topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Definition named 'totalDimensions' in the CubieTopologyCollapse family -- registry statement: Topology Collapse","coq_statement_full":"Definition totalDimensions (p : TrustPolytope) : nat :=\n countFaces p * CELLS_PER_FACE.","coq_verified":"not stated in registry status for this 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FaceHow) then 1 else 0) +\n (* Tier 3: Correlated *)\n (if andb (p FaceWho) (p FaceHow) then 1 else 0) +\n (if andb (p FaceWhere) (p FaceWhat) then 1 else 0) +\n (if andb (p FaceWhat) (p FaceWhy) then 1 else 0) +\n (if andb (p FaceHow) (p FaceWhen) then 1 else 0).","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieTopologyCollapse.v":"83e9c22423a6b62cf9251fef84d405ce2e49bab62583b5c879091250f850826b","lean/CubieTopologyCollapse.lean":"f34ef115e00aa1bc51f272d88d996920d36efe71ad2fc88b6dea54a9afa50a1a"},"files":{"coq_file":"coq/CubieTopologyCollapse.v","lean_file":"lean/CubieTopologyCollapse.lean"},"formal_systems":"Coq+Lean","id":"CUB-0509","invocation":"unwired","kernels":"none","kind":"Definition","lean_statement_full":"def countSeams (p : TrustPolytope) : Nat","lean_verified":"not stated in registry status for this 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+\n (if andb (p FaceWho) (andb (p FaceWhy) (p FaceHow)) then 1 else 0) +\n (if andb (p FaceWho) (andb (p FaceWhen) (p FaceWhat)) then 1 else 0) +\n (if andb (p FaceWho) (andb (p FaceWhen) (p FaceHow)) then 1 else 0) +\n (* Back 4 (WHERE-anchored) *)\n (if andb (p FaceWhere) (andb (p FaceWhy) (p FaceWhat)) then 1 else 0) +\n (if andb (p FaceWhere) (andb (p FaceWhy) (p FaceHow)) then 1 else 0) +\n (if andb (p FaceWhere) (andb (p FaceWhen) (p FaceWhat)) then 1 else 0) +\n (if andb (p FaceWhere) (andb (p FaceWhen) (p FaceHow)) then 1 else 0).","coq_verified":"not stated in registry status for this 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'SeamValid' in the OAI_cubie_trust_compiler_theorems family -- registry statement: OAI TrustCompiler","coq_statement_full":"Definition SeamValid (e : Seam) : Prop :=\n forall r : Requirement, RequirementPass r e.","coq_verified":"not stated in registry status for this row","crate":"cubie-core","deployable":true,"exec_file":"cubie-core/src/site_topology_wiring.rs","exec_fn":"cub_0732_site_tuple_valid","exec_fns":["cub_0732_site_tuple_valid"],"file_shas":{"coq/OAI_cubie_trust_compiler_theorems.v":"b488cbd2a25a9602cf89439ab87cafddfea066e62c9cb11203092d6951f58439","verus/cubie_site_topology_spec.rs":"a66784173ee8b6830fd7d6d11157e7391ae3e7514260c22304ada3cfa1565fae"},"files":{"coq_file":"coq/OAI_cubie_trust_compiler_theorems.v","verus_file":"verus/cubie_site_topology_spec.rs"},"formal_systems":"Coq","id":"CUB-0732","invocation":"runtime","kernels":"VCL","kind":"Definition","lean_statement_full":"","lean_verified":"not stated in registry status for this 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AUTHORIZATION\n-- ==============================================================================\n\nstructure Workflow where\n visibleAPI : Nat\n densityOK : Bool\n path : List SeamEvidence\n\ndef AuthStar (w : Workflow) : Bool","lean_verified":"not stated in registry status for this row","module":"Ramen_v1_18","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","proof_scope":"standalone","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"coq_sha256":"d2c86ca9db7f6bd7...","lean_sha256":"e0d363bec5e40068..."},"source_completeness":"full (CSV-sourced)","statement":"Ramen v1.18","status":"VERIFIED_EXACT","theorem_name":"NoEscalation","use_cases":["topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"FUNCTION-IMPL"} {"axiom_free_status":"axiom_free","axiom_profile":"axiom_free","context_purpose":"DERIVED: Fixpoint named 'path_valid' in the Ramen_v1_18 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true /\\\n AuthStar w_discontinuous = false.","coq_verified":"not stated in registry status for this row","crate":"cubie-core","deployable":true,"exec_file":"cubie-core/src/omega.rs","exec_fn":"cub_0960_t8_7_auth_v113_implies_entropy","exec_fns":["cub_0960_t8_7_auth_v113_implies_entropy"],"file_shas":{"coq/Ramen_v1_18.v":"d2c86ca9db7f6bd734ab9c911dc055b125f33cc00fc3f32ef97118607ff7c196","lean/Ramen_v1_18.lean":"e0d363bec5e40068be97e40ce8c563f28bf9458b32fa3f5eb56b524fe2a39f09","verus/omega_spec.rs":"b4bde577f4bb5ee2abb3438eb3f0f1627d5c0c3f475bdaddd578cbe858200085"},"files":{"coq_file":"coq/Ramen_v1_18.v","lean_file":"lean/Ramen_v1_18.lean","verus_file":"verus/omega_spec.rs"},"formal_systems":"Coq+Lean","id":"CUB-0960","invocation":"runtime","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem discontinuous_path_rejected :\n \u2203 (w_valid w_discontinuous : Workflow),\n w_valid.path.all SeamEvidence.J = true \u2227\n w_discontinuous.path.all SeamEvidence.J = true \u2227\n 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ss_timestamp := timestamp e;\n ss_expiry := expiry e |}.","coq_verified":"not stated in registry status for this row","crate":"cubie-core","deployable":true,"exec_file":"cubie-core/src/omega.rs","exec_fn":"cub_0971_tarpit_no_false_admit","exec_fns":["cub_0971_tarpit_no_false_admit"],"file_shas":{"coq/Ramen_v1_18.v":"d2c86ca9db7f6bd734ab9c911dc055b125f33cc00fc3f32ef97118607ff7c196","lean/Ramen_v1_18.lean":"e0d363bec5e40068be97e40ce8c563f28bf9458b32fa3f5eb56b524fe2a39f09","verus/omega_spec.rs":"b4bde577f4bb5ee2abb3438eb3f0f1627d5c0c3f475bdaddd578cbe858200085"},"files":{"coq_file":"coq/Ramen_v1_18.v","lean_file":"lean/Ramen_v1_18.lean","verus_file":"verus/omega_spec.rs"},"formal_systems":"Coq+Lean","id":"CUB-0971","invocation":"runtime","kernels":"VCL","kind":"Definition","lean_statement_full":"def seam_surface (e : SeamEvidence) : SeamSurface","lean_verified":"not stated in registry status for this 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distinct_nonces : List SeamEvidence \u2192 Bool\n | [] => true\n | x::xs => !(contains_nonce x.nonce xs) && distinct_nonces xs\n\ndef contains_node (n : Nat) : List Nat \u2192 Bool\n | [] => false\n | x::xs => (n == x) || contains_node n xs\n\ndef distinct_nodes : List Nat \u2192 Bool\n | [] => true\n | x::xs => !(contains_node x xs) && distinct_nodes xs\n\ndef extract_targets : List SeamEvidence \u2192 List Nat\n | [] => []\n | e::es => e.target_id :: extract_targets es\n\ndef is_acyclic (p : List SeamEvidence) : Bool","lean_verified":"not stated in registry status for this row","module":"Ramen_v1_19","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","proof_scope":"standalone","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"coq_sha256":"16686adc806d01da...","lean_sha256":"5461536d957bcafc..."},"source_completeness":"full (CSV-sourced)","statement":"Ramen 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n xs\n\ndef distinct_nodes : List Nat \u2192 Bool\n | [] => true\n | x::xs => !(contains_node x xs) && distinct_nodes xs\n\ndef extract_targets : List SeamEvidence \u2192 List Nat\n | [] => []\n | e::es => e.target_id :: extract_targets es\n\ndef is_acyclic (p : List SeamEvidence) : Bool","lean_verified":"not stated in registry status for this row","module":"Ramen_v1_19","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","proof_scope":"standalone","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"coq_sha256":"16686adc806d01da...","lean_sha256":"5461536d957bcafc..."},"source_completeness":"full (CSV-sourced)","statement":"Ramen v1.19","status":"VERIFIED_EXACT","theorem_name":"contains_node","use_cases":["topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"FUNCTION-IMPL"} 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==============================================================================\n-- SECTION III -- WORKFLOW AND AUTHORIZATION\n-- ==============================================================================\n\nstructure Workflow where\n visibleAPI : Nat\n densityOK : Bool\n path : List SeamEvidence\n\ndef AuthStar (w : Workflow) : Bool","lean_verified":"not stated in registry status for this row","module":"Ramen_v1_19","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","proof_scope":"standalone","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"coq_sha256":"16686adc806d01da...","lean_sha256":"5461536d957bcafc..."},"source_completeness":"full (CSV-sourced)","statement":"Ramen v1.19","status":"VERIFIED_EXACT","theorem_name":"NoEscalation","use_cases":["NIST"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"VERUS-BOUND"} 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Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"cub_1638_signal_to_exposure_gap","verification_state":"NOT_VERIFIED","verus_statement_full":"proof fn cub_1638_signal_to_exposure_gap(n: nat)\n ensures gap_pow(10, n) * gap_golden_path(n) <= gap_exposure(n)\n","verus_verified":"PENDING -- verus binary not on PATH in this workspace","verus_via_covers_rescue":"","wiring":"SPEC-ONLY"} {"axiom_free_status":"Coq: AXIOM-FREE (0 axioms, live coqc/coqchk-verified) | Lean: NOT AXIOM-FREE -- depends on: propext","axiom_profile":"0 axioms (Lean 4.30.0 #print axioms: propext only, no sorryAx; Coq text scan: no Axiom/Admitted in coq/CubieBexarMetalV1_4Gap.v; coqc/coqchk not run in this workspace) [SUPERSEDED by live coqc/coqchk 2026-08-15: Print Assumptions confirms 'Closed under the global context' (0 axioms) via live coqc+coqchk in coqorg/coq:8.18, not a text scan -- see docs/evidence/2026-08-15_cub_coq_kernel_verification.md]","context_purpose":"DERIVED: Theorem named 'cub_1639_signal_to_crowd_gap' in the CubieBexarMetalV1_4Gap family -- registry statement: Bexar Metal","coq_statement_full":"Theorem cub_1639_signal_to_crowd_gap : forall N, 5 ^ N * goldenPath N <= crowd N.","coq_verified":"YES -- kernel-checked (Coq)","crate":"","deployable":false,"file_shas":{"coq/CubieBexarMetalV1_4Gap.v":"2b97cc6239e6215527b6a2fec259050beb56c9ecf08cb3df02c23a0c29bb8f7a","lean/CubieBexarMetalV1_4Gap.lean":"a16460cb50113621a2e26ed4c8ae7fe990b50e0a99cbb65abd406af54938f1b8","verus/cubie_bexar_metal_v1_4_gap_spec.rs":"b13cd48520bce5e13f432dfab268573eb3a097960e102d613d9c8c2346b116b5"},"files":{"coq_file":"coq/CubieBexarMetalV1_4Gap.v","lean_file":"lean/CubieBexarMetalV1_4Gap.lean","verus_file":"verus/cubie_bexar_metal_v1_4_gap_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-1639","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_1639_signal_to_crowd_gap (N : Nat) : 5 ^ N * goldenPath N \u2264 crowd N","lean_verified":"YES -- kernel-checked live, Lean 4.30.0","module":"CubieBexarMetalV1_4Gap","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"2b97cc6239e62155...","lean_sha256":"a16460cb50113621..."},"source_completeness":"full (CSV-sourced)","statement":"Bexar Metal","status":"Coq kernel-checked 8.18.0 (coqc+coqchk live, 2026-08-15); 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Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"cub_1640_seam_exposed_ratio","use_cases":["TDX","topology"],"verification_state":"NOT_VERIFIED","verus_statement_full":"proof fn cub_1640_seam_exposed_ratio(n: nat)\n ensures 9 * gap_seam_exposed(n) == 8 * gap_pow(54, n + 1)\n","verus_verified":"PENDING -- verus binary not on PATH in this workspace","verus_via_covers_rescue":"","wiring":"SPEC-ONLY"} {"axiom_free_status":"Coq: AXIOM-FREE (0 axioms, live coqc/coqchk-verified) | Lean: NOT AXIOM-FREE -- depends on: propext","axiom_profile":"0 axioms (Lean 4.30.0 #print axioms: propext only, no sorryAx; Coq text scan: no Axiom/Admitted in coq/CubieBexarMetalV1_4Gap.v; coqc/coqchk not run in this workspace) [SUPERSEDED by live coqc/coqchk 2026-08-15: Print Assumptions confirms 'Closed under the global context' (0 axioms) via live coqc+coqchk in coqorg/coq:8.18, not a text scan -- see docs/evidence/2026-08-15_cub_coq_kernel_verification.md]","context_purpose":"DERIVED: Theorem named 'cub_1641_bounded_depth_bounds_exposure' in the CubieBexarMetalV1_4Gap family -- registry statement: Bexar Metal","coq_statement_full":"Theorem cub_1641_bounded_depth_bounds_exposure : forall N Dmax, N <= Dmax -> exposure N <= exposure Dmax.","coq_verified":"YES -- kernel-checked (Coq)","crate":"","deployable":false,"file_shas":{"coq/CubieBexarMetalV1_4Gap.v":"2b97cc6239e6215527b6a2fec259050beb56c9ecf08cb3df02c23a0c29bb8f7a","lean/CubieBexarMetalV1_4Gap.lean":"a16460cb50113621a2e26ed4c8ae7fe990b50e0a99cbb65abd406af54938f1b8","verus/cubie_bexar_metal_v1_4_gap_spec.rs":"b13cd48520bce5e13f432dfab268573eb3a097960e102d613d9c8c2346b116b5"},"files":{"coq_file":"coq/CubieBexarMetalV1_4Gap.v","lean_file":"lean/CubieBexarMetalV1_4Gap.lean","verus_file":"verus/cubie_bexar_metal_v1_4_gap_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-1641","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_1641_bounded_depth_bounds_exposure (N Dmax : Nat) (h : N \u2264 Dmax) :\n exposure N \u2264 exposure Dmax","lean_verified":"YES -- kernel-checked live, Lean 4.30.0","module":"CubieBexarMetalV1_4Gap","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"2b97cc6239e62155...","lean_sha256":"a16460cb50113621..."},"source_completeness":"full (CSV-sourced)","statement":"Bexar Metal","status":"Coq kernel-checked 8.18.0 (coqc+coqchk live, 2026-08-15); 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Coq text scan: no Axiom/Admitted in coq/CubieBexarMetalV1_4Gap.v; coqc/coqchk not run in this workspace) [SUPERSEDED by live coqc/coqchk 2026-08-15: Print Assumptions confirms 'Closed under the global context' (0 axioms) via live coqc+coqchk in coqorg/coq:8.18, not a text scan -- see docs/evidence/2026-08-15_cub_coq_kernel_verification.md]","context_purpose":"DERIVED: Theorem named 'cub_1644_corner_consensus_weakest' in the CubieBexarMetalV1_4Gap family -- registry statement: Bexar Metal","coq_statement_full":"Theorem cub_1644_corner_consensus_weakest : forall j1 j2 j3,\n cornerConsensus j1 j2 j3 = true -> j1 = true /\\ j2 = true /\\ j3 = true.","coq_verified":"YES -- kernel-checked (Coq)","crate":"","deployable":false,"file_shas":{"coq/CubieBexarMetalV1_4Gap.v":"2b97cc6239e6215527b6a2fec259050beb56c9ecf08cb3df02c23a0c29bb8f7a","lean/CubieBexarMetalV1_4Gap.lean":"a16460cb50113621a2e26ed4c8ae7fe990b50e0a99cbb65abd406af54938f1b8","verus/cubie_bexar_metal_v1_4_gap_spec.rs":"b13cd48520bce5e13f432dfab268573eb3a097960e102d613d9c8c2346b116b5"},"files":{"coq_file":"coq/CubieBexarMetalV1_4Gap.v","lean_file":"lean/CubieBexarMetalV1_4Gap.lean","verus_file":"verus/cubie_bexar_metal_v1_4_gap_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-1644","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_1644_corner_consensus_weakest (j1 j2 j3 : Bool)\n (h : cornerConsensus j1 j2 j3 = true) : j1 = true \u2227 j2 = true \u2227 j3 = true","lean_verified":"YES -- kernel-checked live, Lean 4.30.0","module":"CubieBexarMetalV1_4Gap","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"2b97cc6239e62155...","lean_sha256":"a16460cb50113621..."},"source_completeness":"full (CSV-sourced)","statement":"Bexar Metal","status":"Coq kernel-checked 8.18.0 (coqc+coqchk live, 2026-08-15); 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coqc/coqchk-verified)","axiom_profile":"0 axioms (text scan: no Axiom/Admitted in coq/CubieBexarMetalV1_4Omega.v; not kernel-checked in this workspace) | Lean 4.30.0 print axioms Centillion.CubieBexarMetalV1_4Omega.cub_1679_interface_count: does not depend on any axioms; no sorryAx [SUPERSEDED by live coqc/coqchk 2026-08-15: Print Assumptions confirms 'Closed under the global context' (0 axioms) via live coqc+coqchk in coqorg/coq:8.18, not a text scan -- see docs/evidence/2026-08-15_cub_coq_kernel_verification.md]","context_purpose":"DERIVED: Theorem named 'interface_count' in the CubieBexarMetalV1_4Omega family -- registry statement: Bexar Metal","coq_statement_full":"Theorem cub_1679_interface_count : 24 + 24 = 48. Proof. reflexivity. 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to any bare-metal exec fn/crate)","shas":{"coq_sha256":"b97d336c8a5e340c...","lean_sha256":"c174ee9798757916..."},"source_completeness":"full (CSV-sourced)","statement":"Bexar Metal","status":"Coq kernel-checked 8.18.0 (coqc+coqchk live, 2026-08-15); Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"interface_count","use_cases":["topology"],"verification_state":"NOT_VERIFIED","verus_statement_full":"proof fn cub_1679_interface_count() ensures 24 + 24 == 48","verus_verified":"PENDING -- verus binary not on PATH in this workspace","verus_via_covers_rescue":"","wiring":"SPEC-ONLY"} {"axiom_free_status":"AXIOM-FREE (0 axioms, live coqc/coqchk-verified)","axiom_profile":"0 axioms (text scan: no Axiom/Admitted in coq/CubieBexarMetalV1_4Omega.v; not kernel-checked in this workspace) | Lean 4.30.0 print axioms Centillion.CubieBexarMetalV1_4Omega.cub_1680_interface_dominates: does not depend on any axioms; no sorryAx [SUPERSEDED by live coqc/coqchk 2026-08-15: Print Assumptions confirms 'Closed under the global context' (0 axioms) via live coqc+coqchk in coqorg/coq:8.18, not a text scan -- see docs/evidence/2026-08-15_cub_coq_kernel_verification.md]","context_purpose":"DERIVED: Theorem named 'interface_dominates' in the CubieBexarMetalV1_4Omega family -- registry statement: Bexar Metal","coq_statement_full":"Theorem cub_1680_interface_dominates : 54 - (24 + 24) = 6 /\\ (24 + 24) > 54 - (24 + 24).","coq_verified":"YES -- kernel-checked (Coq)","crate":"","deployable":false,"file_shas":{"coq/CubieBexarMetalV1_4Omega.v":"b97d336c8a5e340c807a0b4e74f0dd443d0491ca4fed9e5595b8da154c5424d8","lean/CubieBexarMetalV1_4Omega.lean":"c174ee97987579161910d938f0ce21fd8cf266f1c586bcb5708d1ffabcbccb03","verus/cubie_bexar_metal_v1_4_omega_spec.rs":"80aea8ff70bba7587f67392679bf268eb3337ba992c6e40d0c234c8fc6aea387"},"files":{"coq_file":"coq/CubieBexarMetalV1_4Omega.v","lean_file":"lean/CubieBexarMetalV1_4Omega.lean","verus_file":"verus/cubie_bexar_metal_v1_4_omega_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-1680","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_1680_interface_dominates : 54 - (24 + 24) = 6 \u2227 (24 + 24) > 54 - (24 + 24)","lean_verified":"YES -- kernel-checked live, Lean 4.30.0","module":"CubieBexarMetalV1_4Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound 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Centillion.CubieBexarMetalV1_4Omega.cub_1681_bexar_pow_le_pow_base: depends on axioms: propext; no sorryAx [SUPERSEDED by live coqc/coqchk 2026-08-15: Print Assumptions confirms 'Closed under the global context' (0 axioms) via live coqc+coqchk in coqorg/coq:8.18, not a text scan -- see docs/evidence/2026-08-15_cub_coq_kernel_verification.md]","context_purpose":"DERIVED: Theorem named 'bexar_pow_le_pow_base' in the CubieBexarMetalV1_4Omega family -- registry statement: Bexar Metal","coq_statement_full":"Theorem cub_1681_bexar_pow_le_pow_base : forall a b n, a <= b -> a ^ n <= b ^ n.","coq_verified":"YES -- kernel-checked 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to any bare-metal exec fn/crate)","shas":{"coq_sha256":"b97d336c8a5e340c...","lean_sha256":"c174ee9798757916..."},"source_completeness":"full (CSV-sourced)","statement":"Bexar Metal","status":"Coq kernel-checked 8.18.0 (coqc+coqchk live, 2026-08-15); Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"bexar_pow_le_pow_base","verification_state":"NOT_VERIFIED","verus_statement_full":"proof fn cub_1681_bexar_pow_le_pow_base(a: nat, b: nat, n: nat)\n requires a <= b\n ensures bexar_pow(a, n) <= bexar_pow(b, n)\n decreases n\n","verus_verified":"PENDING -- verus binary not on PATH in this workspace","verus_via_covers_rescue":"","wiring":"SPEC-ONLY"} {"axiom_free_status":"AXIOM-FREE (0 axioms, live coqc/coqchk-verified)","axiom_profile":"0 axioms (text scan: no Axiom/Admitted in coq/CubieBexarMetalV1_4Omega.v; not kernel-checked in this workspace) | Lean 4.30.0 print axioms Centillion.CubieBexarMetalV1_4Omega.cub_1682_witness_64_byte_atomic: does not depend on any axioms; no sorryAx [SUPERSEDED by live coqc/coqchk 2026-08-15: Print Assumptions confirms 'Closed under the global context' (0 axioms) via live coqc+coqchk in coqorg/coq:8.18, not a text scan -- see docs/evidence/2026-08-15_cub_coq_kernel_verification.md]","context_purpose":"DERIVED: Theorem named 'witness_64_byte_atomic' in the CubieBexarMetalV1_4Omega family -- registry statement: Bexar Metal","coq_statement_full":"Theorem cub_1682_witness_64_byte_atomic : 8 + 8 + 8 + 4 + 4 + 4 + 4 + 4 + 2 + 1 + 1 + 16 = 64.","coq_verified":"YES -- kernel-checked (Coq)","crate":"","deployable":false,"file_shas":{"coq/CubieBexarMetalV1_4Omega.v":"b97d336c8a5e340c807a0b4e74f0dd443d0491ca4fed9e5595b8da154c5424d8","lean/CubieBexarMetalV1_4Omega.lean":"c174ee97987579161910d938f0ce21fd8cf266f1c586bcb5708d1ffabcbccb03","verus/cubie_bexar_metal_v1_4_omega_spec.rs":"80aea8ff70bba7587f67392679bf268eb3337ba992c6e40d0c234c8fc6aea387"},"files":{"coq_file":"coq/CubieBexarMetalV1_4Omega.v","lean_file":"lean/CubieBexarMetalV1_4Omega.lean","verus_file":"verus/cubie_bexar_metal_v1_4_omega_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-1682","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_1682_witness_64_byte_atomic : 8 + 8 + 8 + 4 + 4 + 4 + 4 + 4 + 2 + 1 + 1 + 16 = 64","lean_verified":"YES -- kernel-checked live, Lean 4.30.0","module":"CubieBexarMetalV1_4Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"b97d336c8a5e340c...","lean_sha256":"c174ee9798757916..."},"source_completeness":"full (CSV-sourced)","statement":"Bexar Metal","status":"Coq kernel-checked 8.18.0 (coqc+coqchk live, 2026-08-15); Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"witness_64_byte_atomic","verification_state":"NOT_VERIFIED","verus_statement_full":"proof fn cub_1682_witness_64_byte_atomic() ensures bexar_field_sum() == 64","verus_verified":"PENDING -- verus binary not on PATH in this workspace","verus_via_covers_rescue":"","wiring":"SPEC-ONLY"} {"axiom_free_status":"AXIOM-FREE (0 axioms, live coqc/coqchk-verified)","axiom_profile":"0 axioms (text scan: no Axiom/Admitted in coq/CubieBexarMetalV1_4Omega.v; not kernel-checked in this workspace) | Lean 4.30.0 print axioms Centillion.CubieBexarMetalV1_4Omega.cub_1683_belnap_idem: does not depend on any axioms; no sorryAx [SUPERSEDED by live coqc/coqchk 2026-08-15: Print Assumptions confirms 'Closed under the global context' (0 axioms) via live coqc+coqchk in coqorg/coq:8.18, not a text scan -- see docs/evidence/2026-08-15_cub_coq_kernel_verification.md]","context_purpose":"DERIVED: Theorem named 'belnap_idem' in the CubieBexarMetalV1_4Omega family -- registry statement: Bexar Metal","coq_statement_full":"Theorem cub_1683_belnap_idem : forall a : bool, (a && a)%bool = a.","coq_verified":"YES -- kernel-checked (Coq)","crate":"","deployable":false,"file_shas":{"coq/CubieBexarMetalV1_4Omega.v":"b97d336c8a5e340c807a0b4e74f0dd443d0491ca4fed9e5595b8da154c5424d8","lean/CubieBexarMetalV1_4Omega.lean":"c174ee97987579161910d938f0ce21fd8cf266f1c586bcb5708d1ffabcbccb03","verus/cubie_bexar_metal_v1_4_omega_spec.rs":"80aea8ff70bba7587f67392679bf268eb3337ba992c6e40d0c234c8fc6aea387"},"files":{"coq_file":"coq/CubieBexarMetalV1_4Omega.v","lean_file":"lean/CubieBexarMetalV1_4Omega.lean","verus_file":"verus/cubie_bexar_metal_v1_4_omega_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-1683","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_1683_belnap_idem (a : Bool) : (a && a) = a","lean_verified":"YES -- kernel-checked live, Lean 4.30.0","module":"CubieBexarMetalV1_4Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"b97d336c8a5e340c...","lean_sha256":"c174ee9798757916..."},"source_completeness":"full (CSV-sourced)","statement":"Bexar Metal","status":"Coq kernel-checked 8.18.0 (coqc+coqchk live, 2026-08-15); Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"belnap_idem","verification_state":"NOT_VERIFIED","verus_statement_full":"proof fn cub_1683_belnap_idem(a: bool) ensures bexar_meet(a, a) == a","verus_verified":"PENDING -- verus binary not on PATH in this workspace","verus_via_covers_rescue":"","wiring":"SPEC-ONLY"} {"axiom_free_status":"AXIOM-FREE (0 axioms, live coqc/coqchk-verified)","axiom_profile":"0 axioms (text scan: no Axiom/Admitted in coq/CubieBexarMetalV1_4Omega.v; not kernel-checked in this workspace) | Lean 4.30.0 print axioms Centillion.CubieBexarMetalV1_4Omega.cub_1684_belnap_top_unit: does not depend on any axioms; no sorryAx [SUPERSEDED by live coqc/coqchk 2026-08-15: Print Assumptions confirms 'Closed under the global context' (0 axioms) via live coqc+coqchk in coqorg/coq:8.18, not a text scan -- see docs/evidence/2026-08-15_cub_coq_kernel_verification.md]","context_purpose":"DERIVED: Theorem named 'belnap_top_unit' in the CubieBexarMetalV1_4Omega family -- registry statement: Bexar Metal","coq_statement_full":"Theorem cub_1684_belnap_top_unit : forall a : bool, (a && true)%bool = a.","coq_verified":"YES -- kernel-checked (Coq)","crate":"","deployable":false,"file_shas":{"coq/CubieBexarMetalV1_4Omega.v":"b97d336c8a5e340c807a0b4e74f0dd443d0491ca4fed9e5595b8da154c5424d8","lean/CubieBexarMetalV1_4Omega.lean":"c174ee97987579161910d938f0ce21fd8cf266f1c586bcb5708d1ffabcbccb03","verus/cubie_bexar_metal_v1_4_omega_spec.rs":"80aea8ff70bba7587f67392679bf268eb3337ba992c6e40d0c234c8fc6aea387"},"files":{"coq_file":"coq/CubieBexarMetalV1_4Omega.v","lean_file":"lean/CubieBexarMetalV1_4Omega.lean","verus_file":"verus/cubie_bexar_metal_v1_4_omega_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-1684","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_1684_belnap_top_unit (a : Bool) : (a && true) = a","lean_verified":"YES -- kernel-checked live, Lean 4.30.0","module":"CubieBexarMetalV1_4Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"b97d336c8a5e340c...","lean_sha256":"c174ee9798757916..."},"source_completeness":"full (CSV-sourced)","statement":"Bexar Metal","status":"Coq kernel-checked 8.18.0 (coqc+coqchk live, 2026-08-15); Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"belnap_top_unit","verification_state":"NOT_VERIFIED","verus_statement_full":"proof fn cub_1684_belnap_top_unit(a: bool) ensures bexar_meet(a, true) == a","verus_verified":"PENDING -- verus binary not on PATH in this workspace","verus_via_covers_rescue":"","wiring":"SPEC-ONLY"} {"axiom_free_status":"AXIOM-FREE (0 axioms, live coqc/coqchk-verified)","axiom_profile":"0 axioms (text scan: no Axiom/Admitted in coq/CubieBexarMetalV1_4Omega.v; not kernel-checked in this workspace) | Lean 4.30.0 print axioms Centillion.CubieBexarMetalV1_4Omega.cub_1685_belnap_assoc: does not depend on any axioms; no sorryAx [SUPERSEDED by live coqc/coqchk 2026-08-15: Print Assumptions confirms 'Closed under the global context' (0 axioms) via live coqc+coqchk in coqorg/coq:8.18, not a text scan -- see docs/evidence/2026-08-15_cub_coq_kernel_verification.md]","context_purpose":"DERIVED: Theorem named 'belnap_assoc' in the CubieBexarMetalV1_4Omega family -- registry statement: Bexar Metal","coq_statement_full":"Theorem cub_1685_belnap_assoc : forall a b c : bool, ((a && b) && c)%bool = (a && (b && c))%bool.","coq_verified":"YES -- kernel-checked (Coq)","crate":"","deployable":false,"file_shas":{"coq/CubieBexarMetalV1_4Omega.v":"b97d336c8a5e340c807a0b4e74f0dd443d0491ca4fed9e5595b8da154c5424d8","lean/CubieBexarMetalV1_4Omega.lean":"c174ee97987579161910d938f0ce21fd8cf266f1c586bcb5708d1ffabcbccb03","verus/cubie_bexar_metal_v1_4_omega_spec.rs":"80aea8ff70bba7587f67392679bf268eb3337ba992c6e40d0c234c8fc6aea387"},"files":{"coq_file":"coq/CubieBexarMetalV1_4Omega.v","lean_file":"lean/CubieBexarMetalV1_4Omega.lean","verus_file":"verus/cubie_bexar_metal_v1_4_omega_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-1685","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_1685_belnap_assoc (a b c : Bool) : ((a && b) && c) = (a && (b && c))","lean_verified":"YES -- kernel-checked live, Lean 4.30.0","module":"CubieBexarMetalV1_4Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"b97d336c8a5e340c...","lean_sha256":"c174ee9798757916..."},"source_completeness":"full (CSV-sourced)","statement":"Bexar Metal","status":"Coq kernel-checked 8.18.0 (coqc+coqchk live, 2026-08-15); Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"belnap_assoc","verification_state":"NOT_VERIFIED","verus_statement_full":"proof fn cub_1685_belnap_assoc(a: bool, b: bool, c: bool)\n ensures bexar_meet(bexar_meet(a, b), c) == bexar_meet(a, bexar_meet(b, c))\n","verus_verified":"PENDING -- verus binary not on PATH in this workspace","verus_via_covers_rescue":"","wiring":"SPEC-ONLY"} {"axiom_free_status":"Coq: AXIOM-FREE (0 axioms, live coqc/coqchk-verified) | Lean: NOT AXIOM-FREE -- depends on: propext","axiom_profile":"0 axioms (text scan: no Axiom/Admitted in coq/CubieBexarMetalV1_4Omega.v; not kernel-checked in this workspace) | Lean 4.30.0 print axioms Centillion.CubieBexarMetalV1_4Omega.cub_1686_vn_symmetry: depends on axioms: propext; no sorryAx [SUPERSEDED by live coqc/coqchk 2026-08-15: Print Assumptions confirms 'Closed under the global context' (0 axioms) via live coqc+coqchk in coqorg/coq:8.18, not a text scan -- see docs/evidence/2026-08-15_cub_coq_kernel_verification.md]","context_purpose":"DERIVED: Theorem named 'vn_symmetry' in the CubieBexarMetalV1_4Omega family -- registry statement: Bexar Metal","coq_statement_full":"Theorem cub_1686_vn_symmetry : forall a b x : bool,\n (if negb a && b then Some false else if a && negb b then Some true else None) = Some x ->\n (if negb b && a then Some false else if b && negb a then Some true else None) = Some (negb x).","coq_verified":"YES -- kernel-checked (Coq)","crate":"","deployable":false,"file_shas":{"coq/CubieBexarMetalV1_4Omega.v":"b97d336c8a5e340c807a0b4e74f0dd443d0491ca4fed9e5595b8da154c5424d8","lean/CubieBexarMetalV1_4Omega.lean":"c174ee97987579161910d938f0ce21fd8cf266f1c586bcb5708d1ffabcbccb03","verus/cubie_bexar_metal_v1_4_omega_spec.rs":"80aea8ff70bba7587f67392679bf268eb3337ba992c6e40d0c234c8fc6aea387"},"files":{"coq_file":"coq/CubieBexarMetalV1_4Omega.v","lean_file":"lean/CubieBexarMetalV1_4Omega.lean","verus_file":"verus/cubie_bexar_metal_v1_4_omega_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-1686","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_1686_vn_symmetry (a b x : Bool)\n (h : (if !a && b then some false else if a && !b then some true else none) = some x) :\n (if !b && a then some false else if b && !a then some true else none) = some (!x)","lean_verified":"YES -- kernel-checked live, Lean 4.30.0","module":"CubieBexarMetalV1_4Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"b97d336c8a5e340c...","lean_sha256":"c174ee9798757916..."},"source_completeness":"full (CSV-sourced)","statement":"Bexar Metal","status":"Coq kernel-checked 8.18.0 (coqc+coqchk live, 2026-08-15); Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"vn_symmetry","verification_state":"NOT_VERIFIED","verus_statement_full":"proof fn cub_1686_vn_symmetry(a: bool, b: bool, x: bool)\n requires bexar_vn_extract(a, b) == Some(x)\n ensures bexar_vn_extract(b, a) == Some(!x)\n","verus_verified":"PENDING -- verus binary not on PATH in this workspace","verus_via_covers_rescue":"","wiring":"SPEC-ONLY"} {"axiom_free_status":"AXIOM-FREE (0 axioms, live coqc/coqchk-verified)","axiom_profile":"0 axioms (text scan: no Axiom/Admitted in coq/CubieBexarMetalV1_4Omega.v; not kernel-checked in this workspace) | Lean 4.30.0 print axioms Centillion.CubieBexarMetalV1_4Omega.cub_1687_surface_spoofing_kill: does not depend on any axioms; no sorryAx [SUPERSEDED by live coqc/coqchk 2026-08-15: Print Assumptions confirms 'Closed under the global context' (0 axioms) via live coqc+coqchk in coqorg/coq:8.18, not a text scan -- see docs/evidence/2026-08-15_cub_coq_kernel_verification.md]","context_purpose":"DERIVED: Theorem named 'surface_spoofing_kill' in the CubieBexarMetalV1_4Omega family -- registry statement: Bexar Metal","coq_statement_full":"Theorem cub_1687_surface_spoofing_kill : forall jid jpur jtime jver jsco : bool,\n negb (jid && jpur && jtime && false && jver && jsco) = true.","coq_verified":"YES -- kernel-checked (Coq)","crate":"","deployable":false,"file_shas":{"coq/CubieBexarMetalV1_4Omega.v":"b97d336c8a5e340c807a0b4e74f0dd443d0491ca4fed9e5595b8da154c5424d8","lean/CubieBexarMetalV1_4Omega.lean":"c174ee97987579161910d938f0ce21fd8cf266f1c586bcb5708d1ffabcbccb03","verus/cubie_bexar_metal_v1_4_omega_spec.rs":"80aea8ff70bba7587f67392679bf268eb3337ba992c6e40d0c234c8fc6aea387"},"files":{"coq_file":"coq/CubieBexarMetalV1_4Omega.v","lean_file":"lean/CubieBexarMetalV1_4Omega.lean","verus_file":"verus/cubie_bexar_metal_v1_4_omega_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-1687","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_1687_surface_spoofing_kill (jid jpur jtime jver jsco : Bool) :\n !(jid && jpur && jtime && false && jver && jsco) = true","lean_verified":"YES -- kernel-checked live, Lean 4.30.0","module":"CubieBexarMetalV1_4Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"b97d336c8a5e340c...","lean_sha256":"c174ee9798757916..."},"source_completeness":"full (CSV-sourced)","statement":"Bexar Metal","status":"Coq kernel-checked 8.18.0 (coqc+coqchk live, 2026-08-15); Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"surface_spoofing_kill","use_cases":["QEC","topology"],"verification_state":"NOT_VERIFIED","verus_statement_full":"proof fn cub_1687_surface_spoofing_kill(jid: bool, jpur: bool, jtime: bool, jver: bool, jsco: bool)\n ensures !bexar_seam(jid, jpur, jtime, false, jver, jsco)\n","verus_verified":"PENDING -- verus binary not on PATH in this workspace","verus_via_covers_rescue":"","wiring":"SPEC-ONLY"} {"axiom_free_status":"Coq: AXIOM-FREE (0 axioms, live coqc/coqchk-verified) | Lean: NOT AXIOM-FREE -- depends on: propext","axiom_profile":"0 axioms (text scan: no Axiom/Admitted in coq/CubieBexarMetalV1_4Omega.v; not kernel-checked in this workspace) | Lean 4.30.0 print axioms Centillion.CubieBexarMetalV1_4Omega.cub_1688_seam_requires_lineage: depends on axioms: propext; no sorryAx [SUPERSEDED by live coqc/coqchk 2026-08-15: Print Assumptions confirms 'Closed under the global context' (0 axioms) via live coqc+coqchk in coqorg/coq:8.18, not a text scan -- see docs/evidence/2026-08-15_cub_coq_kernel_verification.md]","context_purpose":"DERIVED: Theorem named 'seam_requires_lineage' in the CubieBexarMetalV1_4Omega family -- registry statement: Bexar Metal","coq_statement_full":"Theorem cub_1688_seam_requires_lineage : forall jid jpur jtime jlin jver jsco : bool,\n (jid && jpur && jtime && jlin && jver && jsco)%bool = true -> jlin = true.","coq_verified":"YES -- kernel-checked (Coq)","crate":"","deployable":false,"file_shas":{"coq/CubieBexarMetalV1_4Omega.v":"b97d336c8a5e340c807a0b4e74f0dd443d0491ca4fed9e5595b8da154c5424d8","lean/CubieBexarMetalV1_4Omega.lean":"c174ee97987579161910d938f0ce21fd8cf266f1c586bcb5708d1ffabcbccb03","verus/cubie_bexar_metal_v1_4_omega_spec.rs":"80aea8ff70bba7587f67392679bf268eb3337ba992c6e40d0c234c8fc6aea387"},"files":{"coq_file":"coq/CubieBexarMetalV1_4Omega.v","lean_file":"lean/CubieBexarMetalV1_4Omega.lean","verus_file":"verus/cubie_bexar_metal_v1_4_omega_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-1688","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_1688_seam_requires_lineage (jid jpur jtime jlin jver jsco : Bool)\n (h : jid && jpur && jtime && jlin && jver && jsco = true) : jlin = true","lean_verified":"YES -- kernel-checked live, Lean 4.30.0","module":"CubieBexarMetalV1_4Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"b97d336c8a5e340c...","lean_sha256":"c174ee9798757916..."},"source_completeness":"full (CSV-sourced)","statement":"Bexar Metal","status":"Coq kernel-checked 8.18.0 (coqc+coqchk live, 2026-08-15); Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"seam_requires_lineage","use_cases":["TDX","topology"],"verification_state":"NOT_VERIFIED","verus_statement_full":"proof fn cub_1688_seam_requires_lineage(jid: bool, jpur: bool, jtime: bool, jlin: bool, jver: bool, jsco: bool)\n requires bexar_seam(jid, jpur, jtime, jlin, jver, jsco)\n ensures jlin\n","verus_verified":"PENDING -- verus binary not on PATH in this workspace","verus_via_covers_rescue":"","wiring":"SPEC-ONLY"} {"axiom_free_status":"Coq: AXIOM-FREE (0 axioms, live coqc/coqchk-verified) | Lean: NOT AXIOM-FREE -- depends on: propext, Classical.choice, Quot.sound","axiom_profile":"0 axioms (text scan: no Axiom/Admitted in coq/CubieBexarMetalV1_4Omega.v; not kernel-checked in this workspace) | Lean 4.30.0 print axioms Centillion.CubieBexarMetalV1_4Omega.cub_1689_goodput_no_overcommit: depends on axioms: propext, Classical.choice, Quot.sound; no sorryAx [SUPERSEDED by live coqc/coqchk 2026-08-15: Print Assumptions confirms 'Closed under the global context' (0 axioms) via live coqc+coqchk in coqorg/coq:8.18, not a text scan -- see docs/evidence/2026-08-15_cub_coq_kernel_verification.md]","context_purpose":"DERIVED: Theorem named 'goodput_no_overcommit' in the CubieBexarMetalV1_4Omega family -- registry statement: Bexar Metal","coq_statement_full":"Theorem cub_1689_goodput_no_overcommit : forall pool cost,\n cost <= pool -> cost + (pool - cost) = pool /\\ (pool - cost) <= pool.","coq_verified":"YES -- kernel-checked (Coq)","crate":"","deployable":false,"file_shas":{"coq/CubieBexarMetalV1_4Omega.v":"b97d336c8a5e340c807a0b4e74f0dd443d0491ca4fed9e5595b8da154c5424d8","lean/CubieBexarMetalV1_4Omega.lean":"c174ee97987579161910d938f0ce21fd8cf266f1c586bcb5708d1ffabcbccb03","verus/cubie_bexar_metal_v1_4_omega_spec.rs":"80aea8ff70bba7587f67392679bf268eb3337ba992c6e40d0c234c8fc6aea387"},"files":{"coq_file":"coq/CubieBexarMetalV1_4Omega.v","lean_file":"lean/CubieBexarMetalV1_4Omega.lean","verus_file":"verus/cubie_bexar_metal_v1_4_omega_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-1689","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_1689_goodput_no_overcommit (pool cost : Nat) (h : cost \u2264 pool) :\n cost + (pool - cost) = pool \u2227 (pool - cost) \u2264 pool","lean_verified":"YES -- kernel-checked live, Lean 4.30.0","module":"CubieBexarMetalV1_4Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"b97d336c8a5e340c...","lean_sha256":"c174ee9798757916..."},"source_completeness":"full (CSV-sourced)","statement":"Bexar Metal","status":"Coq kernel-checked 8.18.0 (coqc+coqchk live, 2026-08-15); Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"goodput_no_overcommit","verification_state":"NOT_VERIFIED","verus_statement_full":"proof fn cub_1689_goodput_no_overcommit(pool: nat, cost: nat)\n requires cost <= pool\n ensures cost + (pool - cost) == pool && (pool - cost) <= pool\n","verus_verified":"PENDING -- verus binary not on PATH in this workspace","verus_via_covers_rescue":"","wiring":"SPEC-ONLY"} {"axiom_free_status":"Coq: AXIOM-FREE (0 axioms, live coqc/coqchk-verified) | Lean: NOT AXIOM-FREE -- depends on: propext, Quot.sound","axiom_profile":"0 axioms (text scan: no Axiom/Admitted in coq/CubieBexarMetalV1_4Omega.v; not kernel-checked in this workspace) | Lean 4.30.0 print axioms Centillion.CubieBexarMetalV1_4Omega.cub_1690_ha_fail_closed: depends on axioms: propext, Quot.sound; no sorryAx [SUPERSEDED by live coqc/coqchk 2026-08-15: Print Assumptions confirms 'Closed under the global context' (0 axioms) via live coqc+coqchk in coqorg/coq:8.18, not a text scan -- see docs/evidence/2026-08-15_cub_coq_kernel_verification.md]","context_purpose":"DERIVED: Theorem named 'ha_fail_closed' in the CubieBexarMetalV1_4Omega family -- registry statement: Bexar Metal","coq_statement_full":"Theorem cub_1690_ha_fail_closed : forall base,\n bexar_applied_cost base false <= bexar_applied_cost base true.","coq_verified":"YES -- kernel-checked (Coq)","crate":"","deployable":false,"file_shas":{"coq/CubieBexarMetalV1_4Omega.v":"b97d336c8a5e340c807a0b4e74f0dd443d0491ca4fed9e5595b8da154c5424d8","lean/CubieBexarMetalV1_4Omega.lean":"c174ee97987579161910d938f0ce21fd8cf266f1c586bcb5708d1ffabcbccb03","verus/cubie_bexar_metal_v1_4_omega_spec.rs":"80aea8ff70bba7587f67392679bf268eb3337ba992c6e40d0c234c8fc6aea387"},"files":{"coq_file":"coq/CubieBexarMetalV1_4Omega.v","lean_file":"lean/CubieBexarMetalV1_4Omega.lean","verus_file":"verus/cubie_bexar_metal_v1_4_omega_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-1690","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_1690_ha_fail_closed (base : Nat) :\n bexarAppliedCost base false \u2264 bexarAppliedCost base true","lean_verified":"YES -- kernel-checked live, Lean 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4.30.0","module":"CubieDriveMathV1_3Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"abc96f0177a114d7...","lean_sha256":"b3be7adc7f090b52..."},"source_completeness":"full (CSV-sourced)","statement":"Drive Math","status":"Coq kernel-checked 8.18.0 (coqc+coqchk live, 2026-08-15); Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"two_pow_pos","verification_state":"NOT_VERIFIED","verus_statement_full":"proof fn cub_1709_two_pow_pos(n: nat)\n ensures dm_pow(2, n) >= 1\n decreases n\n","verus_verified":"PENDING -- verus binary not on PATH in this workspace","verus_via_covers_rescue":"","wiring":"SPEC-ONLY"} {"axiom_free_status":"AXIOM-FREE (0 axioms, live coqc/coqchk-verified)","axiom_profile":"0 axioms (text scan: no Axiom/Admitted in coq/CubieDriveMathV1_3Omega.v; not kernel-checked in this workspace) | Lean 4.30.0 print axioms Centillion.CubieDriveMathV1_3Omega.cub_1710_n_lt_two_pow: does not depend on any axioms; no sorryAx [SUPERSEDED by live coqc/coqchk 2026-08-15: Print Assumptions confirms 'Closed under the global context' (0 axioms) via live coqc+coqchk in coqorg/coq:8.18, not a text scan -- see docs/evidence/2026-08-15_cub_coq_kernel_verification.md]","context_purpose":"DERIVED: Theorem named 'n_lt_two_pow' in the CubieDriveMathV1_3Omega family -- registry statement: Drive Math","coq_statement_full":"Theorem cub_1710_n_lt_two_pow : forall n, n < 2 ^ n.","coq_verified":"YES -- kernel-checked (Coq)","crate":"","deployable":false,"file_shas":{"coq/CubieDriveMathV1_3Omega.v":"abc96f0177a114d7f6b8274a2a56975d4c86a2855cc95e0666466c5e262978cc","lean/CubieDriveMathV1_3Omega.lean":"b3be7adc7f090b52f6b1a4c03948781f9e073087ea2c96d767fe7e33363ba430","verus/cubie_drive_math_v1_3_omega_spec.rs":"3298de214d0e1552a8d4157f602815d9b461bbe0367e63bf93b87882b5626362"},"files":{"coq_file":"coq/CubieDriveMathV1_3Omega.v","lean_file":"lean/CubieDriveMathV1_3Omega.lean","verus_file":"verus/cubie_drive_math_v1_3_omega_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-1710","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_1710_n_lt_two_pow (n : Nat) : n < 2 ^ n","lean_verified":"YES -- kernel-checked live, Lean 4.30.0","module":"CubieDriveMathV1_3Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"abc96f0177a114d7...","lean_sha256":"b3be7adc7f090b52..."},"source_completeness":"full (CSV-sourced)","statement":"Drive Math","status":"Coq kernel-checked 8.18.0 (coqc+coqchk live, 2026-08-15); Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"n_lt_two_pow","verification_state":"NOT_VERIFIED","verus_statement_full":"proof fn cub_1710_n_lt_two_pow(n: nat)\n ensures n < dm_pow(2, n)\n decreases n\n","verus_verified":"PENDING -- verus binary not on PATH in this workspace","verus_via_covers_rescue":"","wiring":"SPEC-ONLY"} {"axiom_free_status":"AXIOM-FREE (0 axioms, live coqc/coqchk-verified)","axiom_profile":"0 axioms (text scan: no Axiom/Admitted in coq/CubieDriveMathV1_3Omega.v; not kernel-checked in this workspace) | Lean 4.30.0 print axioms Centillion.CubieDriveMathV1_3Omega.cub_1711_drive_pow_le_pow_base: does not depend on any axioms; no sorryAx [SUPERSEDED by live coqc/coqchk 2026-08-15: Print Assumptions confirms 'Closed under the global context' (0 axioms) via live coqc+coqchk in coqorg/coq:8.18, not a text scan -- see docs/evidence/2026-08-15_cub_coq_kernel_verification.md]","context_purpose":"DERIVED: Theorem named 'drive_pow_le_pow_base' in the CubieDriveMathV1_3Omega family -- registry statement: Drive Math","coq_statement_full":"Theorem cub_1711_drive_pow_le_pow_base : forall a b n, a <= b -> a ^ n <= b ^ n.","coq_verified":"YES -- kernel-checked (Coq)","crate":"","deployable":false,"file_shas":{"coq/CubieDriveMathV1_3Omega.v":"abc96f0177a114d7f6b8274a2a56975d4c86a2855cc95e0666466c5e262978cc","lean/CubieDriveMathV1_3Omega.lean":"b3be7adc7f090b52f6b1a4c03948781f9e073087ea2c96d767fe7e33363ba430","verus/cubie_drive_math_v1_3_omega_spec.rs":"3298de214d0e1552a8d4157f602815d9b461bbe0367e63bf93b87882b5626362"},"files":{"coq_file":"coq/CubieDriveMathV1_3Omega.v","lean_file":"lean/CubieDriveMathV1_3Omega.lean","verus_file":"verus/cubie_drive_math_v1_3_omega_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-1711","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_1711_drive_pow_le_pow_base (a b n : Nat) (h : a \u2264 b) : a ^ n \u2264 b ^ n","lean_verified":"YES -- kernel-checked live, Lean 4.30.0","module":"CubieDriveMathV1_3Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"abc96f0177a114d7...","lean_sha256":"b3be7adc7f090b52..."},"source_completeness":"full (CSV-sourced)","statement":"Drive Math","status":"Coq kernel-checked 8.18.0 (coqc+coqchk live, 2026-08-15); Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"drive_pow_le_pow_base","verification_state":"NOT_VERIFIED","verus_statement_full":"proof fn cub_1711_drive_pow_le_pow_base(a: nat, b: nat, n: nat)\n requires a <= b\n ensures dm_pow(a, n) <= dm_pow(b, n)\n decreases n\n","verus_verified":"PENDING -- verus binary not on PATH in this workspace","verus_via_covers_rescue":"","wiring":"SPEC-ONLY"} {"axiom_free_status":"AXIOM-FREE (0 axioms, live coqc/coqchk-verified)","axiom_profile":"0 axioms (text scan: no Axiom/Admitted in coq/CubieDriveMathV1_3Omega.v; not kernel-checked in this workspace) | Lean 4.30.0 print axioms Centillion.CubieDriveMathV1_3Omega.cub_1712_geometric_complexity_futility: does not depend on any axioms; no sorryAx [SUPERSEDED by live coqc/coqchk 2026-08-15: Print Assumptions confirms 'Closed under the global context' (0 axioms) via live coqc+coqchk in coqorg/coq:8.18, not a text scan -- see docs/evidence/2026-08-15_cub_coq_kernel_verification.md]","context_purpose":"DERIVED: Theorem named 'geometric_complexity_futility' in the CubieDriveMathV1_3Omega family -- registry statement: Drive Math","coq_statement_full":"Theorem cub_1712_geometric_complexity_futility : forall B base, 2 <= base -> B < dm_coord_chain base B.","coq_verified":"YES -- kernel-checked (Coq)","crate":"","deployable":false,"file_shas":{"coq/CubieDriveMathV1_3Omega.v":"abc96f0177a114d7f6b8274a2a56975d4c86a2855cc95e0666466c5e262978cc","lean/CubieDriveMathV1_3Omega.lean":"b3be7adc7f090b52f6b1a4c03948781f9e073087ea2c96d767fe7e33363ba430","verus/cubie_drive_math_v1_3_omega_spec.rs":"3298de214d0e1552a8d4157f602815d9b461bbe0367e63bf93b87882b5626362"},"files":{"coq_file":"coq/CubieDriveMathV1_3Omega.v","lean_file":"lean/CubieDriveMathV1_3Omega.lean","verus_file":"verus/cubie_drive_math_v1_3_omega_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-1712","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_1712_geometric_complexity_futility (B base : Nat) (h : 2 \u2264 base) :\n B < base ^ B","lean_verified":"YES -- kernel-checked live, Lean 4.30.0","module":"CubieDriveMathV1_3Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"abc96f0177a114d7...","lean_sha256":"b3be7adc7f090b52..."},"source_completeness":"full (CSV-sourced)","statement":"Drive Math","status":"Coq kernel-checked 8.18.0 (coqc+coqchk live, 2026-08-15); Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"geometric_complexity_futility","use_cases":["complexity"],"verification_state":"NOT_VERIFIED","verus_statement_full":"proof fn cub_1712_geometric_complexity_futility(bb: nat, base: nat)\n requires 2 <= base\n ensures bb < dm_coord_chain(base, bb)\n","verus_verified":"PENDING -- verus binary not on PATH in this workspace","verus_via_covers_rescue":"","wiring":"SPEC-ONLY"} {"axiom_free_status":"AXIOM-FREE (0 axioms, live coqc/coqchk-verified)","axiom_profile":"0 axioms (text scan: no Axiom/Admitted in coq/CubieDriveMathV1_3Omega.v; not kernel-checked in this workspace) | Lean 4.30.0 print axioms Centillion.CubieDriveMathV1_3Omega.cub_1713_hypercontraction_decay: does not depend on any axioms; no sorryAx [SUPERSEDED by live coqc/coqchk 2026-08-15: Print Assumptions confirms 'Closed under the global context' (0 axioms) via live coqc+coqchk in coqorg/coq:8.18, not a text scan -- see docs/evidence/2026-08-15_cub_coq_kernel_verification.md]","context_purpose":"DERIVED: Theorem named 'hypercontraction_decay' in the CubieDriveMathV1_3Omega family -- registry statement: Drive Math","coq_statement_full":"Theorem cub_1713_hypercontraction_decay : forall f w n, f <= w -> f ^ n <= w ^ n.","coq_verified":"YES -- kernel-checked (Coq)","crate":"","deployable":false,"file_shas":{"coq/CubieDriveMathV1_3Omega.v":"abc96f0177a114d7f6b8274a2a56975d4c86a2855cc95e0666466c5e262978cc","lean/CubieDriveMathV1_3Omega.lean":"b3be7adc7f090b52f6b1a4c03948781f9e073087ea2c96d767fe7e33363ba430","verus/cubie_drive_math_v1_3_omega_spec.rs":"3298de214d0e1552a8d4157f602815d9b461bbe0367e63bf93b87882b5626362"},"files":{"coq_file":"coq/CubieDriveMathV1_3Omega.v","lean_file":"lean/CubieDriveMathV1_3Omega.lean","verus_file":"verus/cubie_drive_math_v1_3_omega_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-1713","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_1713_hypercontraction_decay (f w n : Nat) (h : f \u2264 w) : f ^ n \u2264 w ^ n","lean_verified":"YES -- kernel-checked live, Lean 4.30.0","module":"CubieDriveMathV1_3Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"abc96f0177a114d7...","lean_sha256":"b3be7adc7f090b52..."},"source_completeness":"full (CSV-sourced)","statement":"Drive Math","status":"Coq kernel-checked 8.18.0 (coqc+coqchk live, 2026-08-15); Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"hypercontraction_decay","verification_state":"NOT_VERIFIED","verus_statement_full":"proof fn cub_1713_hypercontraction_decay(f: nat, w: nat, n: nat)\n requires f <= w\n ensures dm_pow(f, n) <= dm_pow(w, n)\n","verus_verified":"PENDING -- verus binary not on PATH in this workspace","verus_via_covers_rescue":"","wiring":"SPEC-ONLY"} {"axiom_free_status":"Coq: AXIOM-FREE (0 axioms, live coqc/coqchk-verified) | Lean: NOT AXIOM-FREE -- depends on: propext, Quot.sound","axiom_profile":"0 axioms (text scan: no Axiom/Admitted in coq/CubieDriveMathV1_3Omega.v; not kernel-checked in this workspace) | Lean 4.30.0 print axioms Centillion.CubieDriveMathV1_3Omega.cub_1714_fano_error_lower_bound: depends on axioms: propext, Quot.sound; no sorryAx [SUPERSEDED by live coqc/coqchk 2026-08-15: Print Assumptions confirms 'Closed under the global context' (0 axioms) via live coqc+coqchk in coqorg/coq:8.18, not a text scan -- see docs/evidence/2026-08-15_cub_coq_kernel_verification.md]","context_purpose":"DERIVED: Theorem named 'fano_error_lower_bound' in the CubieDriveMathV1_3Omega family -- registry statement: Drive Math","coq_statement_full":"Theorem cub_1714_fano_error_lower_bound : forall rr ii errs,\n rr <= ii + errs -> rr - ii <= errs.","coq_verified":"YES -- kernel-checked (Coq)","crate":"","deployable":false,"file_shas":{"coq/CubieDriveMathV1_3Omega.v":"abc96f0177a114d7f6b8274a2a56975d4c86a2855cc95e0666466c5e262978cc","lean/CubieDriveMathV1_3Omega.lean":"b3be7adc7f090b52f6b1a4c03948781f9e073087ea2c96d767fe7e33363ba430","verus/cubie_drive_math_v1_3_omega_spec.rs":"3298de214d0e1552a8d4157f602815d9b461bbe0367e63bf93b87882b5626362"},"files":{"coq_file":"coq/CubieDriveMathV1_3Omega.v","lean_file":"lean/CubieDriveMathV1_3Omega.lean","verus_file":"verus/cubie_drive_math_v1_3_omega_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-1714","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_1714_fano_error_lower_bound (rr ii errs : Nat) (h : rr \u2264 ii + errs) :\n rr - ii \u2264 errs","lean_verified":"YES -- kernel-checked live, Lean 4.30.0","module":"CubieDriveMathV1_3Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"abc96f0177a114d7...","lean_sha256":"b3be7adc7f090b52..."},"source_completeness":"full (CSV-sourced)","statement":"Drive Math","status":"Coq kernel-checked 8.18.0 (coqc+coqchk live, 2026-08-15); Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"fano_error_lower_bound","verification_state":"NOT_VERIFIED","verus_statement_full":"proof fn cub_1714_fano_error_lower_bound(rr: nat, ii: nat, errs: nat)\n requires rr <= ii + errs\n ensures rr - ii <= errs\n","verus_verified":"PENDING -- verus binary not on PATH in this workspace","verus_via_covers_rescue":"","wiring":"SPEC-ONLY"} {"axiom_free_status":"Coq: AXIOM-FREE (0 axioms, live coqc/coqchk-verified) | Lean: NOT AXIOM-FREE -- depends on: propext, Quot.sound","axiom_profile":"0 axioms (text scan: no Axiom/Admitted in coq/CubieDriveMathV1_3Omega.v; not kernel-checked in this workspace) | Lean 4.30.0 print axioms Centillion.CubieDriveMathV1_3Omega.cub_1715_kl_zero_leak_no_advantage: depends on axioms: propext, Quot.sound; no sorryAx [SUPERSEDED by live coqc/coqchk 2026-08-15: Print Assumptions confirms 'Closed under the global context' (0 axioms) via live coqc+coqchk in coqorg/coq:8.18, not a text scan -- see docs/evidence/2026-08-15_cub_coq_kernel_verification.md]","context_purpose":"DERIVED: Theorem named 'kl_zero_leak_no_advantage' in the CubieDriveMathV1_3Omega family -- registry statement: Drive Math","coq_statement_full":"Theorem cub_1715_kl_zero_leak_no_advantage : forall adv leak,\n adv <= leak -> leak = 0 -> adv = 0.","coq_verified":"YES -- kernel-checked (Coq)","crate":"","deployable":false,"file_shas":{"coq/CubieDriveMathV1_3Omega.v":"abc96f0177a114d7f6b8274a2a56975d4c86a2855cc95e0666466c5e262978cc","lean/CubieDriveMathV1_3Omega.lean":"b3be7adc7f090b52f6b1a4c03948781f9e073087ea2c96d767fe7e33363ba430","verus/cubie_drive_math_v1_3_omega_spec.rs":"3298de214d0e1552a8d4157f602815d9b461bbe0367e63bf93b87882b5626362"},"files":{"coq_file":"coq/CubieDriveMathV1_3Omega.v","lean_file":"lean/CubieDriveMathV1_3Omega.lean","verus_file":"verus/cubie_drive_math_v1_3_omega_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-1715","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_1715_kl_zero_leak_no_advantage (adv leak : Nat) (h1 : adv \u2264 leak) (h2 : leak = 0) :\n adv = 0","lean_verified":"YES -- kernel-checked live, Lean 4.30.0","module":"CubieDriveMathV1_3Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"abc96f0177a114d7...","lean_sha256":"b3be7adc7f090b52..."},"source_completeness":"full (CSV-sourced)","statement":"Drive Math","status":"Coq kernel-checked 8.18.0 (coqc+coqchk live, 2026-08-15); Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"kl_zero_leak_no_advantage","verification_state":"NOT_VERIFIED","verus_statement_full":"proof fn cub_1715_kl_zero_leak_no_advantage(adv: nat, leak: nat)\n requires adv <= leak, leak == 0\n ensures adv == 0\n","verus_verified":"PENDING -- verus binary not on PATH in this workspace","verus_via_covers_rescue":"","wiring":"SPEC-ONLY"} {"axiom_free_status":"AXIOM-FREE (0 axioms, live coqc/coqchk-verified)","axiom_profile":"0 axioms (text scan: no Axiom/Admitted in coq/CubieDriveMathV1_3Omega.v; not kernel-checked in this workspace) | Lean 4.30.0 print axioms Centillion.CubieDriveMathV1_3Omega.cub_1716_topological_entropy_exponential: does not depend on any 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wiring/invocation fields only.","coq_statement_full":"","coq_verified":"AUDIT-ONLY -- no theorem_name in master_theorem_table.csv; kernel status not tracked at row level","crate":"cubie-proof-obligation","deployable":false,"exec_file":"crates/cubie-proof-obligation/src/lib.rs","id":"CUB-2062","invocation":"unwired","kernels":"none","lean_statement_full":"","lean_verified":"AUDIT-ONLY -- no theorem_name in master_theorem_table.csv; kernel status not tracked at row level","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"no","riscv_status":"no","source_completeness":"AUDIT-ONLY (wiring/invocation only, no theorem_name/statement in source)","verus_statement_full":"","verus_verified":"AUDIT-ONLY -- no theorem_name in master_theorem_table.csv; kernel status not tracked at row level","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"not measured for this row","context_purpose":"AUDIT-ONLY row -- no theorem_name/statement in source; see wiring/invocation fields only.","coq_statement_full":"","coq_verified":"AUDIT-ONLY -- no theorem_name in master_theorem_table.csv; kernel status not tracked at row level","crate":"cubie-proof-obligation","deployable":false,"exec_file":"crates/cubie-proof-obligation/src/lib.rs","id":"CUB-2063","invocation":"unwired","kernels":"none","lean_statement_full":"","lean_verified":"AUDIT-ONLY -- no theorem_name in master_theorem_table.csv; kernel status not tracked at row level","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"no","riscv_status":"no","source_completeness":"AUDIT-ONLY (wiring/invocation only, no theorem_name/statement in source)","verus_statement_full":"","verus_verified":"AUDIT-ONLY -- no theorem_name in master_theorem_table.csv; kernel status not tracked at row level","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"not measured for this row","context_purpose":"AUDIT-ONLY row -- no theorem_name/statement in source; see wiring/invocation fields only.","coq_statement_full":"","coq_verified":"AUDIT-ONLY -- no theorem_name in master_theorem_table.csv; kernel status not tracked at row level","crate":"cubie-proof-obligation","deployable":false,"exec_file":"crates/cubie-proof-obligation/src/lib.rs","id":"CUB-2064","invocation":"unwired","kernels":"none","lean_statement_full":"","lean_verified":"AUDIT-ONLY -- no theorem_name in master_theorem_table.csv; kernel status not tracked at row level","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"no","riscv_status":"no","source_completeness":"AUDIT-ONLY (wiring/invocation only, no theorem_name/statement in source)","verus_statement_full":"","verus_verified":"AUDIT-ONLY -- no theorem_name in master_theorem_table.csv; kernel status not tracked at row level","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"not measured for this row","context_purpose":"AUDIT-ONLY row -- no theorem_name/statement in source; see wiring/invocation fields only.","coq_statement_full":"","coq_verified":"AUDIT-ONLY -- no theorem_name in master_theorem_table.csv; kernel status not tracked at row level","crate":"cubie-proof-obligation","deployable":false,"exec_file":"crates/cubie-proof-obligation/src/lib.rs","id":"CUB-2065","invocation":"unwired","kernels":"none","lean_statement_full":"","lean_verified":"AUDIT-ONLY -- no theorem_name in master_theorem_table.csv; kernel status not tracked at row level","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"no","riscv_status":"no","source_completeness":"AUDIT-ONLY (wiring/invocation only, no theorem_name/statement in source)","verus_statement_full":"","verus_verified":"AUDIT-ONLY -- no theorem_name in master_theorem_table.csv; kernel status not tracked at row level","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"not measured for this row","context_purpose":"AUDIT-ONLY row -- no theorem_name/statement in source; see wiring/invocation fields only.","coq_statement_full":"","coq_verified":"AUDIT-ONLY -- no theorem_name in master_theorem_table.csv; kernel status not tracked at row level","crate":"cubie-proof-obligation","deployable":false,"exec_file":"crates/cubie-proof-obligation/src/lib.rs","id":"CUB-2066","invocation":"unwired","kernels":"none","lean_statement_full":"","lean_verified":"AUDIT-ONLY -- no theorem_name in master_theorem_table.csv; kernel status not tracked at row level","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"no","riscv_status":"no","source_completeness":"AUDIT-ONLY (wiring/invocation only, no theorem_name/statement in source)","verus_statement_full":"","verus_verified":"AUDIT-ONLY -- no theorem_name in master_theorem_table.csv; kernel status not tracked at row level","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"not measured for this row","context_purpose":"AUDIT-ONLY row -- no theorem_name/statement in source; see wiring/invocation fields only.","coq_statement_full":"","coq_verified":"AUDIT-ONLY -- no theorem_name in master_theorem_table.csv; kernel status not tracked at row level","crate":"cubie-workflow-recompute","deployable":true,"exec_file":"crates/cubie-workflow-recompute/src/lib.rs","exec_fn":"evaluate_workflow_recompute","exec_fns":["evaluate_workflow_recompute"],"id":"CUB-2067","invocation":"runtime","kernels":"none","lean_statement_full":"","lean_verified":"AUDIT-ONLY -- no theorem_name in master_theorem_table.csv; kernel status not tracked at row level","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","repo":"cubie-tf","riscv":"no","riscv_status":"no","source_completeness":"AUDIT-ONLY (wiring/invocation only, no theorem_name/statement in source)","verus_statement_full":"","verus_verified":"AUDIT-ONLY -- no theorem_name in master_theorem_table.csv; kernel status not tracked at row level","verus_via_covers_rescue":"","wiring":"VERUS-BOUND"} {"axiom_free_status":"not measured for this row","context_purpose":"AUDIT-ONLY row -- no theorem_name/statement in source; see wiring/invocation fields only.","coq_statement_full":"","coq_verified":"AUDIT-ONLY -- no theorem_name in master_theorem_table.csv; kernel status not tracked at row level","crate":"cubie-workflow-recompute","deployable":false,"exec_file":"crates/cubie-workflow-recompute/src/lib.rs","id":"CUB-2068","invocation":"unwired","kernels":"none","lean_statement_full":"","lean_verified":"AUDIT-ONLY -- no theorem_name in master_theorem_table.csv; kernel status not tracked at row level","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"no","riscv_status":"no","source_completeness":"AUDIT-ONLY (wiring/invocation only, no theorem_name/statement in source)","verus_statement_full":"","verus_verified":"AUDIT-ONLY -- no theorem_name in 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row","crate":"","deployable":false,"file_shas":{"coq/C4AuthorizationGateV2_6.v":"17752a64962da8b6ee39ba0ac527950f3d4953e9aa7c7340762e4def9a8d0d80","lean/C4AuthorizationGateV2_6.lean":"487bcf0ad29018f4fa48c2ee381b0ded1a28870ec3bf94dfde3f7b7bdc230599"},"files":{"coq_file":"coq/C4AuthorizationGateV2_6.v","lean_file":"lean/C4AuthorizationGateV2_6.lean"},"formal_systems":"Coq+Lean","id":"CUB-2079","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem intra_realm_requires_subgroup_closure (op : BoundaryCrossingOp) :\n op.is_external = false \u2192\n op.source_realm = op.target_realm \u2192\n intra_realm_subgroup_closed op true = true","lean_verified":"not stated in registry status for this row","module":"C4AuthorizationGateV2_6","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"17752a64962da8b6...","lean_sha256":"487bcf0ad29018f4..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-platform","status":"VERIFIED","theorem_name":"intra_realm_requires_subgroup_closure","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: theorem named 'audit_count_monotone' in the CentillionTrustFabric family -- registry statement: CUB integration: cubie-platform","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"cubie-platform","deployable":false,"exec_file":"cubie-platform/src/admit.rs","file_shas":{"lean/CentillionTrustFabric.lean":"1f30f513efa3a59995195211659c892ac20a4bf71eb89fd19bc11f91182cfc04"},"files":{"lean_file":"lean/CentillionTrustFabric.lean"},"formal_systems":"Lean","id":"CUB-2083","invocation":"unwired","kernels":"none","kind":"theorem","lean_statement_full":"theorem audit_count_monotone (req pol : CubeFlit) :\n (evaluate req pol).auditCount = req.auditCount \u2228\n (evaluate req pol).auditCount = req.auditCount + 1","lean_verified":"not stated in registry status for this row","module":"CentillionTrustFabric","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"lean_sha256":"1f30f513efa3a599..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: 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cubie-platform","status":"VERIFIED","theorem_name":"compromised_excluded_from_wreath","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: theorem named 'misalignment_triggers_amputation' in the CentillionTrustFabric family -- registry statement: CUB integration: cubie-platform","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"cubie-platform","deployable":false,"exec_file":"cubie-platform/src/trust_fabric.rs","file_shas":{"lean/CentillionTrustFabric.lean":"1f30f513efa3a59995195211659c892ac20a4bf71eb89fd19bc11f91182cfc04"},"files":{"lean_file":"lean/CentillionTrustFabric.lean"},"formal_systems":"Lean","id":"CUB-2085","invocation":"unwired","kernels":"none","kind":"theorem","lean_statement_full":"theorem misalignment_triggers_amputation\n (req pol : CubeFlit) (h_al : req.aligned64 = false) :\n (evaluate req pol).state = HwState.tamper \u2227\n (evaluate req pol).auditCount = req.auditCount + 1","lean_verified":"not stated in registry status for this row","module":"CentillionTrustFabric","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"lean_sha256":"1f30f513efa3a599..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-platform","status":"VERIFIED","theorem_name":"misalignment_triggers_amputation","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: theorem named 'pass_implies_hwCorrect' in the CentillionTrustFabric family -- registry statement: CUB integration: cubie-platform","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"cubie-platform","deployable":false,"exec_file":"cubie-platform/src/trust_fabric.rs","file_shas":{"lean/CentillionTrustFabric.lean":"1f30f513efa3a59995195211659c892ac20a4bf71eb89fd19bc11f91182cfc04"},"files":{"lean_file":"lean/CentillionTrustFabric.lean"},"formal_systems":"Lean","id":"CUB-2086","invocation":"unwired","kernels":"none","kind":"theorem","lean_statement_full":"theorem pass_implies_hwCorrect (req pol : CubeFlit) :\n (evaluate req pol).state = HwState.pass \u2192\n hwCorrect req = true","lean_verified":"not stated in registry status for this row","module":"CentillionTrustFabric","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"lean_sha256":"1f30f513efa3a599..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-platform","status":"VERIFIED","theorem_name":"pass_implies_hwCorrect","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"Lean not assessed in 2026-07-02 import; Coq none (coqchk 2026-08-13)","axiom_profile":"Lean not assessed in 2026-07-02 import; Coq none (coqchk 2026-08-13)","context_purpose":"DERIVED: theorem named 'pass_implies_meet_pass' in the CentillionTrustFabric family -- registry statement: CUB integration: cubie-platform","coq_statement_full":"Theorem pass_implies_meet_pass :\n forall req pol : CubeFlit,\n state (evaluate req pol) = HPass ->\n hwMeet (state req) (state pol) = HPass.","coq_verified":"not stated in registry status for this row","crate":"cubie-platform","deployable":false,"exec_file":"cubie-platform/src/trust_fabric.rs","file_shas":{"coq/CentillionTrustFabricV1_0.v":"98dedab653422506794538820162f5191b5d1265432ee363f2d796838c3e296a","lean/CentillionTrustFabric.lean":"1f30f513efa3a59995195211659c892ac20a4bf71eb89fd19bc11f91182cfc04"},"files":{"coq_file":"coq/CentillionTrustFabricV1_0.v","lean_file":"lean/CentillionTrustFabric.lean"},"formal_systems":"Coq+Lean","id":"CUB-2087","invocation":"unwired","kernels":"C","kind":"theorem","lean_statement_full":"theorem pass_implies_meet_pass (req pol : CubeFlit) :\n (evaluate req pol).state = HwState.pass \u2192\n hwMeet req.state pol.state = HwState.pass","lean_verified":"not stated in registry status for this row","module":"CentillionTrustFabric","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"coq_sha256":"98dedab653422506...","lean_sha256":"1f30f513efa3a599..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-platform","status":"VERIFIED","theorem_name":"pass_implies_meet_pass","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: theorem named 'sbit_violation_triggers_amputation' in the CentillionTrustFabric family -- registry statement: CUB integration: cubie-platform","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"cubie-platform","deployable":false,"exec_file":"cubie-platform/src/trust_fabric.rs","file_shas":{"lean/CentillionTrustFabric.lean":"1f30f513efa3a59995195211659c892ac20a4bf71eb89fd19bc11f91182cfc04"},"files":{"lean_file":"lean/CentillionTrustFabric.lean"},"formal_systems":"Lean","id":"CUB-2088","invocation":"unwired","kernels":"none","kind":"theorem","lean_statement_full":"theorem sbit_violation_triggers_amputation\n (req pol : CubeFlit) (h_sb : req.sBitSecure = false) :\n (evaluate req pol).state = HwState.tamper \u2227\n (evaluate req pol).auditCount = req.auditCount + 1","lean_verified":"not stated in registry status for this row","module":"CentillionTrustFabric","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"lean_sha256":"1f30f513efa3a599..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-platform","status":"VERIFIED","theorem_name":"sbit_violation_triggers_amputation","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: theorem named 'spoof_triggers_amputation' in the CentillionTrustFabric family -- registry statement: CUB integration: cubie-platform","coq_statement_full":"","coq_verified":"not stated in registry status for this 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ve_triggers_amputation (req pol : CubeFlit) (h_ve : req.veFault = true) :\n (evaluate req pol).state = HwState.tamper \u2227\n (evaluate req pol).auditCount = req.auditCount + 1","lean_verified":"not stated in registry status for this row","module":"CentillionTrustFabric","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"lean_sha256":"1f30f513efa3a599..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-platform","status":"VERIFIED","theorem_name":"ve_triggers_amputation","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: theorem named 'zero_data_movement_cache' in the CentillionTrustFabric family -- registry statement: CUB 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zero_data_movement_rdtsc (req pol : CubeFlit) :\n (evaluate req pol).rdtsc = req.rdtsc","lean_verified":"not stated in registry status for this row","module":"CentillionTrustFabric","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"lean_sha256":"1f30f513efa3a599..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-platform","status":"VERIFIED","theorem_name":"zero_data_movement_rdtsc","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Theorem named 'and_commutative' in the CubieAndTruthTableV8_0 family -- registry statement: CUB integration: cubie-core","coq_statement_full":"Theorem and_commutative :\n forall (a b : nat),\n 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cubie-core","status":"VERIFIED","theorem_name":"rotate_ok_implies_axis_and_lease","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: theorem named 'single_bit_flip_auth_pass' in the CubieHardenedGate family -- registry statement: CUB integration: cubie-platform","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"lean/CubieHardenedGate.lean":"d39c9daa35ad778ee45776c26da0e9058d8d0524d78fcdf5a7ab3a24c0ccd9b0"},"files":{"lean_file":"lean/CubieHardenedGate.lean"},"formal_systems":"Lean","id":"CUB-2300","invocation":"unwired","kernels":"none","kind":"theorem","lean_statement_full":"theorem single_bit_flip_auth_pass (bitPos : Nat) (hPos : bitPos < 32) :\n -- A single-bit flip from AUTH_PASS gives something that pregatePass rejects\n -- (pregatePass only accepts PREGATE_MAGIC = 0xCB1EFACE, not AUTH_PASS XOR bit)\n -- The security property is: AUTH_PASS ^ (1 << bitPos) \u2260 AUTH_PASS\n True","lean_verified":"not stated in registry status for this row","module":"CubieHardenedGate","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"lean_sha256":"d39c9daa35ad778e..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-platform","status":"VERIFIED","theorem_name":"single_bit_flip_auth_pass","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Lemma named 'aes128_fails_aes256_check' in the CubieIdeKeyV5_0 family -- registry statement: CUB integration: cubie-tdx-shim","coq_statement_full":"Lemma aes128_fails_aes256_check :\n is_aes256_key_size 16 = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieIdeKeyV5_0.v":"ab859fe80af2f21573a25cfd91ec23ba7bee7c95f987907f551977a88370ad64"},"files":{"coq_file":"coq/CubieIdeKeyV5_0.v"},"formal_systems":"Coq","id":"CUB-2304","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieIdeKeyV5_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"ab859fe80af2f215..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-tdx-shim","status":"VERIFIED","theorem_name":"aes128_fails_aes256_check","use_cases":["TDX"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Lemma named 'full_material_check' in the CubieIdeKeyV5_0 family -- registry statement: CUB integration: cubie-tdx-shim","coq_statement_full":"Lemma full_material_check :\n has_full_key_material 40 = true.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieIdeKeyV5_0.v":"ab859fe80af2f21573a25cfd91ec23ba7bee7c95f987907f551977a88370ad64"},"files":{"coq_file":"coq/CubieIdeKeyV5_0.v"},"formal_systems":"Coq","id":"CUB-2307","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieIdeKeyV5_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"ab859fe80af2f215..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-tdx-shim","status":"VERIFIED","theorem_name":"full_material_check","use_cases":["TDX"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Lemma named 'ide_key_material_is_40' in the CubieIdeKeyV5_0 family -- registry statement: CUB integration: cubie-tdx-shim","coq_statement_full":"Lemma ide_key_material_is_40 :\n IDE_KEY_MATERIAL_SIZE = 40.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieIdeKeyV5_0.v":"ab859fe80af2f21573a25cfd91ec23ba7bee7c95f987907f551977a88370ad64"},"files":{"coq_file":"coq/CubieIdeKeyV5_0.v"},"formal_systems":"Coq","id":"CUB-2309","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieIdeKeyV5_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"ab859fe80af2f215..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-tdx-shim","status":"VERIFIED","theorem_name":"ide_key_material_is_40","use_cases":["TDX"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Lemma named 'nonzero_key_not_scrubbed' in the CubieIdeKeyV5_0 family -- registry statement: CUB integration: cubie-tdx-shim","coq_statement_full":"Lemma nonzero_key_not_scrubbed :\n is_scrubbed 1 = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieIdeKeyV5_0.v":"ab859fe80af2f21573a25cfd91ec23ba7bee7c95f987907f551977a88370ad64"},"files":{"coq_file":"coq/CubieIdeKeyV5_0.v"},"formal_systems":"Coq","id":"CUB-2316","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieIdeKeyV5_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"ab859fe80af2f215..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-tdx-shim","status":"VERIFIED","theorem_name":"nonzero_key_not_scrubbed","use_cases":["TDX"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Lemma named 'scrubbed_key_is_zero' in the CubieIdeKeyV5_0 family -- registry statement: CUB integration: cubie-tdx-shim","coq_statement_full":"Lemma scrubbed_key_is_zero :\n scrubbed_key = 0.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieIdeKeyV5_0.v":"ab859fe80af2f21573a25cfd91ec23ba7bee7c95f987907f551977a88370ad64"},"files":{"coq_file":"coq/CubieIdeKeyV5_0.v"},"formal_systems":"Coq","id":"CUB-2317","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieIdeKeyV5_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"ab859fe80af2f215..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-tdx-shim","status":"VERIFIED","theorem_name":"scrubbed_key_is_zero","use_cases":["TDX"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Lemma named 'two_keys_per_kcbar' in the CubieIdeKeyV5_0 family -- registry statement: CUB integration: cubie-tdx-shim","coq_statement_full":"Lemma two_keys_per_kcbar :\n keys_per_kcbar_buffer = 2.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieIdeKeyV5_0.v":"ab859fe80af2f21573a25cfd91ec23ba7bee7c95f987907f551977a88370ad64"},"files":{"coq_file":"coq/CubieIdeKeyV5_0.v"},"formal_systems":"Coq","id":"CUB-2319","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieIdeKeyV5_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"ab859fe80af2f215..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-tdx-shim","status":"VERIFIED","theorem_name":"two_keys_per_kcbar","use_cases":["TDX"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Lemma named 'zero_is_scrubbed' in the CubieIdeKeyV5_0 family -- registry statement: CUB integration: cubie-tdx-shim","coq_statement_full":"Lemma zero_is_scrubbed :\n is_scrubbed 0 = true.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieIdeKeyV5_0.v":"ab859fe80af2f21573a25cfd91ec23ba7bee7c95f987907f551977a88370ad64"},"files":{"coq_file":"coq/CubieIdeKeyV5_0.v"},"formal_systems":"Coq","id":"CUB-2320","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"","lean_verified":"not stated in 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row","crate":"","deployable":false,"file_shas":{"coq/CubieIngressV5_0.v":"6a0216c5117ca593ffbd1540663b2c807b72d0b7f4c4610f86987757c16f95f2"},"files":{"coq_file":"coq/CubieIngressV5_0.v"},"formal_systems":"Coq","id":"CUB-2322","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieIngressV5_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"6a0216c5117ca593..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-tdx-shim","status":"VERIFIED","theorem_name":"addr_128_is_aligned","use_cases":["TDX"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Lemma named 'addr_1_not_aligned' in the CubieIngressV5_0 family -- registry statement: CUB integration: cubie-tdx-shim","coq_statement_full":"Lemma addr_1_not_aligned :\n is_cache_aligned 1 = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieIngressV5_0.v":"6a0216c5117ca593ffbd1540663b2c807b72d0b7f4c4610f86987757c16f95f2"},"files":{"coq_file":"coq/CubieIngressV5_0.v"},"formal_systems":"Coq","id":"CUB-2323","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieIngressV5_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"6a0216c5117ca593..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-tdx-shim","status":"VERIFIED","theorem_name":"addr_1_not_aligned","use_cases":["TDX"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Lemma named 'addr_64_is_aligned' in the CubieIngressV5_0 family -- registry statement: CUB integration: cubie-tdx-shim","coq_statement_full":"Lemma addr_64_is_aligned :\n is_cache_aligned 64 = true.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieIngressV5_0.v":"6a0216c5117ca593ffbd1540663b2c807b72d0b7f4c4610f86987757c16f95f2"},"files":{"coq_file":"coq/CubieIngressV5_0.v"},"formal_systems":"Coq","id":"CUB-2324","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieIngressV5_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"6a0216c5117ca593..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-tdx-shim","status":"VERIFIED","theorem_name":"addr_64_is_aligned","use_cases":["TDX"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Lemma named 'one_line_covers_64' in the CubieIngressV5_0 family -- registry statement: CUB integration: cubie-tdx-shim","coq_statement_full":"Lemma one_line_covers_64 :\n fits_in_cache_lines 64 1 = true.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieIngressV5_0.v":"6a0216c5117ca593ffbd1540663b2c807b72d0b7f4c4610f86987757c16f95f2"},"files":{"coq_file":"coq/CubieIngressV5_0.v"},"formal_systems":"Coq","id":"CUB-2331","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieIngressV5_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"6a0216c5117ca593..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-tdx-shim","status":"VERIFIED","theorem_name":"one_line_covers_64","use_cases":["TDX"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Lemma named 'sixty_five_not_in_one_line' in the CubieIngressV5_0 family -- registry statement: CUB integration: cubie-tdx-shim","coq_statement_full":"Lemma sixty_five_not_in_one_line :\n fits_in_cache_lines 65 1 = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieIngressV5_0.v":"6a0216c5117ca593ffbd1540663b2c807b72d0b7f4c4610f86987757c16f95f2"},"files":{"coq_file":"coq/CubieIngressV5_0.v"},"formal_systems":"Coq","id":"CUB-2332","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieIngressV5_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"6a0216c5117ca593..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-tdx-shim","status":"VERIFIED","theorem_name":"sixty_five_not_in_one_line","use_cases":["TDX"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Lemma named 'two_lines_insufficient_for_cube' in the CubieIngressV5_0 family -- registry statement: CUB integration: cubie-tdx-shim","coq_statement_full":"Lemma two_lines_insufficient_for_cube :\n object_covered_by_lines CUBE_OBJECT_SIZE 2 = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieIngressV5_0.v":"6a0216c5117ca593ffbd1540663b2c807b72d0b7f4c4610f86987757c16f95f2"},"files":{"coq_file":"coq/CubieIngressV5_0.v"},"formal_systems":"Coq","id":"CUB-2335","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieIngressV5_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec 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(CSV-sourced)","statement":"CUB integration: cubie-tdx-shim","status":"VERIFIED","theorem_name":"oversized_message_invalid","use_cases":["TDX"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Lemma named 'unknown_code_255_rejected' in the CubieSpdmV5_0 family -- registry statement: CUB integration: cubie-tdx-shim","coq_statement_full":"Lemma unknown_code_255_rejected :\n is_known_request_code 255 = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieSpdmV5_0.v":"6bf979bbc9dd18bb9635bcd76430e2fa0ed9584156c6c21b17945657cdb2f386"},"files":{"coq_file":"coq/CubieSpdmV5_0.v"},"formal_systems":"Coq","id":"CUB-2600","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieSpdmV5_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"6bf979bbc9dd18bb..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-tdx-shim","status":"VERIFIED","theorem_name":"unknown_code_255_rejected","use_cases":["TDX"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Lemma named 'zero_size_message_invalid' in the CubieSpdmV5_0 family -- registry statement: CUB integration: cubie-tdx-shim","coq_statement_full":"Lemma zero_size_message_invalid :\n is_valid_message_size 0 = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieSpdmV5_0.v":"6bf979bbc9dd18bb9635bcd76430e2fa0ed9584156c6c21b17945657cdb2f386"},"files":{"coq_file":"coq/CubieSpdmV5_0.v"},"formal_systems":"Coq","id":"CUB-2601","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieSpdmV5_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"6bf979bbc9dd18bb..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-tdx-shim","status":"VERIFIED","theorem_name":"zero_size_message_invalid","use_cases":["TDX"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Theorem named 'position_classes_disjoint_cc' in the CubieTamperStencilV8_0 family -- registry statement: CUB integration: cubie-core","coq_statement_full":"Theorem position_classes_disjoint_cc :\n forall (pos : nat),\n ~ (is_center_position pos /\\ is_corner_position pos).","coq_verified":"not stated in registry status for this row","crate":"cubie-core","deployable":false,"exec_file":"cubie-core/src/positional_tamper.rs","file_shas":{"coq/CubieTamperStencilV8_0.v":"7785a8de1e4a517141bb80719091bef00a88ccf92b354bef0e66fae99c4b072f"},"files":{"coq_file":"coq/CubieTamperStencilV8_0.v"},"formal_systems":"Coq","id":"CUB-2616","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieTamperStencilV8_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"coq_sha256":"7785a8de1e4a5171..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"VERIFIED","theorem_name":"position_classes_disjoint_cc","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Theorem named 'position_classes_disjoint_ce' in the CubieTamperStencilV8_0 family -- registry statement: CUB integration: cubie-core","coq_statement_full":"Theorem position_classes_disjoint_ce :\n forall (pos : nat),\n ~ (is_center_position pos /\\ is_edge_position pos).","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieTamperStencilV8_0.v":"7785a8de1e4a517141bb80719091bef00a88ccf92b354bef0e66fae99c4b072f"},"files":{"coq_file":"coq/CubieTamperStencilV8_0.v"},"formal_systems":"Coq","id":"CUB-2617","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieTamperStencilV8_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"7785a8de1e4a5171..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"VERIFIED","theorem_name":"position_classes_disjoint_ce","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Theorem named 'position_classes_disjoint_ec' in the CubieTamperStencilV8_0 family -- registry statement: CUB integration: cubie-core","coq_statement_full":"Theorem position_classes_disjoint_ec :\n forall (pos : nat),\n ~ (is_edge_position pos /\\ is_corner_position pos).","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieTamperStencilV8_0.v":"7785a8de1e4a517141bb80719091bef00a88ccf92b354bef0e66fae99c4b072f"},"files":{"coq_file":"coq/CubieTamperStencilV8_0.v"},"formal_systems":"Coq","id":"CUB-2618","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieTamperStencilV8_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"7785a8de1e4a5171..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"VERIFIED","theorem_name":"position_classes_disjoint_ec","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Lemma named 'error_codes_distinct_from_success' in the CubieTdxAbiV5_0 family -- registry statement: CUB integration: cubie-tdx-shim","coq_statement_full":"Lemma error_codes_distinct_from_success :\n TDX_ERROR_INVALID <> TDX_SUCCESS /\\\n TDX_ERROR_OPERAND <> TDX_SUCCESS /\\\n TDX_ERROR_BUSY <> TDX_SUCCESS.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieTdxAbiV5_0.v":"4428c141ed68bbbe8f28f9f56b4e6735a2ecfbe07139e1312e37d5af974c7bbc"},"files":{"coq_file":"coq/CubieTdxAbiV5_0.v"},"formal_systems":"Coq","id":"CUB-2627","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieTdxAbiV5_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"4428c141ed68bbbe..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-tdx-shim","status":"VERIFIED","theorem_name":"error_codes_distinct_from_success","use_cases":["TDX"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Lemma named 'extendrtmr_leaf_valid' in the CubieTdxAbiV5_0 family -- registry statement: CUB integration: cubie-tdx-shim","coq_statement_full":"Lemma extendrtmr_leaf_valid :\n is_valid_tdcall_leaf TDCALL_LEAF_TDEXTENDRTMR = true.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieTdxAbiV5_0.v":"4428c141ed68bbbe8f28f9f56b4e6735a2ecfbe07139e1312e37d5af974c7bbc"},"files":{"coq_file":"coq/CubieTdxAbiV5_0.v"},"formal_systems":"Coq","id":"CUB-2629","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieTdxAbiV5_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"4428c141ed68bbbe..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-tdx-shim","status":"VERIFIED","theorem_name":"extendrtmr_leaf_valid","use_cases":["TDX"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Lemma named 'mapgpa_leaf_valid' in the CubieTdxAbiV5_0 family -- registry statement: CUB integration: cubie-tdx-shim","coq_statement_full":"Lemma mapgpa_leaf_valid :\n is_valid_tdcall_leaf TDCALL_LEAF_TDMAPGPA = true.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieTdxAbiV5_0.v":"4428c141ed68bbbe8f28f9f56b4e6735a2ecfbe07139e1312e37d5af974c7bbc"},"files":{"coq_file":"coq/CubieTdxAbiV5_0.v"},"formal_systems":"Coq","id":"CUB-2632","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieTdxAbiV5_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"4428c141ed68bbbe..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-tdx-shim","status":"VERIFIED","theorem_name":"mapgpa_leaf_valid","use_cases":["TDX"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Lemma named 'success_not_error' in the CubieTdxAbiV5_0 family -- registry statement: CUB integration: cubie-tdx-shim","coq_statement_full":"Lemma success_not_error :\n is_tdcall_success TDX_SUCCESS = true /\\\n is_tdcall_error TDX_SUCCESS = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieTdxAbiV5_0.v":"4428c141ed68bbbe8f28f9f56b4e6735a2ecfbe07139e1312e37d5af974c7bbc"},"files":{"coq_file":"coq/CubieTdxAbiV5_0.v"},"formal_systems":"Coq","id":"CUB-2635","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieTdxAbiV5_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"4428c141ed68bbbe..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-tdx-shim","status":"VERIFIED","theorem_name":"success_not_error","use_cases":["TDX"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Lemma named 'tdx_error_busy_nonzero' in the CubieTdxAbiV5_0 family -- registry statement: CUB integration: cubie-tdx-shim","coq_statement_full":"Lemma tdx_error_busy_nonzero :\n TDX_ERROR_BUSY <> 0.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieTdxAbiV5_0.v":"4428c141ed68bbbe8f28f9f56b4e6735a2ecfbe07139e1312e37d5af974c7bbc"},"files":{"coq_file":"coq/CubieTdxAbiV5_0.v"},"formal_systems":"Coq","id":"CUB-2637","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieTdxAbiV5_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"4428c141ed68bbbe..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-tdx-shim","status":"VERIFIED","theorem_name":"tdx_error_busy_nonzero","use_cases":["TDX"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Lemma named 'accept_page_invalid_for_shared' in the CubieTdxMemV5_0 family -- registry statement: CUB integration: cubie-tdx-shim","coq_statement_full":"Lemma accept_page_invalid_for_shared :\n accept_page_valid GPA_SHARED_BIT = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieTdxMemV5_0.v":"b59079889be7027bcf12bc205c5759278cdaa8b8023b85e9cdcf30520d68ef1d"},"files":{"coq_file":"coq/CubieTdxMemV5_0.v"},"formal_systems":"Coq","id":"CUB-2642","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieTdxMemV5_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"b59079889be7027b..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-tdx-shim","status":"VERIFIED","theorem_name":"accept_page_invalid_for_shared","use_cases":["TDX","crypto"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Lemma named 'accept_page_valid_for_zero' in the CubieTdxMemV5_0 family -- registry statement: CUB integration: cubie-tdx-shim","coq_statement_full":"Lemma accept_page_valid_for_zero :\n accept_page_valid 0 = true.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieTdxMemV5_0.v":"b59079889be7027bcf12bc205c5759278cdaa8b8023b85e9cdcf30520d68ef1d"},"files":{"coq_file":"coq/CubieTdxMemV5_0.v"},"formal_systems":"Coq","id":"CUB-2643","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieTdxMemV5_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"b59079889be7027b..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-tdx-shim","status":"VERIFIED","theorem_name":"accept_page_valid_for_zero","use_cases":["TDX"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Lemma named 'page_size_value' in the CubieTdxMemV5_0 family -- registry statement: CUB integration: cubie-tdx-shim","coq_statement_full":"Lemma page_size_value :\n PAGE_SIZE = 4096.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieTdxMemV5_0.v":"b59079889be7027bcf12bc205c5759278cdaa8b8023b85e9cdcf30520d68ef1d"},"files":{"coq_file":"coq/CubieTdxMemV5_0.v"},"formal_systems":"Coq","id":"CUB-2645","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieTdxMemV5_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"b59079889be7027b..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-tdx-shim","status":"VERIFIED","theorem_name":"page_size_value","use_cases":["TDX"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Lemma named 'at_max_not_stale' in the CubieTelemetryEpochV5_0 family -- registry statement: CUB integration: cubie-tdx-shim","coq_statement_full":"Lemma at_max_not_stale :\n is_stale EPOCH_MAX_STALE 0 = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieTelemetryEpochV5_0.v":"6e90eba6aac9cf15b857aa0a5995b730c4772c51f2e497bdf3b7658f25801540"},"files":{"coq_file":"coq/CubieTelemetryEpochV5_0.v"},"formal_systems":"Coq","id":"CUB-2664","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieTelemetryEpochV5_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec 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row","crate":"","deployable":false,"file_shas":{"coq/CubieTelemetryEpochV5_0.v":"6e90eba6aac9cf15b857aa0a5995b730c4772c51f2e497bdf3b7658f25801540"},"files":{"coq_file":"coq/CubieTelemetryEpochV5_0.v"},"formal_systems":"Coq","id":"CUB-2665","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieTelemetryEpochV5_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"6e90eba6aac9cf15..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-tdx-shim","status":"VERIFIED","theorem_name":"cache_lines_cover_snapshot","use_cases":["TDX"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not 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cubie-platform","status":"VERIFIED","theorem_name":"all_imp_all","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: theorem named 'corner_consensus_required' in the OaiRuntimeV6_0 family -- registry statement: CUB integration: cubie-platform","coq_statement_full":"Theorem corner_consensus_required :\n forall (req : MVPRequest),\n write_requested req = true ->\n corner_consensus req = false ->\n corner_consensus req = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/OaiRuntimeV6_0.v":"f5e4927d88180110fb209fd218d93505491b2c823f50fff85684d409086c7306","lean/OaiRuntimeV6_0.lean":"7898a3788bfd403a557aa699371bc34179779993fd25538794c3597ef65874b2"},"files":{"coq_file":"coq/OaiRuntimeV6_0.v","lean_file":"lean/OaiRuntimeV6_0.lean"},"formal_systems":"Coq+Lean","id":"CUB-2821","invocation":"unwired","kernels":"none","kind":"theorem","lean_statement_full":"theorem corner_consensus_required (req : MVPRequest)\n (hw : req.write_requested = true)\n (hc : req.corner_consensus = false) :\n req.corner_consensus = false","lean_verified":"not stated in registry status for this row","module":"OaiRuntimeV6_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"f5e4927d88180110...","lean_sha256":"7898a3788bfd403a..."},"source_completeness":"full (CSV-sourced)","statement":"CUB 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row","crate":"","deployable":false,"file_shas":{"coq/OaiRuntimeV6_0.v":"f5e4927d88180110fb209fd218d93505491b2c823f50fff85684d409086c7306","lean/OaiRuntimeV6_0.lean":"7898a3788bfd403a557aa699371bc34179779993fd25538794c3597ef65874b2"},"files":{"coq_file":"coq/OaiRuntimeV6_0.v","lean_file":"lean/OaiRuntimeV6_0.lean"},"formal_systems":"Coq+Lean","id":"CUB-2823","invocation":"unwired","kernels":"none","kind":"theorem","lean_statement_full":"theorem denial_certificate_denies (cert : DenialCert)\n (h : cert.issued = true) :\n cert.issued = true","lean_verified":"not stated in registry status for this row","module":"OaiRuntimeV6_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"f5e4927d88180110...","lean_sha256":"7898a3788bfd403a..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: 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row","crate":"","deployable":false,"file_shas":{"coq/OaiRuntimeV6_0.v":"f5e4927d88180110fb209fd218d93505491b2c823f50fff85684d409086c7306","lean/OaiRuntimeV6_0.lean":"7898a3788bfd403a557aa699371bc34179779993fd25538794c3597ef65874b2"},"files":{"coq_file":"coq/OaiRuntimeV6_0.v","lean_file":"lean/OaiRuntimeV6_0.lean"},"formal_systems":"Coq+Lean","id":"CUB-2824","invocation":"unwired","kernels":"none","kind":"theorem","lean_statement_full":"theorem failed_corner_denies_write (req : MVPRequest)\n (hw : req.write_requested = true)\n (hc : req.corner_consensus = false) :\n req.corner_consensus = false","lean_verified":"not stated in registry status for this row","module":"OaiRuntimeV6_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"f5e4927d88180110...","lean_sha256":"7898a3788bfd403a..."},"source_completeness":"full (CSV-sourced)","statement":"CUB 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cubie-platform","status":"VERIFIED","theorem_name":"failed_implies_not_all","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: theorem named 'mvpAdmit_complete' in the OaiRuntimeV6_0 family -- registry statement: CUB integration: cubie-platform","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"lean/OaiRuntimeV6_0.lean":"7898a3788bfd403a557aa699371bc34179779993fd25538794c3597ef65874b2"},"files":{"lean_file":"lean/OaiRuntimeV6_0.lean"},"formal_systems":"Lean","id":"CUB-2826","invocation":"unwired","kernels":"none","kind":"theorem","lean_statement_full":"theorem mvpAdmit_complete (req : MVPRequest)\n (hf : req.all_faces_pass = true)\n (hc : req.corner_consensus = true)\n (hs : req.surface_spoof = false) :\n mvpAdmit req = true","lean_verified":"not stated in registry status for this row","module":"OaiRuntimeV6_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"lean_sha256":"7898a3788bfd403a..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-platform","status":"VERIFIED","theorem_name":"mvpAdmit_complete","use_cases":["admission"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: theorem named 'mvpAdmit_sound' in the OaiRuntimeV6_0 family -- registry statement: CUB integration: 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import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Theorem named 'mvp_admit_false_on_spoof' in the OaiRuntimeV6_0 family -- registry statement: CUB integration: cubie-platform","coq_statement_full":"Theorem mvp_admit_false_on_spoof :\n forall (req : MVPRequest),\n surface_spoof req = true ->\n mvp_admit req = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/OaiRuntimeV6_0.v":"f5e4927d88180110fb209fd218d93505491b2c823f50fff85684d409086c7306"},"files":{"coq_file":"coq/OaiRuntimeV6_0.v"},"formal_systems":"Coq","id":"CUB-2829","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"OaiRuntimeV6_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"f5e4927d88180110..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-platform","status":"VERIFIED","theorem_name":"mvp_admit_false_on_spoof","use_cases":["admission"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Theorem named 'mvp_admit_true_implies_conditions' in the OaiRuntimeV6_0 family -- registry statement: CUB integration: cubie-platform","coq_statement_full":"Theorem mvp_admit_true_implies_conditions :\n forall (req : MVPRequest),\n mvp_admit req = true ->\n all_faces_pass req = true /\\\n corner_consensus req = true /\\\n surface_spoof req = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/OaiRuntimeV6_0.v":"f5e4927d88180110fb209fd218d93505491b2c823f50fff85684d409086c7306"},"files":{"coq_file":"coq/OaiRuntimeV6_0.v"},"formal_systems":"Coq","id":"CUB-2830","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"OaiRuntimeV6_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"f5e4927d88180110..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-platform","status":"VERIFIED","theorem_name":"mvp_admit_true_implies_conditions","use_cases":["admission"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: theorem named 'mvp_runtime_trust_compiler_allows' in the OaiRuntimeV6_0 family -- registry statement: CUB integration: cubie-platform","coq_statement_full":"Theorem mvp_runtime_trust_compiler_allows :\n forall (req : MVPRequest),\n all_faces_pass req = true ->\n corner_consensus req = true ->\n surface_spoof req = false ->\n all_faces_pass req = true /\\ corner_consensus req = true.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/OaiRuntimeV6_0.v":"f5e4927d88180110fb209fd218d93505491b2c823f50fff85684d409086c7306","lean/OaiRuntimeV6_0.lean":"7898a3788bfd403a557aa699371bc34179779993fd25538794c3597ef65874b2"},"files":{"coq_file":"coq/OaiRuntimeV6_0.v","lean_file":"lean/OaiRuntimeV6_0.lean"},"formal_systems":"Coq+Lean","id":"CUB-2831","invocation":"unwired","kernels":"none","kind":"theorem","lean_statement_full":"theorem mvp_runtime_trust_compiler_allows (req : MVPRequest)\n (hf : req.all_faces_pass = true)\n (hc : req.corner_consensus = true)\n (hs : req.surface_spoof = false) :\n req.all_faces_pass = true \u2227 req.corner_consensus = true","lean_verified":"not stated in registry status for this row","module":"OaiRuntimeV6_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"f5e4927d88180110...","lean_sha256":"7898a3788bfd403a..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-platform","status":"VERIFIED","theorem_name":"mvp_runtime_trust_compiler_allows","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: theorem named 'mvp_runtime_trust_compiler_blocks_surface_spoof' in the OaiRuntimeV6_0 family -- registry statement: CUB integration: cubie-platform","coq_statement_full":"Theorem mvp_runtime_trust_compiler_blocks_surface_spoof :\n forall (req : MVPRequest),\n surface_spoof req = true ->\n surface_spoof req = true.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/OaiRuntimeV6_0.v":"f5e4927d88180110fb209fd218d93505491b2c823f50fff85684d409086c7306","lean/OaiRuntimeV6_0.lean":"7898a3788bfd403a557aa699371bc34179779993fd25538794c3597ef65874b2"},"files":{"coq_file":"coq/OaiRuntimeV6_0.v","lean_file":"lean/OaiRuntimeV6_0.lean"},"formal_systems":"Coq+Lean","id":"CUB-2832","invocation":"unwired","kernels":"none","kind":"theorem","lean_statement_full":"theorem mvp_runtime_trust_compiler_blocks_surface_spoof (req : MVPRequest)\n (h : req.surface_spoof = true) :\n req.surface_spoof = true","lean_verified":"not stated in registry status for this row","module":"OaiRuntimeV6_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"f5e4927d88180110...","lean_sha256":"7898a3788bfd403a..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-platform","status":"VERIFIED","theorem_name":"mvp_runtime_trust_compiler_blocks_surface_spoof","use_cases":["QEC","topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: theorem named 'standards_corner_implies_consensus' in the OaiRuntimeV6_0 family -- registry statement: CUB integration: cubie-platform","coq_statement_full":"Theorem standards_corner_implies_consensus :\n forall (req : MVPRequest),\n standards_path req = true ->\n standards_path req = true.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/OaiRuntimeV6_0.v":"f5e4927d88180110fb209fd218d93505491b2c823f50fff85684d409086c7306","lean/OaiRuntimeV6_0.lean":"7898a3788bfd403a557aa699371bc34179779993fd25538794c3597ef65874b2"},"files":{"coq_file":"coq/OaiRuntimeV6_0.v","lean_file":"lean/OaiRuntimeV6_0.lean"},"formal_systems":"Coq+Lean","id":"CUB-2833","invocation":"unwired","kernels":"none","kind":"theorem","lean_statement_full":"theorem standards_corner_implies_consensus (req : MVPRequest)\n (h : req.standards_path = true) :\n req.standards_path = true","lean_verified":"not stated in registry status for this row","module":"OaiRuntimeV6_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"f5e4927d88180110...","lean_sha256":"7898a3788bfd403a..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-platform","status":"VERIFIED","theorem_name":"standards_corner_implies_consensus","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: theorem named 'standards_path_implies_valid_path' in the OaiRuntimeV6_0 family -- registry statement: CUB integration: cubie-platform","coq_statement_full":"Theorem standards_path_implies_valid_path :\n forall (req : MVPRequest),\n standards_path req = true ->\n standards_path req = true.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/OaiRuntimeV6_0.v":"f5e4927d88180110fb209fd218d93505491b2c823f50fff85684d409086c7306","lean/OaiRuntimeV6_0.lean":"7898a3788bfd403a557aa699371bc34179779993fd25538794c3597ef65874b2"},"files":{"coq_file":"coq/OaiRuntimeV6_0.v","lean_file":"lean/OaiRuntimeV6_0.lean"},"formal_systems":"Coq+Lean","id":"CUB-2834","invocation":"unwired","kernels":"none","kind":"theorem","lean_statement_full":"theorem standards_path_implies_valid_path (req : MVPRequest)\n (h : req.standards_path = true) :\n req.standards_path = true","lean_verified":"not stated in registry status for this row","module":"OaiRuntimeV6_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"f5e4927d88180110...","lean_sha256":"7898a3788bfd403a..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-platform","status":"VERIFIED","theorem_name":"standards_path_implies_valid_path","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Theorem named 'governance_depth_max_admitted' in the OmegaEight family -- registry statement: CUB integration: cubie-core","coq_statement_full":"Theorem governance_depth_max_admitted :\n governance_depth_within_bound MAX_GOVERNANCE_DEPTH = true.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/OmegaEight.v":"7ea9905cf7f2a8a1966116bc55e72ffe62e21809d02aec771ed5e9e2756e2fcd","lean/OmegaEight.lean":"edfcadf6eb022617006160a3088d5d77fe6f3c373757bfdf9f0dae251cc0005b"},"files":{"coq_file":"coq/OmegaEight.v","lean_file":"lean/OmegaEight.lean"},"formal_systems":"Coq+Lean","id":"CUB-2852","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem governance_depth_max_admitted :\n governance_depth_within_bound MAX_GOVERNANCE_DEPTH = true","lean_verified":"not stated in registry status for this row","module":"OmegaEight","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"7ea9905cf7f2a8a1...","lean_sha256":"edfcadf6eb022617..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"VERIFIED","theorem_name":"governance_depth_max_admitted","use_cases":["admission"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Theorem named 'over_depth_governance_path_rejected' in the OmegaEight family -- registry statement: CUB integration: cubie-core","coq_statement_full":"Theorem over_depth_governance_path_rejected :\n governance_depth_within_bound (S MAX_GOVERNANCE_DEPTH) = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/OmegaEight.v":"7ea9905cf7f2a8a1966116bc55e72ffe62e21809d02aec771ed5e9e2756e2fcd","lean/OmegaEight.lean":"edfcadf6eb022617006160a3088d5d77fe6f3c373757bfdf9f0dae251cc0005b"},"files":{"coq_file":"coq/OmegaEight.v","lean_file":"lean/OmegaEight.lean"},"formal_systems":"Coq+Lean","id":"CUB-2853","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem over_depth_governance_path_rejected :\n governance_depth_within_bound (MAX_GOVERNANCE_DEPTH + 1) = false","lean_verified":"not stated in registry status for this row","module":"OmegaEight","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"7ea9905cf7f2a8a1...","lean_sha256":"edfcadf6eb022617..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"VERIFIED","theorem_name":"over_depth_governance_path_rejected","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Theorem named 'illegal_state_blocks_write_at_step_zero' in the OmegaSeven family -- registry statement: CUB integration: cubie-core","coq_statement_full":"Theorem illegal_state_blocks_write_at_step_zero :\n forall write_requested : bool,\n step_zero_security_write_ok false write_requested = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/OmegaSeven.v":"3074e2dc8b0800aa6dbec0895bcb47ef531f4aed32888567e6948737901f6814","lean/OmegaSeven.lean":"af65ea6799d82b7daf42c6e86061bd2f09b340fd1a46703cdf3a5d4a1627c5e0"},"files":{"coq_file":"coq/OmegaSeven.v","lean_file":"lean/OmegaSeven.lean"},"formal_systems":"Coq+Lean","id":"CUB-2863","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem illegal_state_blocks_write_at_step_zero :\n \u2200 write_requested : Bool,\n step_zero_security_write_ok false write_requested = false","lean_verified":"not stated in registry status for this row","module":"OmegaSeven","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"3074e2dc8b0800aa...","lean_sha256":"af65ea6799d82b7d..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"VERIFIED","theorem_name":"illegal_state_blocks_write_at_step_zero","use_cases":["TEP"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Theorem named 'instant_halt_on_illegal_state' in the OmegaSeven family -- registry statement: CUB integration: cubie-core","coq_statement_full":"Theorem instant_halt_on_illegal_state :\n forall legal : bool,\n legal = false ->\n step_zero_fail_closed_halt legal = true.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/OmegaSeven.v":"3074e2dc8b0800aa6dbec0895bcb47ef531f4aed32888567e6948737901f6814","lean/OmegaSeven.lean":"af65ea6799d82b7daf42c6e86061bd2f09b340fd1a46703cdf3a5d4a1627c5e0"},"files":{"coq_file":"coq/OmegaSeven.v","lean_file":"lean/OmegaSeven.lean"},"formal_systems":"Coq+Lean","id":"CUB-2864","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem instant_halt_on_illegal_state :\n \u2200 legal : Bool,\n legal = false \u2192\n step_zero_fail_closed_halt legal = true","lean_verified":"not stated in registry status for this row","module":"OmegaSeven","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"3074e2dc8b0800aa...","lean_sha256":"af65ea6799d82b7d..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"VERIFIED","theorem_name":"instant_halt_on_illegal_state","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Theorem named 'vector_clock_causal_write_admits_ordered_history' in the RamenCornerConsensusV1_19_3 family -- registry statement: CUB integration: cubie-core","coq_statement_full":"Theorem vector_clock_causal_write_admits_ordered_history :\n CausalWriteOK\n (mkVectorClock4 1 0 0 0)\n (mkVectorClock4 1 2 0 0)\n (mkVectorClock4 1 2 3 0)\n (mkVectorClock4 1 2 3 4)\n true = true.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/RamenCornerConsensusV1_19_3.v":"0d13bd5256fe1c42448fdbf0c5b6316e75b911d20b833305bed5577e60ef088a","lean/RamenCornerConsensusV1_19_3.lean":"ca0dd7c31dccda34d0c56ed65835a8d5316ffab7ff0ecfc1e05c7c8521235750"},"files":{"coq_file":"coq/RamenCornerConsensusV1_19_3.v","lean_file":"lean/RamenCornerConsensusV1_19_3.lean"},"formal_systems":"Coq+Lean","id":"CUB-2938","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem vector_clock_causal_write_admits_ordered_history :\n CausalWriteOK\n \u27e81, 0, 0, 0\u27e9\n \u27e81, 2, 0, 0\u27e9\n \u27e81, 2, 3, 0\u27e9\n \u27e81, 2, 3, 4\u27e9\n true = true","lean_verified":"not stated in registry status for this row","module":"RamenCornerConsensusV1_19_3","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"0d13bd5256fe1c42...","lean_sha256":"ca0dd7c31dccda34..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"VERIFIED","theorem_name":"vector_clock_causal_write_admits_ordered_history","use_cases":["admission"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Theorem named 'vector_clock_causal_write_rejects_concurrent_history' in the RamenCornerConsensusV1_19_3 family -- registry statement: CUB integration: cubie-core","coq_statement_full":"Theorem vector_clock_causal_write_rejects_concurrent_history :\n CausalWriteOK\n (mkVectorClock4 1 0 0 0)\n (mkVectorClock4 0 5 0 0)\n (mkVectorClock4 1 1 1 0)\n (mkVectorClock4 1 2 2 1)\n true = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/RamenCornerConsensusV1_19_3.v":"0d13bd5256fe1c42448fdbf0c5b6316e75b911d20b833305bed5577e60ef088a","lean/RamenCornerConsensusV1_19_3.lean":"ca0dd7c31dccda34d0c56ed65835a8d5316ffab7ff0ecfc1e05c7c8521235750"},"files":{"coq_file":"coq/RamenCornerConsensusV1_19_3.v","lean_file":"lean/RamenCornerConsensusV1_19_3.lean"},"formal_systems":"Coq+Lean","id":"CUB-2939","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem vector_clock_causal_write_rejects_concurrent_history :\n CausalWriteOK\n \u27e81, 0, 0, 0\u27e9\n \u27e80, 5, 0, 0\u27e9\n \u27e81, 1, 1, 0\u27e9\n \u27e81, 2, 2, 1\u27e9\n true = false","lean_verified":"not stated in registry status for this row","module":"RamenCornerConsensusV1_19_3","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"0d13bd5256fe1c42...","lean_sha256":"ca0dd7c31dccda34..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"VERIFIED","theorem_name":"vector_clock_causal_write_rejects_concurrent_history","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Theorem named 'vector_clock_causal_write_rejects_policy_deny' in the RamenCornerConsensusV1_19_3 family -- registry statement: CUB integration: cubie-core","coq_statement_full":"Theorem vector_clock_causal_write_rejects_policy_deny :\n CausalWriteOK\n (mkVectorClock4 1 0 0 0)\n (mkVectorClock4 1 2 0 0)\n (mkVectorClock4 1 2 3 0)\n (mkVectorClock4 1 2 3 4)\n false = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/RamenCornerConsensusV1_19_3.v":"0d13bd5256fe1c42448fdbf0c5b6316e75b911d20b833305bed5577e60ef088a","lean/RamenCornerConsensusV1_19_3.lean":"ca0dd7c31dccda34d0c56ed65835a8d5316ffab7ff0ecfc1e05c7c8521235750"},"files":{"coq_file":"coq/RamenCornerConsensusV1_19_3.v","lean_file":"lean/RamenCornerConsensusV1_19_3.lean"},"formal_systems":"Coq+Lean","id":"CUB-2940","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem vector_clock_causal_write_rejects_policy_deny :\n CausalWriteOK\n \u27e81, 0, 0, 0\u27e9\n \u27e81, 2, 0, 0\u27e9\n \u27e81, 2, 3, 0\u27e9\n \u27e81, 2, 3, 4\u27e9\n false = false","lean_verified":"not stated in registry status for this row","module":"RamenCornerConsensusV1_19_3","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec 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{"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Lemma named 'genuine_corner_K' in the ToRCornerSpoofingV1_31 family -- registry statement: CUB integration: cubie-core","coq_statement_full":"Lemma genuine_corner_K : CornerK genuine_corner = true.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/ToRCornerSpoofingV1_31.v":"5d49eb7fee490deafcef680364e32ddb643f38838be376b84f6e67f91ae6a204"},"files":{"coq_file":"coq/ToRCornerSpoofingV1_31.v"},"formal_systems":"Coq","id":"CUB-2989","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"ToRCornerSpoofingV1_31","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec 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row","crate":"","deployable":false,"file_shas":{"coq/ToRCornerSpoofingV1_31.v":"5d49eb7fee490deafcef680364e32ddb643f38838be376b84f6e67f91ae6a204"},"files":{"coq_file":"coq/ToRCornerSpoofingV1_31.v"},"formal_systems":"Coq","id":"CUB-2990","invocation":"unwired","kernels":"none","kind":"Lemma","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"ToRCornerSpoofingV1_31","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"5d49eb7fee490dea..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"VERIFIED","theorem_name":"genuine_seam_J","use_cases":["TDX","topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Theorem named 'policy_alone_cannot_grant_write' in the ToRCornerSpoofingV1_31 family -- registry statement: CUB integration: cubie-core","coq_statement_full":"Theorem policy_alone_cannot_grant_write :\n forall c : RackCorner,\n CornerK c = false ->\n WriteOK c true = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/ToRCornerSpoofingV1_31.v":"5d49eb7fee490deafcef680364e32ddb643f38838be376b84f6e67f91ae6a204"},"files":{"coq_file":"coq/ToRCornerSpoofingV1_31.v"},"formal_systems":"Coq","id":"CUB-2991","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"ToRCornerSpoofingV1_31","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"5d49eb7fee490dea..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"VERIFIED","theorem_name":"policy_alone_cannot_grant_write","use_cases":["consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Theorem named 'single_seam_failure_defeats_corner' in the ToRCornerSpoofingV1_31 family -- registry statement: CUB integration: cubie-core","coq_statement_full":"Theorem single_seam_failure_defeats_corner :\n forall c : RackCorner,\n J (s1 c) = false \\/ J (s2 c) = false \\/ J (s3 c) = false ->\n CornerK c = false.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/ToRCornerSpoofingV1_31.v":"5d49eb7fee490deafcef680364e32ddb643f38838be376b84f6e67f91ae6a204"},"files":{"coq_file":"coq/ToRCornerSpoofingV1_31.v"},"formal_systems":"Coq","id":"CUB-2992","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"ToRCornerSpoofingV1_31","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"5d49eb7fee490dea..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"VERIFIED","theorem_name":"single_seam_failure_defeats_corner","use_cases":["TDX","topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} 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2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Theorem named 'spoofing_blindness' in the ToRCornerSpoofingV1_31 family -- registry statement: CUB integration: cubie-core","coq_statement_full":"Theorem spoofing_blindness :\n ~ (forall c1 c2 : RackCorner,\n project_corner c1 shared_surface = project_corner c2 shared_surface ->\n CornerK c1 = CornerK c2).","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/ToRCornerSpoofingV1_31.v":"5d49eb7fee490deafcef680364e32ddb643f38838be376b84f6e67f91ae6a204"},"files":{"coq_file":"coq/ToRCornerSpoofingV1_31.v"},"formal_systems":"Coq","id":"CUB-2995","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"ToRCornerSpoofingV1_31","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not 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assembledCoherent_implies_edges (c : AssembledCube)\n (h : assembledCoherentBool c = true) : allEdgesConsistent c = true","lean_verified":"not stated in registry status for this row","module":"cubieq_omega_incremental_append","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"lean_sha256":"a3e0ed86574341c2..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"VERIFIED","theorem_name":"assembledCoherent_implies_edges","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: theorem named 'assembledCoherent_implies_faces' in the cubieq_omega_incremental_append family -- 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row","module":"cubieq_omega_incremental_append","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"c9909a8b2c202fe7...","lean_sha256":"a3e0ed86574341c2..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"VERIFIED","theorem_name":"catalog_match_purges_memory","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: theorem named 'classifyPartialAccess_twentyOne' in the cubieq_omega_incremental_append family -- registry statement: CUB integration: cubie-core","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"lean/cubieq_omega_incremental_append.lean":"a3e0ed86574341c2d85140b85c12fb9b3f4fa5730f84c56cc00c6b771091ccf2"},"files":{"lean_file":"lean/cubieq_omega_incremental_append.lean"},"formal_systems":"Lean","id":"CUB-3006","invocation":"unwired","kernels":"none","kind":"theorem","lean_statement_full":"theorem classifyPartialAccess_twentyOne :\n classifyPartialAccess 21 = .PA_Inconsistent","lean_verified":"not stated in registry status for this row","module":"cubieq_omega_incremental_append","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"lean_sha256":"a3e0ed86574341c2..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"VERIFIED","theorem_name":"classifyPartialAccess_twentyOne","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: theorem named 'classifyPartialAccess_zero' in the cubieq_omega_incremental_append family -- registry statement: CUB integration: cubie-core","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"lean/cubieq_omega_incremental_append.lean":"a3e0ed86574341c2d85140b85c12fb9b3f4fa5730f84c56cc00c6b771091ccf2"},"files":{"lean_file":"lean/cubieq_omega_incremental_append.lean"},"formal_systems":"Lean","id":"CUB-3007","invocation":"unwired","kernels":"none","kind":"theorem","lean_statement_full":"theorem classifyPartialAccess_zero :\n classifyPartialAccess 0 = .PA_Solved","lean_verified":"not stated in registry status for this row","module":"cubieq_omega_incremental_append","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"lean_sha256":"a3e0ed86574341c2..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"VERIFIED","theorem_name":"classifyPartialAccess_zero","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: theorem named 'consumeParams_length' in the cubieq_omega_incremental_append family -- registry statement: CUB integration: cubie-core","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"lean/cubieq_omega_incremental_append.lean":"a3e0ed86574341c2d85140b85c12fb9b3f4fa5730f84c56cc00c6b771091ccf2"},"files":{"lean_file":"lean/cubieq_omega_incremental_append.lean"},"formal_systems":"Lean","id":"CUB-3011","invocation":"unwired","kernels":"none","kind":"theorem","lean_statement_full":"theorem consumeParams_length (ps : List LinearHandoffParam) :\n (consumeParams ps).length = ps.length","lean_verified":"not stated in registry status for this row","module":"cubieq_omega_incremental_append","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"lean_sha256":"a3e0ed86574341c2..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"VERIFIED","theorem_name":"consumeParams_length","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Theorem named 'expiration_purges_memory' in the cubieq_omega_incremental_append family -- registry statement: CUB integration: cubie-core","coq_statement_full":"Theorem expiration_purges_memory :\n forall ac ledger catalog req M,\n catalog_matches catalog (request_anon_pointer req) = false ->\n internally_expired ledger (request_anon_pointer req) = true ->\n kinetic_token_decision ac ledger catalog req M = PurgeTokenFromMemory.","coq_verified":"not stated in registry status for this 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row","module":"cubieq_omega_incremental_append","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"c9909a8b2c202fe7...","lean_sha256":"a3e0ed86574341c2..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"VERIFIED","theorem_name":"expiration_purges_memory","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Theorem named 'structural_incoherence_trips_absolute_block' in the cubieq_omega_incremental_append family -- registry statement: CUB integration: cubie-core","coq_statement_full":"Theorem structural_incoherence_trips_absolute_block :\n forall ac ledger catalog req M safe,\n catalog_matches catalog (request_anon_pointer req) = false ->\n internally_expired ledger (request_anon_pointer req) = false ->\n evaluate_grand_fusion_certified req M = inr safe ->\n assembled_coherent ac = false ->\n kinetic_token_decision ac ledger catalog req M = InvalidateAndBurnAccess.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/cubieq_omega_incremental_append.v":"c9909a8b2c202fe72a5136b46a2b80ec5a66892550138e2ea63b29630a2bb672","lean/cubieq_omega_incremental_append.lean":"a3e0ed86574341c2d85140b85c12fb9b3f4fa5730f84c56cc00c6b771091ccf2"},"files":{"coq_file":"coq/cubieq_omega_incremental_append.v","lean_file":"lean/cubieq_omega_incremental_append.lean"},"formal_systems":"Coq+Lean","id":"CUB-3020","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem structural_incoherence_trips_absolute_block\n (ac : AssembledCube) (ledger : ExpirationLedger)\n (catalog : BadActorCatalog) (req : ActiveRequest) (M : LocalManifold)\n (safe : GrandFusionSafe req M)\n (hCat : catalog.catalogMatches (requestAnonPointer req) = false)\n (hExp : ledger.internallyExpired (requestAnonPointer req) = false)\n (hSafe : evaluateGrandFusionCertified req M = .inr safe)\n (hCoh : assembledCoherentBool ac = false) :\n kineticTokenDecision ac ledger catalog req M = .InvalidateAndBurnAccess","lean_verified":"not stated in registry status for this row","module":"cubieq_omega_incremental_append","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"c9909a8b2c202fe7...","lean_sha256":"a3e0ed86574341c2..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"VERIFIED","theorem_name":"structural_incoherence_trips_absolute_block","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: theorem named 'authV1_10_implies_edge_corner_ok' in the cubieq_omega_incremental_next_addendum family -- registry statement: CUB integration: cubie-core","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"lean/cubieq_omega_incremental_next_addendum.lean":"d631e4c0629b4d6a8c5049f16de291b2ba27067cab0500751e6636d8608e4358"},"files":{"lean_file":"lean/cubieq_omega_incremental_next_addendum.lean"},"formal_systems":"Lean","id":"CUB-3026","invocation":"unwired","kernels":"none","kind":"theorem","lean_statement_full":"theorem authV1_10_implies_edge_corner_ok\n (ac : AssembledCube) (req : ActiveRequest) (M : LocalManifold)\n (env : OmegaAuthEnvelope)\n (h : authV1_10Bool ac req M env = true) :\n edgeCornerOkBool ac = true","lean_verified":"not stated in registry status for this row","module":"cubieq_omega_incremental_next_addendum","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"lean_sha256":"d631e4c0629b4d6a..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"VERIFIED","theorem_name":"authV1_10_implies_edge_corner_ok","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: theorem named 'authV1_10_implies_evidence_ok' in the cubieq_omega_incremental_next_addendum family -- registry statement: CUB integration: cubie-core","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"lean/cubieq_omega_incremental_next_addendum.lean":"d631e4c0629b4d6a8c5049f16de291b2ba27067cab0500751e6636d8608e4358"},"files":{"lean_file":"lean/cubieq_omega_incremental_next_addendum.lean"},"formal_systems":"Lean","id":"CUB-3027","invocation":"unwired","kernels":"none","kind":"theorem","lean_statement_full":"theorem authV1_10_implies_evidence_ok\n (ac : AssembledCube) (req : ActiveRequest) (M : LocalManifold)\n (env : OmegaAuthEnvelope)\n (h : authV1_10Bool ac req M env = true) :\n evidenceRecordOkBool env.oaeEvidence = true","lean_verified":"not stated in registry status for this row","module":"cubieq_omega_incremental_next_addendum","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"lean_sha256":"d631e4c0629b4d6a..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"VERIFIED","theorem_name":"authV1_10_implies_evidence_ok","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: theorem named 'authV1_10_implies_grand_fusion_ok' in the cubieq_omega_incremental_next_addendum family -- registry statement: CUB integration: cubie-core","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"lean/cubieq_omega_incremental_next_addendum.lean":"d631e4c0629b4d6a8c5049f16de291b2ba27067cab0500751e6636d8608e4358"},"files":{"lean_file":"lean/cubieq_omega_incremental_next_addendum.lean"},"formal_systems":"Lean","id":"CUB-3028","invocation":"unwired","kernels":"none","kind":"theorem","lean_statement_full":"theorem authV1_10_implies_grand_fusion_ok\n (ac : AssembledCube) (req : ActiveRequest) (M : LocalManifold)\n (env : OmegaAuthEnvelope)\n (h : authV1_10Bool ac req M env = true) :\n grandFusionOkBool req M = true","lean_verified":"not stated in registry status for this row","module":"cubieq_omega_incremental_next_addendum","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"lean_sha256":"d631e4c0629b4d6a..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"VERIFIED","theorem_name":"authV1_10_implies_grand_fusion_ok","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: theorem named 'authV1_10_implies_mode_ok' in the cubieq_omega_incremental_next_addendum family -- registry statement: CUB integration: cubie-core","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"lean/cubieq_omega_incremental_next_addendum.lean":"d631e4c0629b4d6a8c5049f16de291b2ba27067cab0500751e6636d8608e4358"},"files":{"lean_file":"lean/cubieq_omega_incremental_next_addendum.lean"},"formal_systems":"Lean","id":"CUB-3029","invocation":"unwired","kernels":"none","kind":"theorem","lean_statement_full":"theorem authV1_10_implies_mode_ok\n (ac : AssembledCube) (req : ActiveRequest) (M : LocalManifold)\n (env : OmegaAuthEnvelope)\n (h : authV1_10Bool ac req M env = true) :\n readWriteModeOkBool ac env.oaeAction = true","lean_verified":"not stated in registry status for this row","module":"cubieq_omega_incremental_next_addendum","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"lean_sha256":"d631e4c0629b4d6a..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"VERIFIED","theorem_name":"authV1_10_implies_mode_ok","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Theorem named 'bigraph_place_assoc' in the v1_3_DriveMathFormalization_0521 family -- registry statement: CUB integration: cubie-core","coq_statement_full":"Theorem bigraph_place_assoc : forall h g f,\n composePlace (composePlace h g) f = composePlace h (composePlace g f).","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/v1_3_DriveMathFormalization_0521.v":"31f1a158dcca755dc450c6bcf998c166f2d92e9fa6c8670025817a2e9114c6a7"},"files":{"coq_file":"coq/v1_3_DriveMathFormalization_0521.v"},"formal_systems":"Coq","id":"CUB-3041","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"v1_3_DriveMathFormalization_0521","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"31f1a158dcca755d..."},"source_completeness":"full 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Proof. destruct a; reflexivity. Qed.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/v1_4_BexarMetalFormalization_0521.v":"e592e75425d096618db9353f47141aa419fbfb059d6afdf071574aa5dfede7ea"},"files":{"coq_file":"coq/v1_4_BexarMetalFormalization_0521.v"},"formal_systems":"Coq","id":"CUB-3058","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"v1_4_BexarMetalFormalization_0521","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"e592e75425d09661..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"VERIFIED","theorem_name":"belnap_idem","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"ALIASED"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Theorem named 'belnap_top_unit' in the v1_4_BexarMetalFormalization_0521 family -- registry statement: CUB integration: cubie-core","coq_statement_full":"Theorem belnap_top_unit : forall a, belnapMeet a true = a. Proof. destruct a; reflexivity. Qed.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/v1_4_BexarMetalFormalization_0521.v":"e592e75425d096618db9353f47141aa419fbfb059d6afdf071574aa5dfede7ea"},"files":{"coq_file":"coq/v1_4_BexarMetalFormalization_0521.v"},"formal_systems":"Coq","id":"CUB-3059","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"v1_4_BexarMetalFormalization_0521","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"e592e75425d09661..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"VERIFIED","theorem_name":"belnap_top_unit","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this 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true.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/v1_4_BexarMetalFormalization_0521.v":"e592e75425d096618db9353f47141aa419fbfb059d6afdf071574aa5dfede7ea"},"files":{"coq_file":"coq/v1_4_BexarMetalFormalization_0521.v"},"formal_systems":"Coq","id":"CUB-3061","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"v1_4_BexarMetalFormalization_0521","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"e592e75425d09661..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"VERIFIED","theorem_name":"corner_consensus_weakest","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this 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AXIOM-FREE (0 axioms, live coqc/coqchk-verified) | Lean: NOT AXIOM-FREE -- depends on: propext","axiom_profile":"0 axioms (Lean 4.30.0 print axioms: propext only, no sorryAx; Coq text scan: no Axiom/Admitted in coq/CubieBexarMetalV1_4Gap.v; coqc/coqchk not run in this workspace) [SUPERSEDED by live coqc/coqchk 2026-08-15: Print Assumptions confirms 'Closed under the global context' (0 axioms) via live coqc+coqchk in coqorg/coq:8.18, not a text scan -- see docs/evidence/2026-08-15_cub_coq_kernel_verification.md]","context_purpose":"DERIVED: Theorem named 'denial_admit_iff_zero' in the v1_4_BexarMetalFormalization_0521 family -- registry statement: CUB integration: cubie-core","coq_statement_full":"Theorem cub_3064_denial_admit_iff_zero : forall d, admits d = true <-> denialCode d = 0.","coq_verified":"YES -- kernel-checked (Coq)","crate":"","deployable":false,"file_shas":{"coq/CubieBexarMetalV1_4Gap.v":"2b97cc6239e6215527b6a2fec259050beb56c9ecf08cb3df02c23a0c29bb8f7a","lean/CubieBexarMetalV1_4Gap.lean":"a16460cb50113621a2e26ed4c8ae7fe990b50e0a99cbb65abd406af54938f1b8","verus/cubie_bexar_metal_v1_4_gap_spec.rs":"b13cd48520bce5e13f432dfab268573eb3a097960e102d613d9c8c2346b116b5"},"files":{"coq_file":"coq/CubieBexarMetalV1_4Gap.v","lean_file":"lean/CubieBexarMetalV1_4Gap.lean","verus_file":"verus/cubie_bexar_metal_v1_4_gap_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3064","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_3064_denial_admit_iff_zero (d : Denial) : admits d = true \u2194 denialCode d = 0","lean_verified":"YES -- kernel-checked live, Lean 4.30.0","module":"v1_4_BexarMetalFormalization_0521","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"2b97cc6239e62155...","lean_sha256":"a16460cb50113621..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"Coq kernel-checked 8.18.0 (coqc+coqchk live, 2026-08-15); Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"denial_admit_iff_zero","use_cases":["admission"],"verification_state":"NOT_VERIFIED","verus_statement_full":"proof fn cub_3064_denial_admit_iff_zero(d: GapDenial)\n ensures gap_admits(d) <==> gap_denial_code(d) == 0\n","verus_verified":"PENDING -- verus binary not on PATH in this workspace","verus_via_covers_rescue":"","wiring":"SPEC-ONLY"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Theorem named 'goodput_no_overcommit' in the v1_4_BexarMetalFormalization_0521 family -- registry statement: CUB integration: cubie-core","coq_statement_full":"Theorem goodput_no_overcommit : forall pool cost, cost <= pool ->\n cost + (pool - cost) = pool /\\ pool - cost <= pool.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/v1_4_BexarMetalFormalization_0521.v":"e592e75425d096618db9353f47141aa419fbfb059d6afdf071574aa5dfede7ea"},"files":{"coq_file":"coq/v1_4_BexarMetalFormalization_0521.v"},"formal_systems":"Coq","id":"CUB-3065","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"v1_4_BexarMetalFormalization_0521","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"e592e75425d09661..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: 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2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Theorem named 'interface_count' in the v1_4_BexarMetalFormalization_0521 family -- registry statement: CUB integration: cubie-core","coq_statement_full":"Theorem interface_count : interfaceSites = 48. Proof. reflexivity. Qed.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/v1_4_BexarMetalFormalization_0521.v":"e592e75425d096618db9353f47141aa419fbfb059d6afdf071574aa5dfede7ea"},"files":{"coq_file":"coq/v1_4_BexarMetalFormalization_0521.v"},"formal_systems":"Coq","id":"CUB-3067","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"v1_4_BexarMetalFormalization_0521","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"e592e75425d09661..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"VERIFIED","theorem_name":"interface_count","use_cases":["topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"ALIASED"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: Theorem named 'interface_dominates' in the v1_4_BexarMetalFormalization_0521 family -- registry statement: CUB integration: cubie-core","coq_statement_full":"Theorem interface_dominates :\n totalSites - interfaceSites = 6 /\\ interfaceSites > totalSites - interfaceSites.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/v1_4_BexarMetalFormalization_0521.v":"e592e75425d096618db9353f47141aa419fbfb059d6afdf071574aa5dfede7ea"},"files":{"coq_file":"coq/v1_4_BexarMetalFormalization_0521.v"},"formal_systems":"Coq","id":"CUB-3068","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"v1_4_BexarMetalFormalization_0521","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"e592e75425d09661..."},"source_completeness":"full (CSV-sourced)","statement":"CUB integration: cubie-core","status":"VERIFIED","theorem_name":"interface_dominates","use_cases":["topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"ALIASED"} {"axiom_free_status":"not assessed in 2026-07-02 import","axiom_profile":"not assessed in 2026-07-02 import","context_purpose":"DERIVED: theorem named 'interface_law_8_over_9' in the v1_4_BexarMetalFormalization_0521 family -- registry statement: CUB integration: cubie-core","coq_statement_full":"Theorem interface_law_8_over_9 : 9 * interfaceSites = 8 * totalSites. Proof. reflexivity. Qed.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/v1_4_BexarMetalFormalization_0521.v":"e592e75425d096618db9353f47141aa419fbfb059d6afdf071574aa5dfede7ea","lean/CubieBexarMetalV1_4.lean":"59a78fa85e5feac85697b47b4fec39cef41bc11551a186e29323b9592cd75dc7"},"files":{"coq_file":"coq/v1_4_BexarMetalFormalization_0521.v","lean_file":"lean/CubieBexarMetalV1_4.lean"},"formal_systems":"Coq+Lean","id":"CUB-3069","invocation":"unwired","kernels":"none","kind":"theorem","lean_statement_full":"theorem interface_law_8_over_9 : 9 * interfaceSites = 8 * totalSites","lean_verified":"not stated in registry status for this row","module":"v1_4_BexarMetalFormalization_0521","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"e592e75425d09661...","lean_sha256":"59a78fa85e5feac8..."},"source_completeness":"full 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Proof. reflexivity. 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master_theorem_table.csv; kernel status not tracked at row level","verus_via_covers_rescue":"","wiring":"VERUS-BOUND"} {"axiom_free_status":"none (coqchk Axioms: ; Lean #print axioms: propext + Classical.choice + Quot.sound, core omega footprint)","axiom_profile":"none (coqchk Axioms: ; Lean #print axioms: propext + Classical.choice + Quot.sound, core omega footprint)","context_purpose":"DERIVED: Theorem named 'cub_3166_poison_jump_old_accepts_new_rejects' in the SeqFreshnessWraparoundSafe family -- registry statement: Wraparound-safe sequence freshness (wave3 lane C repair of the replay.rs u64::MAX acceptance, P3-#553)","coq_statement_full":"Theorem cub_3166_poison_jump_old_accepts_new_rejects :\n forall M w,\n 1 < M -> w < M - 1 ->\n sequence_id_fresh_old 0 (M - 1) /\\ ~ seq_fresh_wraparound_safe M 0 (M - 1) w.","coq_verified":"not stated in registry status for this row","crate":"cubie-core","deployable":true,"exec_file":"cubie-core/src/replay.rs","exec_fn":"cub_3166_sequence_id_fresh_wraparound_safe","exec_fns":["cub_3166_sequence_id_fresh_wraparound_safe"],"file_shas":{"coq/CUB_3166_SeqFreshnessWraparoundSafeReal.v":"601026103a7f1d491e52a58b3100b60782cdb1ad18df79c43aaaa26786c41f60","lean/CUB_3166_SeqFreshnessWraparoundSafeReal.lean":"f8c27a17c0d8622b6cf14c4cbef2a8fcac289d3d411363890214cfe8b135e300","verus/CUB_3166_seq_freshness_wraparound_safe_real_spec.rs":"419c3c203c2d79633ba7eb702d7fee4a93bbd7ad04c6475ccc0c16bd85a480d9"},"files":{"coq_file":"coq/CUB_3166_SeqFreshnessWraparoundSafeReal.v","lean_file":"lean/CUB_3166_SeqFreshnessWraparoundSafeReal.lean","verus_file":"verus/CUB_3166_seq_freshness_wraparound_safe_real_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3166","invocation":"runtime","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_3166_poison_jump_old_accepts_new_rejects (M w : Nat)\n (hM : 1 < M) (hw : w < M - 1) :\n sequenceIdFreshOld 0 (M - 1) \u2227 \u00ac seqFreshWraparoundSafe M 0 (M - 1) w","lean_verified":"not stated in registry status for this row","module":"SeqFreshnessWraparoundSafe","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","proof_scope":"standalone","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"coq_sha256":"601026103a7f1d49...","lean_sha256":"f8c27a17c0d8622b..."},"source_completeness":"full (CSV-sourced)","statement":"Wraparound-safe sequence freshness (wave3 lane C repair of the replay.rs u64::MAX acceptance, P3-#553)","status":"VERIFIED","theorem_name":"cub_3166_poison_jump_old_accepts_new_rejects","verification_state":"VERIFIED","verus_statement_full":"proof fn cub_3166_poison_jump_old_accepts_new_rejects(window: u64)\n requires\n window < u64::MAX,\n ensures\n spec_sequence_id_fresh_old_3166(0u64, u64::MAX),\n !spec_seq_fresh_wraparound_safe_3166(0u64, u64::MAX, window),\n","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"VERUS-BOUND"} {"axiom_free_status":"not measured for this row","context_purpose":"AUDIT-ONLY row -- no theorem_name/statement in source; see wiring/invocation fields only.","coq_statement_full":"","coq_verified":"AUDIT-ONLY -- no theorem_name in master_theorem_table.csv; kernel status not tracked at row level","crate":"cubie-core","deployable":true,"exec_file":"cubie-core/src/execution_physics.rs","exec_fn":"is_isolated","exec_fns":["is_isolated"],"file_shas":{"verus/CUB_3167_tarpit_isolation_contract_real_spec.rs":"73ca0196f29ff8742a535b0d2298e4bd3673178e8af25034d9d5b8bc50e2042d"},"files":{"verus_file":"verus/CUB_3167_tarpit_isolation_contract_real_spec.rs"},"id":"CUB-3167","invocation":"runtime","kernels":"VCL","lean_statement_full":"","lean_verified":"AUDIT-ONLY -- no theorem_name in master_theorem_table.csv; kernel status not tracked at row 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mcp ->\n binding_passes expected inference ->\n binding_matches mcp inference.","coq_verified":"not stated in registry status for this row","crate":"mcp-sidecar","deployable":false,"exec_file":"agentic-cybersecurity/cubie-wwt-gateway/crates/mcp-sidecar/src/main.rs","file_shas":{"coq/CUB_3168_GatewayBinding.v":"b342a709b7936d0c48dea0ff6aa2d8e8159c0c2ed2947bd88f1a6115b3b097c9","lean/CUB_3168_GatewayBinding.lean":"56f881571cbc8ac072696998e333c3642645f8740ca8378bee57ad86cd89edd0","verus/CUB_3168_gateway_binding_spec.rs":"98fe1446f47f15c2d2b89a5bbd804edf461e23d7388d570e68fc6da06725bcda"},"files":{"coq_file":"coq/CUB_3168_GatewayBinding.v","lean_file":"lean/CUB_3168_GatewayBinding.lean","verus_file":"verus/CUB_3168_gateway_binding_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3168","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_3168_gateway_parity\n (expected mcp inference : GatewayBinding)\n (hmcp : bindingPasses expected mcp)\n (hinference : bindingPasses expected inference) :\n bindingMatches mcp inference","lean_verified":"not stated in registry status for this row","module":"GatewayCanonicalBinding","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"no","riscv_status":"no","shas":{"coq_sha256":"b342a709b7936d0c...","lean_sha256":"56f881571cbc8ac0..."},"source_completeness":"full (CSV-sourced)","statement":"Shared MCP and pre-inference gateway canonical binding, including explicit RuntimePlan, ShadowCubie, and mirror commitments","status":"VERIFIED","theorem_name":"cub_3168_gateway_parity","use_cases":["crypto","gateway"],"verification_state":"VERIFIED","verus_statement_full":"pub proof fn cub_3168_gateway_parity(\n expected: GatewayBinding,\n mcp: GatewayBinding,\n inference: GatewayBinding,\n)\n requires\n binding_passes(expected, mcp),\n binding_passes(expected, inference),\n ensures\n mcp.program == inference.program,\n mcp.topology == inference.topology,\n mcp.profile == inference.profile,\n mcp.policy == inference.policy,\n mcp.verifier == inference.verifier,\n mcp.runtime_plan == inference.runtime_plan,","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"none (coqchk closed; Lean #print axioms: none)","axiom_profile":"none (coqchk closed; Lean #print axioms: none)","context_purpose":"DERIVED: Theorem named 'cub_3169_allow_requires_solved_counts' in the RuntimeBareMetalAttestation family -- registry statement: Runtime bare-metal V2 attestation coherence","coq_statement_full":"Theorem cub_3169_allow_requires_solved_counts :\n forall output faces seams vertices,\n coherent true output faces seams vertices = true ->\n output = true /\\ faces = 6 /\\ seams = 12 /\\ vertices = 8.","coq_verified":"not stated in registry status for this row","crate":"bare-metal","deployable":true,"exec_file":"bare-metal/src/runtime_proof.rs","exec_fn":"cub_3169_attestation_coherent","exec_fns":["cub_3169_attestation_coherent"],"file_shas":{"coq/CUB_3169_RuntimeBareMetalAttestation.v":"a64cb31ef8f9a11fd4b497dcb78f0588e59725af2fd935daece686c7bc74228a","lean/CUB_3169_RuntimeBareMetalAttestation.lean":"38db6132c5e03d0455a2ea6eb757c5428cfad0bd40fcb56b4cda893fc6c345d0","verus/CUB_3169_runtime_bare_metal_attestation_spec.rs":"7774c36c57046e262f400f555b3f43ea3cd7cae412ff75e6832884e2bfddd310"},"files":{"coq_file":"coq/CUB_3169_RuntimeBareMetalAttestation.v","lean_file":"lean/CUB_3169_RuntimeBareMetalAttestation.lean","verus_file":"verus/CUB_3169_runtime_bare_metal_attestation_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3169","invocation":"runtime","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_3169_allow_requires_solved_counts\n (output : Bool) (faces seams vertices : Nat)\n (h : coherent true output faces seams vertices = true) :\n output = true \u2227 faces = 6 \u2227 seams = 12 \u2227 vertices = 8","lean_verified":"not stated in registry status for this row","module":"RuntimeBareMetalAttestation","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","proof_scope":"standalone","repo":"cubie-tf","riscv":"no","riscv_status":"no","shas":{"coq_sha256":"a64cb31ef8f9a11f...","lean_sha256":"38db6132c5e03d04..."},"source_completeness":"full (CSV-sourced)","statement":"Runtime bare-metal V2 attestation coherence","status":"VERIFIED","theorem_name":"cub_3169_allow_requires_solved_counts","use_cases":["NIST"],"verification_state":"VERIFIED","verus_statement_full":"pub proof fn cub_3169_allow_requires_solved_counts(\n output_is_allow: bool,\n faces: u8,\n seams: u8,\n vertices: u8,\n)\n requires coherent(true, output_is_allow, faces, seams, vertices),\n ensures\n output_is_allow,\n faces == 6,\n seams == 12,\n vertices == 8,\n","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"VERUS-BOUND"} {"axiom_free_status":"none (coqchk closed; Lean #print axioms: none)","axiom_profile":"none (coqchk closed; Lean #print axioms: none)","context_purpose":"DERIVED: Theorem named 'cub_3170_match_iff_both_bytes_equal' in the RuntimeQecObservation family -- registry statement: Live QEC observation matches V2 attestation bytes","coq_statement_full":"Theorem cub_3170_match_iff_both_bytes_equal :\n forall ls as_ lc ac,\n observation_matches ls as_ lc ac = true <-> ls = as_ /\\ lc = ac.","coq_verified":"not stated in registry status for this row","crate":"cubie-qec","deployable":true,"exec_file":"cubie-qec/src/runtime_proof.rs","exec_fn":"cub_3170_observation_matches_attestation","exec_fns":["cub_3170_observation_matches_attestation"],"file_shas":{"coq/CUB_3170_RuntimeQecObservation.v":"5f8dd147d93a86f7d3f661dd996dab9437c8f4abaa0e186bc8fc28bb942e808f","lean/CUB_3170_RuntimeQecObservation.lean":"ea2312c213e6b9cbe3f16bf23463b96032175089162068dcdd6be1552b7bdcbd","verus/CUB_3170_runtime_qec_observation_spec.rs":"d73074b17f64a90cea39e5b66c7f75f4befc98de9df493e0917d3039fc1598df"},"files":{"coq_file":"coq/CUB_3170_RuntimeQecObservation.v","lean_file":"lean/CUB_3170_RuntimeQecObservation.lean","verus_file":"verus/CUB_3170_runtime_qec_observation_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3170","invocation":"runtime","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_3170_match_iff_both_bytes_equal (ls as_ lc ac : Nat) :\n observationMatches ls as_ lc ac = true \u2194 ls = as_ \u2227 lc = ac","lean_verified":"not stated in registry status for this row","module":"RuntimeQecObservation","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","proof_scope":"standalone","repo":"cubie-tf","riscv":"no","riscv_status":"no","shas":{"coq_sha256":"5f8dd147d93a86f7...","lean_sha256":"ea2312c213e6b9cb..."},"source_completeness":"full (CSV-sourced)","statement":"Live QEC observation matches V2 attestation bytes","status":"VERIFIED","theorem_name":"cub_3170_match_iff_both_bytes_equal","use_cases":["NIST","QEC"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"VERUS-BOUND"} {"axiom_free_status":"none (coqchk closed; Lean #print axioms: none)","axiom_profile":"none (coqchk closed; Lean #print axioms: none)","context_purpose":"DERIVED: Theorem named 'cub_3171_shadow_is_verdict_neutral' in the OpenvinoShadowSemantics family -- registry statement: OpenVINO shadow screening is observable and verdict-neutral","coq_statement_full":"Theorem cub_3171_shadow_is_verdict_neutral :\n forall allowed why,\n egress_allowed (apply_shadow allowed why) = true\n /\\ screened (apply_shadow allowed why) = true\n /\\ shadow_denied (apply_shadow allowed why) = negb allowed\n /\\ reason (apply_shadow allowed why) = why.","coq_verified":"not stated in registry status for this 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true\n \u2227 (applyShadow allowed reason).screened = true\n \u2227 (applyShadow allowed reason).shadowDenied = !allowed\n \u2227 (applyShadow allowed reason).reason = reason","lean_verified":"not stated in registry status for this row","module":"OpenvinoShadowSemantics","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","proof_scope":"standalone","repo":"cubie-tf","riscv":"no","riscv_status":"no","shas":{"coq_sha256":"37d920c45a161c1a...","lean_sha256":"f9d988b69c90b9f3..."},"source_completeness":"full (CSV-sourced)","statement":"OpenVINO shadow screening is observable and verdict-neutral","status":"VERIFIED","theorem_name":"cub_3171_shadow_is_verdict_neutral","use_cases":["crypto"],"verification_state":"VERIFIED","verus_statement_full":"pub proof fn cub_3171_shadow_is_verdict_neutral(verdict_allowed: bool, reason: u8)\n ensures\n apply_shadow(verdict_allowed, reason).egress_allowed,\n apply_shadow(verdict_allowed, reason).screened,\n apply_shadow(verdict_allowed, reason).shadow_denied == !verdict_allowed,\n apply_shadow(verdict_allowed, reason).reason == reason,\n","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"VERUS-BOUND"} {"axiom_free_status":"none (coqchk closed; Lean #print axioms: none)","axiom_profile":"none (coqchk closed; Lean #print axioms: none)","context_purpose":"DERIVED: Theorem named 'cub_3172_only_satisfied_requirements_are_clean' in the MetadataRequirementsFailClosed family -- registry statement: Metadata proof requirements fail closed for declared artifacts and routes","coq_statement_full":"Theorem cub_3172_only_satisfied_requirements_are_clean :\n forall missing required matches,\n metadata_requirement_code missing required matches = 0 ->\n missing = 0 /\\ (required = false \\/ matches = true).","coq_verified":"not stated in registry status for this 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routeMatches : Bool)\n (h : metadataRequirementCode missing required routeMatches = 0) :\n missing = 0 \u2227 (required = false \u2228 routeMatches = true)","lean_verified":"not stated in registry status for this row","module":"MetadataRequirementsFailClosed","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","proof_scope":"standalone","repo":"cubie-tf","riscv":"no","riscv_status":"no","shas":{"coq_sha256":"9f2012ae940fb4e9...","lean_sha256":"e23fc377a903a582..."},"source_completeness":"full (CSV-sourced)","statement":"Metadata proof requirements fail closed for declared artifacts and routes","status":"VERIFIED","theorem_name":"cub_3172_only_satisfied_requirements_are_clean","verification_state":"VERIFIED","verus_statement_full":"pub proof fn cub_3172_only_satisfied_requirements_are_clean(\n missing: u16,\n route_required: bool,\n route_matches: bool,\n)\n requires metadata_requirement_code(missing, route_required, route_matches) == 0,\n ensures\n missing == 0,\n !route_required || route_matches,\n","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"VERUS-BOUND"} {"axiom_free_status":"none","axiom_profile":"none","context_purpose":"DERIVED: Theorem named 'agent_anomaly_iff_nonzero' in the AgentRuntimeObservation family -- registry statement: Agent detector syndrome and anomaly coherence","coq_statement_full":"Theorem agent_anomaly_iff_nonzero :\n forall syndrome,\n agent_anomaly syndrome = true <-> syndrome <> 0%N.","coq_verified":"not stated in registry status for this 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false.","coq_verified":"not stated in registry status for this row","crate":"cubie-workflow-recompute","deployable":true,"exec_file":"crates/cubie-workflow-recompute/src/runtime_proof.rs","exec_fn":"cub_3175_capacity_declared","exec_fns":["cub_3175_capacity_declared"],"file_shas":{"coq/CUB_3175_WorkflowCapacityDeclaration.v":"410ea14ca9e054e2d6fab73bb636eec85ef8b050c63b1a0bdd1675db3e0e8039","lean/CUB_3175_WorkflowCapacityDeclaration.lean":"9ee4e49bc28a476dc6851c50c538a195ad5af68d3c376d8a97fe464b24138112","verus/CUB_3175_workflow_capacity_declaration_spec.rs":"91e3d57a95846e754fb300f89cccde0f04a07d8302956e645cf7c22f095180b0"},"files":{"coq_file":"coq/CUB_3175_WorkflowCapacityDeclaration.v","lean_file":"lean/CUB_3175_WorkflowCapacityDeclaration.lean","verus_file":"verus/CUB_3175_workflow_capacity_declaration_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3175","invocation":"runtime","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem zero_capacity_is_undeclared : capacityDeclared 0 0 = false","lean_verified":"not stated in registry status for this row","module":"WorkflowCapacityDeclaration","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","proof_scope":"standalone","repo":"cubie-tf","riscv":"no","riscv_status":"no","shas":{"coq_sha256":"410ea14ca9e054e2...","lean_sha256":"9ee4e49bc28a476d..."},"source_completeness":"full (CSV-sourced)","statement":"Workflow capacity must be explicitly nonzero","status":"VERIFIED","theorem_name":"zero_capacity_is_undeclared","verification_state":"VERIFIED","verus_statement_full":"proof fn zero_capacity_is_undeclared()\n ensures !capacity_declared(0, 0),\n","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"VERUS-BOUND"} {"axiom_free_status":"none","axiom_profile":"none","context_purpose":"DERIVED: Theorem named 'unready_allow_is_rejected' in the TdxPreAdmitFailClosed family -- registry statement: TDX ingress gates admission and fails 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row","module":"TdxPreAdmitFailClosed","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","proof_scope":"standalone","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"coq_sha256":"15107d40ea22955d...","lean_sha256":"87d5d72746fb5011..."},"source_completeness":"full (CSV-sourced)","statement":"TDX ingress gates admission and fails closed","status":"VERIFIED","theorem_name":"unready_allow_is_rejected","use_cases":["TDX","admission"],"verification_state":"VERIFIED","verus_statement_full":"proof fn unready_allow_is_rejected()\n ensures !tdx_fail_closed(false, true),\n","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"VERUS-BOUND"} {"axiom_free_status":"none","axiom_profile":"none","context_purpose":"DERIVED: Theorem named 'any_failed_descriptor_gate_rejects' in the EpochDescriptorRuntime family -- registry statement: Epoch descriptor runtime gates form one fail-closed readiness decision","coq_statement_full":"Theorem any_failed_descriptor_gate_rejects :\n epoch_descriptor_ready false true true = false /\\\n epoch_descriptor_ready true false true = false /\\\n epoch_descriptor_ready true true false = false.","coq_verified":"not stated in registry status for this row","crate":"cubie-epoch-descriptor","deployable":true,"exec_file":"crates/cubie-epoch-descriptor/src/predicates.rs","exec_fn":"cub_3177_epoch_descriptor_ready","exec_fns":["cub_3177_epoch_descriptor_ready"],"file_shas":{"coq/CUB_3177_EpochDescriptorRuntime.v":"b2cb7c6bd3094731e3b3b09616ca7673943bfe62b844b64849a9d97e1c7f1f58","lean/CUB_3177_EpochDescriptorRuntime.lean":"8c3c73d0e790911585c3e281787ec90f2ad585b8a878c059321ca0eac08426ca","verus/CUB_3177_epoch_descriptor_runtime_spec.rs":"735cf37422e8a5ba72c3427056e26e9e0d9b47492621495df78b0df9f55432fa"},"files":{"coq_file":"coq/CUB_3177_EpochDescriptorRuntime.v","lean_file":"lean/CUB_3177_EpochDescriptorRuntime.lean","verus_file":"verus/CUB_3177_epoch_descriptor_runtime_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3177","invocation":"runtime","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem any_failed_descriptor_gate_rejects :\n And (epochDescriptorReady false true true = false)\n (And (epochDescriptorReady true false true = false)\n (epochDescriptorReady true true false = false))","lean_verified":"not stated in registry status for this row","module":"EpochDescriptorRuntime","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","proof_scope":"standalone","repo":"cubie-tf","riscv":"no","riscv_status":"no","shas":{"coq_sha256":"b2cb7c6bd3094731...","lean_sha256":"8c3c73d0e7909115..."},"source_completeness":"full (CSV-sourced)","statement":"Epoch descriptor runtime gates form one fail-closed readiness decision","status":"VERIFIED","theorem_name":"any_failed_descriptor_gate_rejects","verification_state":"VERIFIED","verus_statement_full":"proof fn any_failed_descriptor_gate_rejects()\n ensures\n !epoch_descriptor_ready(false, true, true),\n !epoch_descriptor_ready(true, false, true),\n !epoch_descriptor_ready(true, true, false),\n","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"VERUS-BOUND"} {"axiom_free_status":"none","axiom_profile":"none","context_purpose":"DERIVED: Theorem named 'above_maximum_days_reject' in the OscalCivilDateBounds family -- registry statement: OSCAL civil-date conversion ends at RFC3339 year 9999","coq_statement_full":"Theorem above_maximum_days_reject :\n forall days, 2932896 < days -> ~ civil_days_supported days.","coq_verified":"not stated in registry status for this 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false false false = false /\\\n report_type_is_tdx false true false false false false false false = false /\\\n report_type_is_tdx false false true false false false false false = false /\\\n report_type_is_tdx false false false true false false false false = false /\\\n report_type_is_tdx false false false false true false false false = false /\\\n report_type_is_tdx false false false false false true false false = false /\\\n report_type_is_tdx false false false false false false true false = false /\\\n report_type_is_tdx false false false false false false false true = false.","coq_verified":"not stated in registry status for this 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false)\n (And (reportTypeIsTdx false false true false false false false false = false)\n (And (reportTypeIsTdx false false false true false false false false = false)\n (And (reportTypeIsTdx false false false false true false false false = false)\n (And (reportTypeIsTdx false false false false false true false false = false)\n (And (reportTypeIsTdx false false false false false false true false = false)\n (reportTypeIsTdx false false false false false false false true = false)))))))","lean_verified":"not stated in registry status for this row","module":"TdxReportType","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","proof_scope":"standalone","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"coq_sha256":"17925685c093c059...","lean_sha256":"3b8e677ec05947e8..."},"source_completeness":"full (CSV-sourced)","statement":"TDX report type accepts only a zero 64-bit REPORTTYPE field","status":"VERIFIED","theorem_name":"any_nonzero_report_type_byte_rejects","use_cases":["TDX"],"verification_state":"VERIFIED","verus_statement_full":"proof fn any_nonzero_report_type_byte_rejects()\n ensures\n !report_type_is_tdx(1, 0, 0, 0, 0, 0, 0, 0),\n !report_type_is_tdx(0, 1, 0, 0, 0, 0, 0, 0),\n !report_type_is_tdx(0, 0, 1, 0, 0, 0, 0, 0),\n !report_type_is_tdx(0, 0, 0, 1, 0, 0, 0, 0),\n !report_type_is_tdx(0, 0, 0, 0, 1, 0, 0, 0),\n !report_type_is_tdx(0, 0, 0, 0, 0, 1, 0, 0),\n !report_type_is_tdx(0, 0, 0, 0, 0, 0, 1, 0),\n !report_type_is_tdx(0, 0, 0, 0, 0, 0, 0, 1),\n","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"VERUS-BOUND"} {"axiom_free_status":"none","axiom_profile":"none","context_purpose":"DERIVED: Theorem named 'missing_governance_precondition_rejects' in the GovernanceRuntimeAllow family -- registry statement: Governance preserves allow only with a healthy precondition","coq_statement_full":"Theorem missing_governance_precondition_rejects :\n governance_allow false false = false /\\\n governance_allow false true = false.","coq_verified":"not stated in registry status for this row","crate":"tf-governance","deployable":true,"exec_file":"controlplane/tf-governance/src/fail_closed.rs","exec_fn":"cub_3180_governance_allow","exec_fns":["cub_3180_governance_allow"],"file_shas":{"coq/CUB_3180_GovernanceRuntimeAllow.v":"ee3e591f28f3e6fa34f91723a5325ca01d60e84b081ebfbfb8e252697fb6a386","lean/CUB_3180_GovernanceRuntimeAllow.lean":"f1c1b12d17adcfad64689bc2a503c54802a9d80f8f850d5eb56cb3ff007ae6e6","verus/CUB_3180_governance_runtime_allow_spec.rs":"88f2b1462d65095875e41ecb99e29324f1767edef05317fe70f988beab4835bd"},"files":{"coq_file":"coq/CUB_3180_GovernanceRuntimeAllow.v","lean_file":"lean/CUB_3180_GovernanceRuntimeAllow.lean","verus_file":"verus/CUB_3180_governance_runtime_allow_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3180","invocation":"runtime","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem missing_governance_precondition_rejects :\n And (governanceAllow false false = false)\n (governanceAllow false true = false)","lean_verified":"not 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equality is byte-complete and fail-closed","coq_statement_full":"Theorem changed_policy_hash_rejects :\n governance_policy_hash_equal false = false.","coq_verified":"not stated in registry status for this row","crate":"tf-governance","deployable":true,"exec_file":"controlplane/tf-governance/src/orbit.rs","exec_fn":"cub_3181_governance_policy_hash_equal","exec_fns":["cub_3181_governance_policy_hash_equal"],"file_shas":{"coq/CUB_3181_GovernancePolicyHash.v":"d18fd4d79c234fa380b3b7c32a63077fd2e8c74f50f51764264c880834946e69","lean/CUB_3181_GovernancePolicyHash.lean":"56f6f91757d0f1460446f453dda9dfa591bb8e2198dab0302a9ae38fd5c4773b","verus/CUB_3181_governance_policy_hash_spec.rs":"8ec064fb0cf7fc2feb94e46a761dd74177b1af2928c001703216c08c8ebca2a3"},"files":{"coq_file":"coq/CUB_3181_GovernancePolicyHash.v","lean_file":"lean/CUB_3181_GovernancePolicyHash.lean","verus_file":"verus/CUB_3181_governance_policy_hash_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3181","invocation":"runtime","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem changed_policy_hash_rejects :\n governancePolicyHashEqual false = false","lean_verified":"not stated in registry status for this 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outside_freshness_window_rejects :\n forall drift window,\n drift > window ->\n identity_fresh drift window = false.","coq_verified":"not stated in registry status for this row","crate":"tf-identity","deployable":true,"exec_file":"controlplane/tf-identity/src/trust_chain.rs","exec_fn":"cub_3182_identity_fresh","exec_fns":["cub_3182_identity_fresh"],"file_shas":{"coq/CUB_3182_IdentityFreshness.v":"b1fbd452777dd8c4a2510e54620033745de14503fdc1f45369fbfdf721797a93","lean/CUB_3182_IdentityFreshness.lean":"2c4a53ddfbc97493a3e9c71769573d6aedcf5fb578898da9c26d652e88dfbdcc","verus/CUB_3182_identity_freshness_spec.rs":"e7e2bc4b8631c06579057db3ef9bee12062018f6f57fc0a2652240e020ff3c32"},"files":{"coq_file":"coq/CUB_3182_IdentityFreshness.v","lean_file":"lean/CUB_3182_IdentityFreshness.lean","verus_file":"verus/CUB_3182_identity_freshness_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3182","invocation":"runtime","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem outside_freshness_window_rejects\n (drift window : Nat) (h : window < drift) :\n identityFresh drift window = false","lean_verified":"not stated in registry status for this row","module":"IdentityFreshness","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","proof_scope":"standalone","repo":"cubie-tf","riscv":"no","riscv_status":"no","shas":{"coq_sha256":"b1fbd452777dd8c4...","lean_sha256":"2c4a53ddfbc97493..."},"source_completeness":"full (CSV-sourced)","statement":"Identity temporal coherence is symmetric and bounded","status":"VERIFIED","theorem_name":"outside_freshness_window_rejects","verification_state":"VERIFIED","verus_statement_full":"proof fn outside_freshness_window_rejects(drift: nat, window: nat)\n requires drift > window,\n ensures !identity_fresh(drift, window),\n","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"FUNCTION-IMPL"} {"axiom_free_status":"none","axiom_profile":"none","context_purpose":"DERIVED: Theorem named 'trusted_vlan_implies_allowed' in the SentinelGate family -- registry statement: Trusted VLAN routing requires the full sentinel gate","coq_statement_full":"Theorem trusted_vlan_implies_allowed :\n forall allowed failed_percolation_only,\n sentinel_target_vlan allowed failed_percolation_only = 100 ->\n allowed = true.","coq_verified":"not stated in registry status for this row","crate":"omega_core","deployable":true,"exec_file":"core-manifold/omega_core/src/lib.rs","exec_fn":"cub_3183_sentinel_gate_model","exec_fns":["cub_3183_sentinel_gate_model"],"file_shas":{"coq/CUB_3183_SentinelGate.v":"bfd9c75dec52211e9a77963e567b5ef321739cafffe73c35c8505931cc56fe62","lean/CUB_3183_SentinelGate.lean":"1a99488ef8dfa5b6ad22243cad4110f77d22af7ad67b6bdce53efee127761cba","verus/CUB_3183_sentinel_gate_spec.rs":"668afc6341b4112ea7d6c9a4f2b7431c66ccfeec9165106e4cb8c555ca32508f"},"files":{"coq_file":"coq/CUB_3183_SentinelGate.v","lean_file":"lean/CUB_3183_SentinelGate.lean","verus_file":"verus/CUB_3183_sentinel_gate_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3183","invocation":"runtime","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem trusted_vlan_implies_allowed (allowed failedPercolationOnly : Bool)\n (h : sentinelTargetVlan allowed failedPercolationOnly = 100) :\n allowed = true","lean_verified":"not stated in registry status for this row","module":"SentinelGate","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","proof_scope":"standalone","repo":"cubie-tf","riscv":"no","riscv_status":"no","shas":{"coq_sha256":"bfd9c75dec52211e...","lean_sha256":"1a99488ef8dfa5b6..."},"source_completeness":"full (CSV-sourced)","statement":"Trusted VLAN routing requires the full sentinel gate","status":"VERIFIED","theorem_name":"trusted_vlan_implies_allowed","use_cases":["topology"],"verification_state":"VERIFIED","verus_statement_full":"proof fn trusted_vlan_implies_allowed(allowed: bool, failed_percolation_only: bool)\n ensures sentinel_target_vlan(allowed, failed_percolation_only) == 100 ==> allowed,\n","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"FUNCTION-IMPL"} {"axiom_free_status":"none","axiom_profile":"none","context_purpose":"DERIVED: Theorem named 'out_of_range_step_rejects' in the PriorStepMask family -- registry statement: Orchestrator step masks enforce shift bounds before proof invocation","coq_statement_full":"Theorem out_of_range_step_rejects :\n forall step_id,\n step_id >= 32 ->\n orchestrator_step_in_domain step_id = false.","coq_verified":"not stated in registry status for this row","crate":"tf-orchestrator","deployable":true,"exec_file":"core-manifold/tf-orchestrator/src/lib.rs","exec_fn":"cub_3184_prior_step_mask","exec_fns":["cub_3184_prior_step_mask"],"file_shas":{"coq/CUB_3184_PriorStepMask.v":"c7302f6152e765d728bfe6a55ee2446f869aaf7c59a0a463a363fbc6a4389db1","lean/CUB_3184_PriorStepMask.lean":"d3b00dc2c5774275a94199d857f5209b0b9bd3864f92d8fe1ff534cebe5dd6a3","verus/CUB_3184_prior_step_mask_spec.rs":"4625b6c5a2d8667e3ecd58893eda8e89894e21777d81108ed0d7c6f444b6c63a"},"files":{"coq_file":"coq/CUB_3184_PriorStepMask.v","lean_file":"lean/CUB_3184_PriorStepMask.lean","verus_file":"verus/CUB_3184_prior_step_mask_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3184","invocation":"runtime","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem out_of_range_step_rejects\n (stepId : Nat) (h : 32 <= stepId) :\n orchestratorStepInDomain stepId = false","lean_verified":"not stated in registry status for this row","module":"PriorStepMask","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","proof_scope":"standalone","repo":"cubie-tf","riscv":"no","riscv_status":"no","shas":{"coq_sha256":"c7302f6152e765d7...","lean_sha256":"d3b00dc2c5774275..."},"source_completeness":"full (CSV-sourced)","statement":"Orchestrator step masks enforce shift bounds before proof invocation","status":"VERIFIED","theorem_name":"out_of_range_step_rejects","use_cases":["TEP","topology"],"verification_state":"VERIFIED","verus_statement_full":"proof fn out_of_range_step_rejects(step_id: nat)\n requires step_id >= 32,\n ensures !orchestrator_step_in_domain(step_id),\n","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"FUNCTION-IMPL"} {"axiom_free_status":"none","axiom_profile":"none","context_purpose":"DERIVED: Theorem named 'denied_byte_is_zero' in the MintDenyAirgap family -- registry statement: A denied ephemeral mint emits no key or quote bytes","coq_statement_full":"Theorem denied_byte_is_zero :\n forall candidate,\n mint_output_byte false candidate = 0.","coq_verified":"not stated in registry status for this row","crate":"omega_minter","deployable":true,"exec_file":"core-manifold/omega_minter/src/lib.rs","exec_fn":"cub_3185_mint_airgap_bound","exec_fns":["cub_3185_mint_airgap_bound"],"file_shas":{"coq/CUB_3185_MintDenyAirgap.v":"8a9a73cb783c76efff4f5c97c2b9c6b2a31cd5523723b808b5153c84b1131b33","lean/CUB_3185_MintDenyAirgap.lean":"b452b768d1a18246b09dcbc2ae673ceea74f31a5b4abc4849fa0d89199c41300","verus/CUB_3185_mint_deny_airgap_spec.rs":"cd837c0f5bacd3403ff548fd2ed927de22caeba4696918b2d0a6f45f6603414f"},"files":{"coq_file":"coq/CUB_3185_MintDenyAirgap.v","lean_file":"lean/CUB_3185_MintDenyAirgap.lean","verus_file":"verus/CUB_3185_mint_deny_airgap_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3185","invocation":"runtime","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem denied_byte_is_zero (candidate : Nat) :\n mintOutputByte false candidate = 0","lean_verified":"not stated in registry status for this row","module":"MintDenyAirgap","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","proof_scope":"standalone","repo":"cubie-tf","riscv":"no","riscv_status":"no","shas":{"coq_sha256":"8a9a73cb783c76ef...","lean_sha256":"b452b768d1a18246..."},"source_completeness":"full (CSV-sourced)","statement":"A denied ephemeral mint emits no key or quote bytes","status":"VERIFIED","theorem_name":"denied_byte_is_zero","use_cases":["topology"],"verification_state":"VERIFIED","verus_statement_full":"proof fn denied_byte_is_zero(candidate: u8)\n ensures mint_output_byte(false, candidate) == 0u8,\n","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"FUNCTION-IMPL"} {"axiom_free_status":"none","axiom_profile":"none","context_purpose":"DERIVED: Theorem named 'excessive_steps_reject' in the BoundedGrgRuntime family -- registry statement: Checked GRG recurrence rejects excessive work and arithmetic overflow","coq_statement_full":"Theorem excessive_steps_reject :\n forall n,\n n > 64 ->\n runtime_accepts_steps n = false.","coq_verified":"not stated in registry status for this row","crate":"tf-core","deployable":true,"exec_file":"core-manifold/tf-core/src/theorems.rs","exec_fn":"cub_3186_checked_grg_runtime","exec_fns":["cub_3186_checked_grg_runtime"],"file_shas":{"coq/CUB_3186_BoundedGrgRuntime.v":"21dc55c323d94526ea2306ecdefa2b89517fbb63fd93c7386c285d5f080b0358","lean/CUB_3186_BoundedGrgRuntime.lean":"26a98b4b0b348660117af792aeb660e5131d42456555e69b3fe00f420231602f","verus/CUB_3186_bounded_grg_runtime_spec.rs":"da904b37edecd878eea94792f044aa200180c513273ea81dfa00a8e17df4e419"},"files":{"coq_file":"coq/CUB_3186_BoundedGrgRuntime.v","lean_file":"lean/CUB_3186_BoundedGrgRuntime.lean","verus_file":"verus/CUB_3186_bounded_grg_runtime_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3186","invocation":"runtime","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem excessive_steps_reject (n : Nat) (h : 64 < n) :\n runtimeAcceptsSteps n = false","lean_verified":"not stated in registry status for this row","module":"BoundedGrgRuntime","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","proof_scope":"standalone","repo":"cubie-tf","riscv":"no","riscv_status":"no","shas":{"coq_sha256":"21dc55c323d94526...","lean_sha256":"26a98b4b0b348660..."},"source_completeness":"full (CSV-sourced)","statement":"Checked GRG recurrence rejects excessive work and arithmetic overflow","status":"VERIFIED","theorem_name":"excessive_steps_reject","use_cases":["TEP","topology"],"verification_state":"VERIFIED","verus_statement_full":"proof fn excessive_steps_reject(n: nat)\n requires n > 64,\n ensures !runtime_accepts_steps(n),\n","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"FUNCTION-IMPL"} {"axiom_free_status":"none","axiom_profile":"none","context_purpose":"DERIVED: Theorem named 'mask_one_iff_all_gates' in the FourGateMask family -- registry statement: Four-gate constant-time mask is one iff every gate passes","coq_statement_full":"Theorem mask_one_iff_all_gates :\n forall gpu_ok hmac_ok pcie_ok consent_ok,\n four_gate_mask gpu_ok hmac_ok pcie_ok consent_ok = 1 <->\n gpu_ok = true /\\ hmac_ok = true /\\ pcie_ok = true /\\ consent_ok = true.","coq_verified":"not stated in registry status for this row","crate":"cubie-core","deployable":true,"exec_file":"cubie-core/src/constant_time.rs","exec_fn":"cub_3187_four_gate_mask","exec_fns":["cub_3187_four_gate_mask"],"file_shas":{"coq/CUB_3187_FourGateMask.v":"76dc4bae7d991ba031b4d5f305963569279b37e92c8e7705015a966cde79c68c","lean/CUB_3187_FourGateMask.lean":"f80ccca041fd84adbd9d60a896aafa4befe684351bc7784412e984b231a24496","verus/CUB_3187_four_gate_mask_spec.rs":"851ceefeb46428143d7977f3c485f696b93c242f4fde87f45d0b236b54bb07f9"},"files":{"coq_file":"coq/CUB_3187_FourGateMask.v","lean_file":"lean/CUB_3187_FourGateMask.lean","verus_file":"verus/CUB_3187_four_gate_mask_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3187","invocation":"runtime","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem mask_one_iff_all_gates\n (gpuOk hmacOk pcieOk consentOk : Bool) :\n fourGateMask gpuOk hmacOk pcieOk consentOk = 1 \u2194\n gpuOk = true \u2227 hmacOk = true \u2227 pcieOk = true \u2227 consentOk = true","lean_verified":"not stated in registry status for this row","module":"FourGateMask","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","proof_scope":"standalone","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"coq_sha256":"76dc4bae7d991ba0...","lean_sha256":"f80ccca041fd84ad..."},"source_completeness":"full (CSV-sourced)","statement":"Four-gate constant-time mask is one iff every gate passes","status":"VERIFIED","theorem_name":"mask_one_iff_all_gates","verification_state":"VERIFIED","verus_statement_full":"proof fn mask_one_iff_all_gates(\n gpu_ok: bool,\n hmac_ok: bool,\n pcie_ok: bool,\n consent_ok: bool,\n)\n ensures\n (four_gate_mask(gpu_ok, hmac_ok, pcie_ok, consent_ok) == 1)\n <==> (gpu_ok && hmac_ok && pcie_ok && consent_ok),\n","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"VERUS-BOUND"} {"axiom_free_status":"none","axiom_profile":"none","context_purpose":"DERIVED: Theorem named 'below_threshold_not_shattered' in the MetaCubeShatter family -- registry statement: Meta-cube shatter latches exactly at its bounce threshold","coq_statement_full":"Theorem below_threshold_not_shattered :\n forall bounces threshold,\n bounces < threshold ->\n shatter_latched bounces threshold = false.","coq_verified":"not stated in registry status for this row","crate":"cubie-tep","deployable":true,"exec_file":"cubie-tep/src/meta_cube.rs","exec_fn":"cub_3188_shatter_latched","exec_fns":["cub_3188_shatter_latched"],"file_shas":{"coq/CUB_3188_MetaCubeShatter.v":"56b8efe2e4f3323065972760f830b8ca7804d3073968c7acee8495c2e5588ff5","lean/CUB_3188_MetaCubeShatter.lean":"192c33d42fb6ab5661e4595bd8f3d2c1fcf06539f4c4091c97cd158fd80fdb55","verus/CUB_3188_meta_cube_shatter_spec.rs":"4ec5a0498bf6ea7e8570052cec17f634cb135536d8dd823ee0650e53c4de8e75"},"files":{"coq_file":"coq/CUB_3188_MetaCubeShatter.v","lean_file":"lean/CUB_3188_MetaCubeShatter.lean","verus_file":"verus/CUB_3188_meta_cube_shatter_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3188","invocation":"runtime","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem below_threshold_not_shattered\n (bounces threshold : Nat) (h : bounces < threshold) :\n shatterLatched bounces threshold = false","lean_verified":"not stated in registry status for this row","module":"MetaCubeShatter","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","proof_scope":"standalone","repo":"cubie-tf","riscv":"no","riscv_status":"no","shas":{"coq_sha256":"56b8efe2e4f33230...","lean_sha256":"192c33d42fb6ab56..."},"source_completeness":"full (CSV-sourced)","statement":"Meta-cube shatter latches exactly at its bounce threshold","status":"VERIFIED","theorem_name":"below_threshold_not_shattered","use_cases":["TEP","crypto"],"verification_state":"VERIFIED","verus_statement_full":"proof fn below_threshold_not_shattered(bounces: nat, threshold: nat)\n requires bounces < threshold,\n ensures !shatter_latched(bounces, threshold),\n","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"FUNCTION-IMPL"} {"axiom_free_status":"none","axiom_profile":"none","context_purpose":"DERIVED: Theorem named 'cub_3189_shard_frontier' in the StickerCompilerShardLowerBound family -- registry statement: K_lower is the minimum shard count and no placement fits below it","coq_statement_full":"Theorem cub_3189_shard_frontier :\n forall k ra rp rt, fits3 k ra rp rt <-> k >= k_lower3 ra rp rt.","coq_verified":"not stated in registry status for this row","crate":"cubie-wwt-gateway","deployable":false,"exec_file":"agentic-cybersecurity/cubie-wwt-gateway/src/ledger.rs","file_shas":{"coq/CUB_3189_3194_StickerCompiler.v":"47443e95095d2d99466aa25ad60ce023f0b25475daf2bacfddbca8b224069b83","lean/CUB_3189_3194_StickerCompiler.lean":"99cd95727c7af0ef97bbc1a079bca18853828a1d0f7bad32af3fc3012db46504","verus/CUB_3189_3194_sticker_compiler_spec.rs":"d0e18da28eb2cde874e864fa303dd6015717f532e7b88e78fdf233a279cb12d7"},"files":{"coq_file":"coq/CUB_3189_3194_StickerCompiler.v","lean_file":"lean/CUB_3189_3194_StickerCompiler.lean","verus_file":"verus/CUB_3189_3194_sticker_compiler_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3189","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_3189_shard_frontier (k a p t : Nat) :\n CapacityHolds k a p t \u2194 k \u2265 kLower a p t","lean_verified":"not stated in registry status for this row","module":"StickerCompilerShardLowerBound","no_holes":true,"production_consumption":"PROOF-ARTIFACT-RUNTIME","proof_artifact_integrity":"EMBEDDED-SHA256-VALIDATED","proof_bundle_id":"sticker-compiler-proof-family-v1","proof_consumer":"sticker_precompile.shard_frontier","proof_consumption":"RUNTIME-CONSUMER-WIRED","proof_consumption_condition":"consumed during keyed precompile and independently recomputed when the signed compiled-sticker store loads; the request ledger carries the resulting receipt digest","proof_kernels_execute_at_request_time":false,"proof_policy_effect":"signed_compile_receipt_required","proof_runtime_boundary":"abstract mirrors plus exact runtime observations, not executable theorem calls; invalid bundle/digest/observation refuses store activation before request forwarding","proof_scope":"standalone","repo":"cubie-tf","riscv":"no","riscv_status":"no","shas":{"coq_sha256":"47443e95095d2d99...","lean_sha256":"99cd95727c7af0ef..."},"source_completeness":"full (CSV-sourced)","statement":"K_lower is the minimum shard count and no placement fits below it","status":"VERIFIED","theorem_name":"cub_3189_shard_frontier","use_cases":["crypto","gateway","consent"],"verification_state":"VERIFIED","verus_statement_full":"pub proof fn cub_3189_shard_frontier(k: int, ra: int, rp: int, rt: int)\n ensures\n fits3(k, ra, rp, rt) <==> k >= k_lower3(ra, rp, rt),\n","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"none","axiom_profile":"none","context_purpose":"DERIVED: Theorem named 'cub_3190_bound_achieved' in the StickerCompilerConstructiveKLower family -- registry statement: The K_lower shard bound is achievable in the abstract lattice (fits at k=K_lower)","coq_statement_full":"Theorem cub_3190_bound_achieved :\n forall ra rp rt, fits3 (k_lower3 ra rp rt) ra rp rt.","coq_verified":"not stated in registry status for this row","crate":"cubie-wwt-gateway","deployable":false,"exec_file":"agentic-cybersecurity/cubie-wwt-gateway/src/proof_runtime.rs","file_shas":{"coq/CUB_3189_3194_StickerCompiler.v":"47443e95095d2d99466aa25ad60ce023f0b25475daf2bacfddbca8b224069b83","lean/CUB_3189_3194_StickerCompiler.lean":"99cd95727c7af0ef97bbc1a079bca18853828a1d0f7bad32af3fc3012db46504","verus/CUB_3189_3194_sticker_compiler_spec.rs":"d0e18da28eb2cde874e864fa303dd6015717f532e7b88e78fdf233a279cb12d7"},"files":{"coq_file":"coq/CUB_3189_3194_StickerCompiler.v","lean_file":"lean/CUB_3189_3194_StickerCompiler.lean","verus_file":"verus/CUB_3189_3194_sticker_compiler_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3190","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_3190_bound_achieved (a p t : Nat) : CapacityHolds (kLower a p t) a p t","lean_verified":"not stated in registry status for this row","module":"StickerCompilerConstructiveKLower","no_holes":true,"production_consumption":"PROOF-ARTIFACT-RUNTIME","proof_artifact_integrity":"EMBEDDED-SHA256-VALIDATED","proof_bundle_id":"sticker-compiler-proof-family-v1","proof_consumer":"sticker_precompile.shard_emission","proof_consumption":"RUNTIME-CONSUMER-WIRED","proof_consumption_condition":"consumed during keyed precompile and independently recomputed when the signed compiled-sticker store loads; the request ledger carries the resulting receipt digest","proof_kernels_execute_at_request_time":false,"proof_policy_effect":"signed_compile_receipt_required","proof_runtime_boundary":"abstract mirrors plus exact runtime observations, not executable theorem calls; invalid bundle/digest/observation refuses store activation before request forwarding","proof_scope":"standalone","repo":"cubie-tf","riscv":"no","riscv_status":"no","shas":{"coq_sha256":"47443e95095d2d99...","lean_sha256":"99cd95727c7af0ef..."},"source_completeness":"full (CSV-sourced)","statement":"The K_lower shard bound is achievable in the abstract lattice (fits at k=K_lower)","status":"VERIFIED","theorem_name":"cub_3190_bound_achieved","use_cases":["crypto","gateway"],"verification_state":"VERIFIED","verus_statement_full":"pub proof fn cub_3190_bound_achieved(ra: int, rp: int, rt: int)\n ensures\n fits3(k_lower3(ra, rp, rt), ra, rp, rt),\n","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"none","axiom_profile":"none","context_purpose":"DERIVED: Theorem named 'cub_3191_alias_resolves' in the StickerCompilerAliasResolution family -- registry statement: Canonical shared-metric alias resolution: consistent references to one metric resolve to one version","coq_statement_full":"Theorem cub_3191_alias_resolves :\n forall m1 v1 m2 v2 : nat,\n m1 = m2 -> (m1 = m2 -> v1 = v2) -> v1 = v2.","coq_verified":"not stated in registry status for this row","crate":"cubie-wwt-gateway","deployable":false,"exec_file":"agentic-cybersecurity/cubie-wwt-gateway/src/proof_runtime.rs","file_shas":{"coq/CUB_3189_3194_StickerCompiler.v":"47443e95095d2d99466aa25ad60ce023f0b25475daf2bacfddbca8b224069b83","lean/CUB_3189_3194_StickerCompiler.lean":"99cd95727c7af0ef97bbc1a079bca18853828a1d0f7bad32af3fc3012db46504","verus/CUB_3189_3194_sticker_compiler_spec.rs":"d0e18da28eb2cde874e864fa303dd6015717f532e7b88e78fdf233a279cb12d7"},"files":{"coq_file":"coq/CUB_3189_3194_StickerCompiler.v","lean_file":"lean/CUB_3189_3194_StickerCompiler.lean","verus_file":"verus/CUB_3189_3194_sticker_compiler_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3191","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_3191_alias_resolves (m1 v1 m2 v2 : Nat)\n (hm : m1 = m2) (h : m1 = m2 \u2192 v1 = v2) : v1 = v2","lean_verified":"not stated in registry status for this row","module":"StickerCompilerAliasResolution","no_holes":true,"production_consumption":"PROOF-ARTIFACT-RUNTIME","proof_artifact_integrity":"EMBEDDED-SHA256-VALIDATED","proof_bundle_id":"sticker-compiler-proof-family-v1","proof_consumer":"sticker_precompile.witness_lowering","proof_consumption":"RUNTIME-CONSUMER-WIRED","proof_consumption_condition":"consumed during keyed precompile and independently recomputed when the signed compiled-sticker store loads; the request ledger carries the resulting receipt digest","proof_kernels_execute_at_request_time":false,"proof_policy_effect":"signed_compile_receipt_required","proof_runtime_boundary":"abstract mirrors plus exact runtime observations, not executable theorem calls; invalid bundle/digest/observation refuses store activation before request forwarding","proof_scope":"standalone","repo":"cubie-tf","riscv":"no","riscv_status":"no","shas":{"coq_sha256":"47443e95095d2d99...","lean_sha256":"99cd95727c7af0ef..."},"source_completeness":"full (CSV-sourced)","statement":"Canonical shared-metric alias resolution: consistent references to one metric resolve to one version","status":"VERIFIED","theorem_name":"cub_3191_alias_resolves","use_cases":["crypto","complexity","gateway"],"verification_state":"VERIFIED","verus_statement_full":"pub proof fn cub_3191_alias_resolves(m1: int, v1: int, m2: int, v2: int)\n requires\n m1 == m2,\n alias_ok(m1, v1, m2, v2),\n ensures\n v1 == v2,\n","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"none","axiom_profile":"none","context_purpose":"DERIVED: Theorem named 'cub_3192_complete_iff' in the StickerCompilerPlacementGrade family -- registry statement: Placement grade never exceeds total and is complete iff every item is realised","coq_statement_full":"Theorem cub_3192_complete_iff :\n forall ga gp gt na np nt,\n ga <= na -> gp <= np -> gt <= nt ->\n (grade ga gp gt = na + np + nt <-> (ga = na /\\ gp = np /\\ gt = nt)).","coq_verified":"not stated in registry status for this 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in registry status for this row","module":"StickerCompilerPlacementGrade","no_holes":true,"production_consumption":"PROOF-ARTIFACT-RUNTIME","proof_artifact_integrity":"EMBEDDED-SHA256-VALIDATED","proof_bundle_id":"sticker-compiler-proof-family-v1","proof_consumer":"sticker_precompile.placement_verification","proof_consumption":"RUNTIME-CONSUMER-WIRED","proof_consumption_condition":"consumed during keyed precompile and independently recomputed when the signed compiled-sticker store loads; the request ledger carries the resulting receipt digest","proof_kernels_execute_at_request_time":false,"proof_policy_effect":"signed_compile_receipt_required","proof_runtime_boundary":"abstract mirrors plus exact runtime observations, not executable theorem calls; invalid bundle/digest/observation refuses store activation before request 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(CSV-sourced)","statement":"Any mismatch among the recomputed commitment fields implies not-verified (divergence)","status":"VERIFIED","theorem_name":"cub_3193_mismatch_detected","use_cases":["gateway"],"verification_state":"VERIFIED","verus_statement_full":"pub proof fn cub_3193_mismatch_detected(\n rk: int, dk: int, rs: int, ds: int, rh: int, dh: int,\n)\n requires\n rk != dk || rs != ds || rh != dh,\n ensures\n !verified(rk, dk, rs, ds, rh, dh),\n","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"none","axiom_profile":"none","context_purpose":"DERIVED: Theorem named 'cub_3194_unsupported_forbids_pass' in the StickerCompilerVerdictBoundary family -- registry statement: PASS requires supported+approved+non-contradictory; unsupported forbids PASS","coq_statement_full":"Theorem cub_3194_unsupported_forbids_pass :\n forall s a c, s = false -> ~ pass_ok s a c.","coq_verified":"not stated in registry 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registry statement: Unified admission capstone: V(cells)=fold-fuse join (order-independent, monotone, gauge-invariant); LEMMA U0 the majority-3 vote is inadmissible (non-monotone) so the join replaces it by necessity; total deterministic 4-way AdmissionDecision projection; Admit gated on clause-4 risk (CUB-3198) + clause-5 lease (CUB-3195) witnesses","coq_statement_full":"Theorem u0_vote_inadmissible : ~ admissible maj3.","coq_verified":"not stated in registry status for this 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named 'cub_3200_present_pass_or_fail' in the StickerRuntimeCellEquality family -- registry statement: Present-value runtime cell equals the abstraction projection of the transformed field (PASS/FAIL only; never FLUID/TAMPER)","coq_statement_full":"Theorem cub_3200_present_pass_or_fail :\n forall kind param norm,\n presentVerdictTag kind param norm = tag_pass\n \\/ presentVerdictTag kind param norm = tag_fail.","coq_verified":"PENDING -- coqc/coqchk not on PATH in this workspace","crate":"cubie-core","deployable":false,"exec_file":"cubie-core/src/fluid_spine.rs","file_shas":{"coq/CUB_3200_3204_StickerRuntime.v":"c4ce3f025d03d5860747960491a3c397c16e63d13bc1702680adf58a6ccfdf3a","lean/CUB_3200_3204_StickerRuntime.lean":"789608cb8815bc49203f05ebaeacc793fa04c0e88599bdec1f70776ee2958dd2","verus/CUB_3200_3204_sticker_runtime_spec.rs":"af47a64fee1ff60a5cd9cb6ed25fa86852a73ebaeec172829ebcc75e1d1311e4"},"files":{"coq_file":"coq/CUB_3200_3204_StickerRuntime.v","lean_file":"lean/CUB_3200_3204_StickerRuntime.lean","verus_file":"verus/CUB_3200_3204_sticker_runtime_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3200","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_3200_present_pass_or_fail (t v : Int) :\n presentVerdictTagGe t v = tagPass \u2228 presentVerdictTagGe t v = tagFail","lean_verified":"not stated in registry status for this row","module":"StickerRuntimeCellEquality","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"coq_sha256":"c4ce3f025d03d586...","lean_sha256":"789608cb8815bc49..."},"source_completeness":"full (CSV-sourced)","statement":"Present-value runtime cell equals the abstraction projection of the transformed field (PASS/FAIL only; never FLUID/TAMPER)","status":"PENDING-COQ-KERNEL","theorem_name":"cub_3200_present_pass_or_fail","verification_state":"NOT_VERIFIED","verus_statement_full":"pub proof fn cub_3200_present_pass_or_fail(kind: int, param: int, norm: int)\n ensures\n present_verdict_tag(kind, param, norm) == tag_pass()\n || present_verdict_tag(kind, param, norm) == tag_fail(),\n","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"none","axiom_profile":"none","context_purpose":"DERIVED: Theorem named 'cub_3201_offset_monotone' in the StickerRuntimeTransformTotality family -- registry statement: TransformV1::apply is a total panic-free fixed-point: clamp stays in range and is idempotent, Offset saturates and is monotone, zero denominator degrades to identity","coq_statement_full":"Theorem cub_3201_offset_monotone :\n forall lo hi r1 r2 delta,\n lo <= hi -> r1 <= r2 -> satAdd lo hi r1 delta <= satAdd lo hi r2 delta.","coq_verified":"PENDING -- coqc/coqchk not on PATH in this workspace","crate":"cubie-core","deployable":false,"exec_file":"cubie-core/src/sticker_runtime.rs","file_shas":{"coq/CUB_3200_3204_StickerRuntime.v":"c4ce3f025d03d5860747960491a3c397c16e63d13bc1702680adf58a6ccfdf3a","lean/CUB_3200_3204_StickerRuntime.lean":"789608cb8815bc49203f05ebaeacc793fa04c0e88599bdec1f70776ee2958dd2","verus/CUB_3200_3204_sticker_runtime_spec.rs":"af47a64fee1ff60a5cd9cb6ed25fa86852a73ebaeec172829ebcc75e1d1311e4"},"files":{"coq_file":"coq/CUB_3200_3204_StickerRuntime.v","lean_file":"lean/CUB_3200_3204_StickerRuntime.lean","verus_file":"verus/CUB_3200_3204_sticker_runtime_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3201","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_3201_offset_monotone (lo hi r1 r2 delta : Int)\n (h : lo \u2264 hi) (hr : r1 \u2264 r2) :\n satAdd lo hi r1 delta \u2264 satAdd lo hi r2 delta","lean_verified":"not stated in registry status for this row","module":"StickerRuntimeTransformTotality","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"coq_sha256":"c4ce3f025d03d586...","lean_sha256":"789608cb8815bc49..."},"source_completeness":"full (CSV-sourced)","statement":"TransformV1::apply is a total panic-free fixed-point: clamp stays in range and is idempotent, Offset saturates and is monotone, zero denominator degrades to identity","status":"PENDING-COQ-KERNEL","theorem_name":"cub_3201_offset_monotone","verification_state":"NOT_VERIFIED","verus_statement_full":"pub proof fn cub_3201_offset_monotone(r1: int, r2: int, delta: int, lo: int, hi: int)\n requires\n r1 <= r2,\n lo <= hi,\n ensures\n sat_add(r1, delta, lo, hi) <= sat_add(r2, delta, lo, hi),\n","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"none","axiom_profile":"none","context_purpose":"DERIVED: Theorem named 'cub_3202_ge_lt_complement' in the StickerRuntimeAbstractionTotality family -- registry statement: AbstractionV1::apply is a total deterministic projection to a cell state; ThresholdGe and ThresholdLt are exact complements at every value","coq_statement_full":"Theorem cub_3202_ge_lt_complement :\n forall t v, abstPass 1 t v = negb (abstPass 2 t v).","coq_verified":"PENDING -- coqc/coqchk not on PATH in this workspace","crate":"cubie-core","deployable":false,"exec_file":"cubie-core/src/sticker_runtime.rs","file_shas":{"coq/CUB_3200_3204_StickerRuntime.v":"c4ce3f025d03d5860747960491a3c397c16e63d13bc1702680adf58a6ccfdf3a","lean/CUB_3200_3204_StickerRuntime.lean":"789608cb8815bc49203f05ebaeacc793fa04c0e88599bdec1f70776ee2958dd2","verus/CUB_3200_3204_sticker_runtime_spec.rs":"af47a64fee1ff60a5cd9cb6ed25fa86852a73ebaeec172829ebcc75e1d1311e4"},"files":{"coq_file":"coq/CUB_3200_3204_StickerRuntime.v","lean_file":"lean/CUB_3200_3204_StickerRuntime.lean","verus_file":"verus/CUB_3200_3204_sticker_runtime_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3202","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_3202_ge_lt_complement (t v : Int) : PassGe t v \u2194 \u00ac PassLt t v","lean_verified":"not stated in registry status for this row","module":"StickerRuntimeAbstractionTotality","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"coq_sha256":"c4ce3f025d03d586...","lean_sha256":"789608cb8815bc49..."},"source_completeness":"full (CSV-sourced)","statement":"AbstractionV1::apply is a total deterministic projection to a cell state; ThresholdGe and ThresholdLt are exact complements at every value","status":"PENDING-COQ-KERNEL","theorem_name":"cub_3202_ge_lt_complement","use_cases":["NIST"],"verification_state":"NOT_VERIFIED","verus_statement_full":"pub proof fn cub_3202_ge_lt_complement(t: int, v: int)\n ensures\n abst_pass(1, t, v) == !abst_pass(2, t, v),\n","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"none","axiom_profile":"none","context_purpose":"DERIVED: Theorem named 'cub_3203_pass_iff_all_pass' in the StickerRuntimeVerdictLattice family -- registry statement: Verdict composition is the TAMPER>FAIL>FLUID>PASS max-lattice: PASS only if every cell passes, any FLUID/TAMPER forbids PASS, composition is monotone","coq_statement_full":"Theorem cub_3203_pass_iff_all_pass :\n forall a b,\n tag_pass <= a <= tag_tamper -> tag_pass <= b <= tag_tamper ->\n (vmax a b = tag_pass <-> (a = tag_pass /\\ b = tag_pass)).","coq_verified":"PENDING -- coqc/coqchk not on PATH in this workspace","crate":"cubie-core","deployable":false,"exec_file":"cubie-core/src/sticker_runtime.rs","file_shas":{"coq/CUB_3200_3204_StickerRuntime.v":"c4ce3f025d03d5860747960491a3c397c16e63d13bc1702680adf58a6ccfdf3a","lean/CUB_3200_3204_StickerRuntime.lean":"789608cb8815bc49203f05ebaeacc793fa04c0e88599bdec1f70776ee2958dd2","verus/CUB_3200_3204_sticker_runtime_spec.rs":"af47a64fee1ff60a5cd9cb6ed25fa86852a73ebaeec172829ebcc75e1d1311e4"},"files":{"coq_file":"coq/CUB_3200_3204_StickerRuntime.v","lean_file":"lean/CUB_3200_3204_StickerRuntime.lean","verus_file":"verus/CUB_3200_3204_sticker_runtime_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3203","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_3203_pass_iff_all_pass (a b : Int)\n (ha : tagPass \u2264 a \u2227 a \u2264 tagTamper) (hb : tagPass \u2264 b \u2227 b \u2264 tagTamper) :\n vmax a b = tagPass \u2194 (a = tagPass \u2227 b = tagPass)","lean_verified":"not stated in registry status for this row","module":"StickerRuntimeVerdictLattice","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"coq_sha256":"c4ce3f025d03d586...","lean_sha256":"789608cb8815bc49..."},"source_completeness":"full (CSV-sourced)","statement":"Verdict composition is the TAMPER>FAIL>FLUID>PASS max-lattice: PASS only if every cell passes, any FLUID/TAMPER forbids PASS, composition is monotone","status":"PENDING-COQ-KERNEL","theorem_name":"cub_3203_pass_iff_all_pass","use_cases":["crypto"],"verification_state":"NOT_VERIFIED","verus_statement_full":"pub proof fn cub_3203_pass_iff_all_pass(a: int, b: int)\n requires\n tag_pass() <= a <= tag_tamper(),\n tag_pass() <= b <= tag_tamper(),\n ensures\n (vmax(a, b) == tag_pass()) <==> (a == tag_pass() && b == tag_pass()),\n","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"none","axiom_profile":"none","context_purpose":"DERIVED: Theorem named 'cub_3204_order_sensitive' in the StickerRuntimeReceiptDeterminism family -- registry statement: Decision receipt is a deterministic, order-sensitive, program-hash-binding commitment over the program hash and ordered cell outcomes","coq_statement_full":"Theorem cub_3204_order_sensitive :\n forall ph c0 c1, c0 <> c1 -> commit2 ph c0 c1 <> commit2 ph c1 c0.","coq_verified":"PENDING -- coqc/coqchk not on PATH in this workspace","crate":"cubie-core","deployable":false,"exec_file":"cubie-core/src/sticker_runtime.rs","file_shas":{"coq/CUB_3200_3204_StickerRuntime.v":"c4ce3f025d03d5860747960491a3c397c16e63d13bc1702680adf58a6ccfdf3a","lean/CUB_3200_3204_StickerRuntime.lean":"789608cb8815bc49203f05ebaeacc793fa04c0e88599bdec1f70776ee2958dd2","verus/CUB_3200_3204_sticker_runtime_spec.rs":"af47a64fee1ff60a5cd9cb6ed25fa86852a73ebaeec172829ebcc75e1d1311e4"},"files":{"coq_file":"coq/CUB_3200_3204_StickerRuntime.v","lean_file":"lean/CUB_3200_3204_StickerRuntime.lean","verus_file":"verus/CUB_3200_3204_sticker_runtime_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3204","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_3204_order_sensitive (ph c0 c1 : Int) (h : c0 \u2260 c1) :\n commit2 ph c0 c1 \u2260 commit2 ph c1 c0","lean_verified":"not stated in registry status for this row","module":"StickerRuntimeReceiptDeterminism","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"coq_sha256":"c4ce3f025d03d586...","lean_sha256":"789608cb8815bc49..."},"source_completeness":"full (CSV-sourced)","statement":"Decision receipt is a deterministic, order-sensitive, program-hash-binding commitment over the program hash and ordered cell outcomes","status":"PENDING-COQ-KERNEL","theorem_name":"cub_3204_order_sensitive","use_cases":["NIST"],"verification_state":"NOT_VERIFIED","verus_statement_full":"pub proof fn cub_3204_order_sensitive(ph: int, c0: int, c1: int)\n requires\n c0 != c1,\n ensures\n commit2(ph, c0, c1) != commit2(ph, c1, c0),\n","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"none (coqchk Axioms: )","axiom_profile":"none (coqchk Axioms: )","context_purpose":"DERIVED: Theorem named 'delta_fold_coherence' in the DeltaFoldCoherence family -- registry statement: Delta-fold coherence + streaming/batch representation independence: fold_left(fuse,l,acc)=fold_right(fuse,acc,l); V_from(acc,l++d)=fuse(V_from(acc,l),V(d)); verdict invariant under ANY evidence-list permutation (full S_n, extending CUB-3199's adjacent-swap generator); appending a delta never lowers knowledge; FLUID is a stream trap state","coq_statement_full":"Theorem delta_fold_coherence : forall acc l d,\n verdict_from acc (l ++ d) = fuse (verdict_from acc l) (verdict d).","coq_verified":"not stated in registry status for this row","crate":"cubie-tep","deployable":true,"exec_file":"cubie-tep/src/delta_fold.rs","exec_fn":"cub_3205_delta_reverdict_bits","exec_fns":["cub_3205_delta_reverdict_bits"],"file_shas":{"coq/CUB_3205_DeltaFoldCoherenceReal.v":"e9c33e3f1bda78e4ed4b34d84db61a96c261b4b596bdb21585ad7b99f8f18f00","lean/CUB_3205_DeltaFoldCoherenceReal.lean":"d760dbc95c65c0eeec581258cfa4ab94865aadc2722542e5ba47b7bd8cc38a60","verus/CUB_3205_delta_fold_spec.rs":"d39dc9f2cef1a29584dd90052c963cc2e4eb9b38eb90bee39705be65f2716593"},"files":{"coq_file":"coq/CUB_3205_DeltaFoldCoherenceReal.v","lean_file":"lean/CUB_3205_DeltaFoldCoherenceReal.lean","verus_file":"verus/CUB_3205_delta_fold_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3205","invocation":"runtime","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem delta_fold_coherence (acc : Cell) (l d : List Cell) :\n verdictFrom acc (l ++ d) = fuse (verdictFrom acc l) (verdict d)","lean_verified":"not stated in registry status for this row","module":"DeltaFoldCoherence","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","proof_scope":"standalone","repo":"cubie-tf","riscv":"no","riscv_status":"no","shas":{"coq_sha256":"e9c33e3f1bda78e4...","lean_sha256":"d760dbc95c65c0ee..."},"source_completeness":"full (CSV-sourced)","statement":"Delta-fold coherence + streaming/batch representation independence: fold_left(fuse,l,acc)=fold_right(fuse,acc,l); V_from(acc,l++d)=fuse(V_from(acc,l),V(d)); verdict invariant under ANY evidence-list permutation (full S_n, extending CUB-3199's adjacent-swap generator); appending a delta never lowers knowledge; FLUID is a stream trap state","status":"VERIFIED","theorem_name":"delta_fold_coherence","use_cases":["TEP"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"VERUS-BOUND"} {"axiom_free_status":"none","axiom_profile":"none","context_purpose":"DERIVED: Theorem named 'cub_3206_tighten_only' in the CubieOperatorResourceHotGateV1_0 family -- registry statement: OperatorResource hot-gate tighten-only + MMIO enforce authorization","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"cubie-wwt-gateway","deployable":true,"exec_file":"agentic-cybersecurity/cubie-wwt-gateway/src/enforcement_hot_gate_predicates.rs","exec_fn":"hot_gate_armed_spec","exec_fns":["hot_gate_armed_spec","mmio_enforce_auth_active","tighten_verdict_rank"],"file_shas":{"coq/CubieOperatorResourceHotGateV1_0.v":"ca4439e23d099a8cae3ff8e8bc58bcb13e4ef9f65fc63c5d0cff78d89dd004cd","lean/CubieOperatorResourceHotGateV1_0.lean":"32604c0a8a675022e1d61af9dc2209029a06e41b30bf68fcecd5c6079eb25585","verus/cubie_operator_resource_hot_gate_spec.rs":"ec8023649695046ccc76279bad906431c90597753db4738614f297968ab2b650"},"files":{"coq_file":"coq/CubieOperatorResourceHotGateV1_0.v","lean_file":"lean/CubieOperatorResourceHotGateV1_0.lean","verus_file":"verus/cubie_operator_resource_hot_gate_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3206","invocation":"runtime","invocation_role":"DECISION-PATH-DISARMED-BY-DEFAULT","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_3206_tighten_only (current proposed : Nat)\n (hc : validVerdictRank current) (hp : validVerdictRank proposed) :\n (tightenVerdictRank current proposed).2 = true \u2192\n (tightenVerdictRank current proposed).1 > current \u2227\n (tightenVerdictRank current proposed).1 = proposed","lean_verified":"not stated in registry status for this row","module":"CubieOperatorResourceHotGateV1_0","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","proof_scope":"standalone","repo":"cubie-tf","riscv":"no","riscv_status":"no","shas":{"coq_sha256":"ca4439e23d099a8c...","lean_sha256":"32604c0a8a675022..."},"source_completeness":"full (CSV-sourced)","statement":"OperatorResource hot-gate tighten-only + MMIO enforce authorization","status":"VERIFIED","theorem_name":"cub_3206_tighten_only","use_cases":["gateway"],"verification_state":"VERIFIED","verus_statement_full":"proof fn cub_3206_tighten_only(current: u8, proposed: u8)\n requires\n valid_verdict_rank(current),\n valid_verdict_rank(proposed),\n ensures\n (","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"VERUS-BOUND"} {"axiom_free_status":"none (coqchk Axioms: )","axiom_profile":"none (coqchk Axioms: )","context_purpose":"DERIVED: Theorem named 'cell_meet' in the CubieAntiUpgradeCellMeetV1_0 family -- registry statement: Anti-upgrade cell meet bound to shipping snap","coq_statement_full":"Definition cell_meet (a b : nat) : nat :=\n match a, b with\n | 0, _ => 0\n | _, 0 => 0\n | 1, 1 => 1\n | 1, 2 => 0\n | 1, 3 => 1\n | 2, 1 => 0\n | 2, 2 => 2\n | 2, 3 => 2\n | 3, 1 => 1\n | 3, 2 => 2\n | 3, 3 => 3\n | _, _ => 0\n end.","coq_verified":"not stated in registry status for this row","crate":"cubie-core","deployable":false,"exec_file":"cubie-core/src/compile.rs","file_shas":{"coq/CubieAntiUpgradeCellMeetV1_0.v":"d47e44e9aeda7dbbb678ed3b26199590b61e455b86aa8d1921f86f7ba9015ad6","lean/CubieAntiUpgradeCellMeetV1_0.lean":"1ef4fbc4be0fdd2f2ccb0acef26619fa7bc6a6cd4882eea3556b4b5e3a2a6c46","verus/CUB_3207_anti_upgrade_cell_meet_spec.rs":"67af82c06967f01dc26f28b0cab6695bc4de560108944d77c8408a35004b31e1"},"files":{"coq_file":"coq/CubieAntiUpgradeCellMeetV1_0.v","lean_file":"lean/CubieAntiUpgradeCellMeetV1_0.lean","verus_file":"verus/CUB_3207_anti_upgrade_cell_meet_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3207","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubieAntiUpgradeCellMeetV1_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"coq_sha256":"d47e44e9aeda7dbb...","lean_sha256":"1ef4fbc4be0fdd2f..."},"source_completeness":"full (CSV-sourced)","statement":"Anti-upgrade cell meet bound to shipping snap","status":"VERIFIED","theorem_name":"cell_meet","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"none","axiom_profile":"none","context_purpose":"DERIVED: Theorem named 'cub_3208_compose_pass_nonempty' in the CubieEvidenceNonVacuityV1_0 family -- registry statement: Empty witness set / empty cell fold cannot PASS; shipping evidence_nonempty + compose gate","coq_statement_full":"Theorem cub_3208_compose_pass_nonempty :\n forall cells : list Verdict, fst (compose cells) = VPass -> cells <> [].","coq_verified":"not stated in registry status for this row","crate":"cubie-core","deployable":false,"exec_file":"cubie-core/src/sticker_compiler.rs","file_shas":{"coq/CubieEvidenceNonVacuityV1_0.v":"b68f716751f7819c9eb9d26caa8175ac18e6a42c42d3c1f246ac29d1b1c6a6fc","lean/CubieEvidenceNonVacuityV1_0.lean":"42830bbbece25e3a9471844d2cd33eed6f67e170ea3da80e09abbef2c6b799ca","verus/CUB_3208_evidence_nonvacuity_spec.rs":"15fef1d1c2f0a35c5a2de912a3a68e3c38e321d1103b8b78b669840b64b04e5e"},"files":{"coq_file":"coq/CubieEvidenceNonVacuityV1_0.v","lean_file":"lean/CubieEvidenceNonVacuityV1_0.lean","verus_file":"verus/CUB_3208_evidence_nonvacuity_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3208","invocation":"unwired","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_3208_compose_pass_nonempty (cells : List Verdict)\n (h : (compose cells).fst = Verdict.pass) : cells \u2260 []","lean_verified":"not stated in registry status for this 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cub_3209_compile_verified_requires_verified :\n forall (co : CompileOutcome) (verify : nat -> VerifyResult)\n (c : VerifiedProgram),\n compile_verified co verify = Some c ->\n exists p, co = Compiled p /\\ verify p = Verified.","coq_verified":"not stated in registry status for this 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statement: Placement cell-domain safety + typed placement boundary","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"cubie-wwt-gateway","deployable":false,"exec_file":"agentic-cybersecurity/cubie-wwt-gateway/src/placement_map.rs","files":{},"formal_systems":"Verus","id":"CUB-3220","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"CubiePlacementCellSafetyV1_0","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"no","riscv_status":"no","shas":{"coq_sha256":"pending","lean_sha256":"pending"},"source_completeness":"full (CSV-sourced)","statement":"Placement cell-domain safety + typed placement boundary","status":"IN_PROGRESS","theorem_name":"placement_cell_in_range","use_cases":["gateway"],"verification_state":"NOT_VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this 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row","crate":"cubie-core","deployable":false,"exec_file":"cubie-core/src/lane_receipt_set_v2.rs","files":{},"formal_systems":"RuntimeProperty","id":"CUB-3223","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"StickerLaneNonCircularEvidence","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"coq_sha256":"pending","lean_sha256":"pending"},"source_completeness":"full (CSV-sourced)","statement":"Sticker lane consumes sticker compiler/runtime evidence digests","status":"IN_PROGRESS","theorem_name":"sticker_evidence_digest","verification_state":"NOT_VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"none","axiom_profile":"none","context_purpose":"DERIVED: Theorem named 'decision_receipt_v2' in the DecisionReceiptV2Binding family -- registry statement: Versioned domain-separated DecisionReceiptV2 binds request/policy/schema/compiler/evidence/freshness/signer","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"cubie-core","deployable":false,"exec_file":"cubie-core/src/decision_receipt_v2.rs","files":{},"formal_systems":"RuntimeProperty","id":"CUB-3224","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"DecisionReceiptV2Binding","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"coq_sha256":"pending","lean_sha256":"pending"},"source_completeness":"full (CSV-sourced)","statement":"Versioned domain-separated DecisionReceiptV2 binds 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row","crate":"","deployable":false,"files":{},"formal_systems":"RuntimeProperty","id":"CUB-3226","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"ProvenanceProductionVerifyContext","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"pending","lean_sha256":"pending"},"source_completeness":"full (CSV-sourced)","statement":"Production provenance verify(VerificationContext, LiveEpochKeyStore, ReplayStore)","status":"IN_PROGRESS","theorem_name":"verify_production","verification_state":"NOT_VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"none","axiom_profile":"none","context_purpose":"DERIVED: Theorem named 'observation_snapshot' in the ObservationSnapshotV1UnboundFluid family -- registry statement: ObservationSnapshotV1 unbound default projects Fluid never PASS-from-absence","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"cubie-core","deployable":false,"exec_file":"cubie-core/src/observation_snapshot.rs","files":{},"formal_systems":"RuntimeProperty","id":"CUB-3227","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"ObservationSnapshotV1UnboundFluid","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"coq_sha256":"pending","lean_sha256":"pending"},"source_completeness":"full (CSV-sourced)","statement":"ObservationSnapshotV1 unbound default projects Fluid never PASS-from-absence","status":"IN_PROGRESS","theorem_name":"observation_snapshot","verification_state":"NOT_VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"none","axiom_profile":"none","context_purpose":"DERIVED: Theorem named 'logical_work_container_v1' in the LogicalWorkContainerV1Identity family -- registry statement: Authoritative LogicalWorkContainerV1 identity fields from authenticated sources only","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"cubie-wwt-gateway","deployable":false,"exec_file":"agentic-cybersecurity/cubie-wwt-gateway/src/native_control_plane/logical_container.rs","files":{},"formal_systems":"RuntimeProperty","id":"CUB-3228","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"LogicalWorkContainerV1Identity","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"no","riscv_status":"no","shas":{"coq_sha256":"pending","lean_sha256":"pending"},"source_completeness":"full (CSV-sourced)","statement":"Authoritative LogicalWorkContainerV1 identity fields from authenticated sources only","status":"IN_PROGRESS","theorem_name":"logical_work_container_v1","use_cases":["gateway"],"verification_state":"NOT_VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"none","axiom_profile":"none","context_purpose":"DERIVED: Theorem named 'admit_telemetry_record' in the AdmitTelemetryEnqueueNoIo family -- registry statement: Admit record path is bounded nonblocking enqueue without filesystem I/O","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"cubie-platform","deployable":false,"exec_file":"cubie-platform/src/admit_telemetry.rs","files":{},"formal_systems":"RuntimeProperty","id":"CUB-3229","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"AdmitTelemetryEnqueueNoIo","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"yes","riscv_status":"yes","shas":{"coq_sha256":"pending","lean_sha256":"pending"},"source_completeness":"full (CSV-sourced)","statement":"Admit record path is bounded nonblocking enqueue without filesystem I/O","status":"IN_PROGRESS","theorem_name":"admit_telemetry_record","use_cases":["admission"],"verification_state":"NOT_VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'cub_3230_authority_preemption_prevented' in the RoleAwareToolInstructionPrevention family -- registry statement: Tool-origin authority/preemption or explicit override evidence is blocked without making user-origin text satisfy the indirect-instruction predicate","coq_statement_full":"Theorem cub_3230_authority_preemption_prevented :\n forall policy_allow evidence_valid,\n blocked_and_prevented\n policy_allow evidence_valid true true true false = true.","coq_verified":"not stated in registry status for this row","crate":"cubie-wwt-gateway","deployable":true,"exec_file":"agentic-cybersecurity/cubie-wwt-gateway/src/tool_instruction_predicates.rs","exec_fn":"cub_3230_tool_instruction_from_facts","exec_fns":["cub_3230_tool_instruction_from_facts"],"file_shas":{"coq/CUB_3230_RoleAwareToolInstructionPrevention.v":"f9e1474345640fc583a92f17a0d021618d9c75cceb379fbe2db5e4cfcff66075","lean/CUB_3230_RoleAwareToolInstructionPrevention.lean":"dd15ea863a56d5d74e14d4d5ef53ef155f9bb14b9d6da006597d55203dfdecb0","verus/CUB_3230_role_aware_tool_instruction_prevention_spec.rs":"da470969d48337b343a59d7b3f600122df08950d8598f421b3d84709cbf6ead7"},"files":{"coq_file":"coq/CUB_3230_RoleAwareToolInstructionPrevention.v","lean_file":"lean/CUB_3230_RoleAwareToolInstructionPrevention.lean","verus_file":"verus/CUB_3230_role_aware_tool_instruction_prevention_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3230","invocation":"runtime","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_3230_authority_preemption_prevented\n (policyAllow evidenceValid : Bool) :\n blockedAndPrevented policyAllow evidenceValid true true true false = true","lean_verified":"not stated in registry status for this row","module":"RoleAwareToolInstructionPrevention","no_holes":true,"production_consumption":"EXECUTABLE-AND-PROOF-ARTIFACT","proof_artifact_integrity":"EMBEDDED-SHA256-VALIDATED","proof_bundle_id":"wwt-tool-instruction-prevention-v1","proof_consumer":"trust_core.signed_context_admission","proof_consumption":"RUNTIME-CONSUMER-WIRED","proof_consumption_condition":"consumed only when the signed-context admission backend executes; HostSim and classifier-only paths do not consume it","proof_kernels_execute_at_request_time":false,"proof_policy_effect":"authoritative_tighten_only","proof_runtime_boundary":"signed-context only; invalid bundle fails closed; HostSim remains advisory and does not consume or control the receipt","proof_scope":"standalone","repo":"cubie-tf","riscv":"no","riscv_status":"no","shas":{"coq_sha256":"f9e1474345640fc5...","lean_sha256":"dd15ea863a56d5d7..."},"source_completeness":"full (CSV-sourced)","statement":"Tool-origin authority/preemption or explicit override evidence is blocked without making user-origin text satisfy the indirect-instruction predicate","status":"VERIFIED","theorem_name":"cub_3230_authority_preemption_prevented","use_cases":["gateway"],"verification_state":"VERIFIED","verus_statement_full":"proof fn cub_3230_authority_preemption_prevented(\n policy_allow: bool,\n evidence_valid: bool,\n)\n ensures\n blocked_and_prevented(\n policy_allow,\n evidence_valid,\n true,\n true,\n true,\n false,\n ),\n","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"VERUS-BOUND"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'cub_3231_maximal_feasible_prefix' in the BoundedToolScanOptimality family -- registry statement: The selected prefix min(input_len cap) is within both limits and maximal among all feasible prefixes","coq_statement_full":"Theorem cub_3231_maximal_feasible_prefix :\n forall input_len cap candidate,\n candidate <= input_len ->\n candidate <= cap ->\n candidate <= bounded_prefix input_len cap.","coq_verified":"not stated in registry status for this row","crate":"cubie-wwt-gateway","deployable":true,"exec_file":"agentic-cybersecurity/cubie-wwt-gateway/src/tool_instruction_predicates.rs","exec_fn":"cub_3231_bounded_scan_prefix_len","exec_fns":["cub_3231_bounded_scan_prefix_len"],"file_shas":{"coq/CUB_3231_BoundedToolScanOptimality.v":"66b1e6054756ec6bec67250e440d851ecd25d5f4f622f000839651737f1607f4","lean/CUB_3231_BoundedToolScanOptimality.lean":"399dd1747ee2a78a1eda52112bf33408926d7bd12c10edb6461cb61833875495","verus/CUB_3231_bounded_tool_scan_optimality_spec.rs":"237b8cc4a0214393897ecfb8d2e4a4dc7a5238feafbb7bc6cfda2c59bd73a979"},"files":{"coq_file":"coq/CUB_3231_BoundedToolScanOptimality.v","lean_file":"lean/CUB_3231_BoundedToolScanOptimality.lean","verus_file":"verus/CUB_3231_bounded_tool_scan_optimality_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3231","invocation":"runtime","kernels":"VCL","kind":"Theorem","lean_statement_full":"theorem cub_3231_maximal_feasible_prefix\n (inputLen cap candidate : Nat)\n (hInput : candidate \u2264 inputLen)\n (hCap : candidate \u2264 cap) :\n candidate \u2264 boundedPrefix inputLen cap","lean_verified":"not stated in registry status for this row","module":"BoundedToolScanOptimality","no_holes":true,"production_consumption":"EXECUTABLE-AND-PROOF-ARTIFACT","proof_artifact_integrity":"EMBEDDED-SHA256-VALIDATED","proof_bundle_id":"wwt-tool-instruction-prevention-v1","proof_consumer":"trust_core.signed_context_admission","proof_consumption":"RUNTIME-CONSUMER-WIRED","proof_consumption_condition":"consumed only when the signed-context admission backend executes; HostSim and classifier-only paths do not consume it","proof_kernels_execute_at_request_time":false,"proof_policy_effect":"authoritative_tighten_only","proof_runtime_boundary":"signed-context only; invalid bundle fails closed; HostSim remains advisory and does not consume or control the receipt","proof_scope":"standalone","repo":"cubie-tf","riscv":"no","riscv_status":"no","shas":{"coq_sha256":"66b1e6054756ec6b...","lean_sha256":"399dd1747ee2a78a..."},"source_completeness":"full (CSV-sourced)","statement":"The selected prefix min(input_len cap) is within both limits and maximal among all feasible prefixes","status":"VERIFIED","theorem_name":"cub_3231_maximal_feasible_prefix","use_cases":["gateway"],"verification_state":"VERIFIED","verus_statement_full":"proof fn cub_3231_maximal_feasible_prefix(\n input_len: nat,\n cap: nat,\n candidate: nat,\n)\n requires\n candidate <= input_len,\n candidate <= cap,\n ensures\n candidate <= bounded_prefix(input_len, cap),\n","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"VERUS-BOUND"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'center_cell_in_face' in the CanonicalSlotVerify family -- registry statement: Canonical slot opposite-axis seam rejection and center-cell identity under Order B faces","coq_statement_full":"Theorem center_cell_in_face :\n forall face, face < 6 ->\n face * 9 <= center_cell face < face * 9 + 9\n /\\ center_cell face = face * 9 + 4.","coq_verified":"not stated in registry status for this 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status for this row","crate":"cubie-wwt-gateway","deployable":false,"exec_file":"agentic-cybersecurity/cubie-wwt-gateway/src/native_control_plane/route_plan_v1.rs","exec_fn":"plan","exec_fns":["plan"],"files":{},"formal_systems":"RuntimeProperty","id":"CUB-3263","invocation":"runtime","kernels":"none","kind":"Theorem","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"RoutePlanV1WouldRoute","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","repo":"cubie-tf","riscv":"no","riscv_status":"no","shas":{"coq_sha256":"pending","lean_sha256":"pending"},"source_completeness":"full (CSV-sourced)","statement":"Topology-aware RoutePlanV1 records would_route vs actual upstream; disaggregate only when isolation beats KV/network cost","status":"IN_PROGRESS","theorem_name":"route_plan_v1","use_cases":["TEP","gateway","topology"],"verification_state":"NOT_VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"none","axiom_profile":"none","context_purpose":"DERIVED: Theorem named 'backpressure_v1' in the ClosedLoopBackpressureNotices family -- registry statement: Signed pressure notices with TTL/hysteresis/recovery; congestion vs health-fault; would_defer/would_reroute never authorization failure","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"cubie-wwt-gateway","deployable":false,"exec_file":"agentic-cybersecurity/cubie-wwt-gateway/src/native_control_plane/backpressure_v1.rs","exec_fn":"verify_signature","exec_fns":["issue","sign","verify_signature","decide"],"files":{},"formal_systems":"RuntimeProperty","id":"CUB-3264","invocation":"runtime","kernels":"CL","kind":"Theorem","lean_statement_full":"","lean_verified":"not stated in registry status for this row","module":"ClosedLoopBackpressureNotices","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","repo":"cubie-tf","riscv":"no","riscv_status":"no","shas":{"coq_sha256":"pending","lean_sha256":"pending"},"source_completeness":"full (CSV-sourced)","statement":"Signed pressure notices with TTL/hysteresis/recovery; congestion vs health-fault; would_defer/would_reroute never authorization failure","status":"IN_PROGRESS","theorem_name":"backpressure_v1","use_cases":["gateway"],"verification_state":"NOT_VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"DOC-REFERENCE"} {"axiom_free_status":"AXIOM-FREE (0 axioms)","axiom_profile":"0 axioms","context_purpose":"DERIVED: Theorem named 'stickers_is_arity' in the CubieArityMeet family -- registry statement: Arity unification: sticker count = arity = blast radius; Belnap 2-bit meet PASS meet FAIL = TAMPER corner coherence","coq_statement_full":"Theorem stickers_is_arity : forall c, sticker_count c = arity c.","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"coq/CubieArityMeet.v":"5deb8ed249f81a3fae30ebe583d9a6c1c21b71e071b333e27a049fd2935ce22d","lean/CubieArityMeet.lean":"3c5be4f8f07ef14f19606cbc6be96152bd2552cbaa228b08a170ebbca9d59411"},"files":{"coq_file":"coq/CubieArityMeet.v","lean_file":"lean/CubieArityMeet.lean"},"formal_systems":"Coq+Lean+Verus","id":"CUB-3265","invocation":"unwired","kernels":"none","kind":"Theorem","lean_statement_full":"theorem stickers_is_arity (c : CarrierClass) : stickerCount c = arity c","lean_verified":"not stated in registry status for this row","module":"CubieArityMeet","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","shas":{"coq_sha256":"5deb8ed249f81a3f...","lean_sha256":"3c5be4f8f07ef14f..."},"source_completeness":"full (CSV-sourced)","statement":"Arity unification: sticker count = arity = blast radius; Belnap 2-bit meet PASS meet FAIL = TAMPER corner coherence","status":"VERIFIED","theorem_name":"stickers_is_arity","verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":"","wiring":"CSV-LEGACY"} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: CMI Turing-machine model plus the class DEFINITIONS P and NP over a binary alphabet. Class_P was machine-checked VACUOUS in its loose form and was tightened (fixed budget + required halting); Class_NP was NOT vacuous and got the same form for consistency. Both confirmed satisfiable (not over-tight). Definitions only -- proves nothing about P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityCore.v":"00c41e1b499c97ac38931797c7c63bb3cae3e24e09c4b7fc3409884b4f6ae1a9"},"files":{"coq_file":"proofs/coq/ComplexityCore.v"},"id":"CUB-COMPLEXITY-001","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"","source_completeness":"full (CSV-sourced)","statement":"CMI Turing-machine model plus the class DEFINITIONS P and NP over a binary alphabet. Class_P was machine-checked VACUOUS in its loose form and was tightened (fixed budget + required halting); Class_NP was NOT vacuous and got the same form for consistency. Both confirmed satisfiable (not over-tight). Definitions only -- proves nothing about P vs NP.","status":"definition","use_cases":["admission","complexity"],"verification_state":"NOT_VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Binary serialization of a TSP decision instance and the TSP decision language L_TSP (a CMI Language). Definition only. (compute_tour_cost fixed: a v::_ as t match parsed as tail-of-tail and summed alternating pairs -- a latent bug nothing constrained; now a clean head-carrying helper summing consecutive edges.)","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityTspLanguage.v":"e73ede21ff4f78be3db4c072381b2d91f86a95be47c78c7bbefc746443d9ec73"},"files":{"coq_file":"proofs/coq/ComplexityTspLanguage.v"},"id":"CUB-COMPLEXITY-002","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"","source_completeness":"full (CSV-sourced)","statement":"Binary serialization of a TSP decision instance and the TSP decision language L_TSP (a CMI Language). Definition only. (compute_tour_cost fixed: a v::_ as t match parsed as tail-of-tail and summed alternating pairs -- a latent bug nothing constrained; now a clean head-carrying helper summing consecutive edges.)","status":"definition","use_cases":["TSP","complexity"],"verification_state":"NOT_VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Executable poly-time NP-RELATION checker for TSP (Hamiltonicity + budget) -- Verus companion to L_TSP. Verus-verified: panic-free/in-bounds/terminating and postcondition BUDGET-SOUNDNESS (is_valid => cost <= budget). Structural checks execute but are NOT lifted into the spec; NOT a proof that L_TSP in NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/verus/complexity_tsp_np_verifier.rs":"bb05be9b6a3e042f6ffaa5a42a5fbd83f71a353cd457f7ea2cb4bf8aee7738b4"},"files":{"verus_file":"proofs/verus/complexity_tsp_np_verifier.rs"},"id":"CUB-COMPLEXITY-002-V","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"verified-checker","proof_scope":"standalone","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"verify_satisficing_witness","source_completeness":"full (CSV-sourced)","statement":"Executable poly-time NP-RELATION checker for TSP (Hamiltonicity + budget) -- Verus companion to L_TSP. Verus-verified: panic-free/in-bounds/terminating and postcondition BUDGET-SOUNDNESS (is_valid => cost <= budget). Structural checks execute but are NOT lifted into the spec; NOT a proof that L_TSP in NP.","status":"proven","use_cases":["admission","TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Canonical polynomial-time many-one reduction relation poly_reduces over the faithful finite STM: TapeSym has distinct Blank and Bit bool constructors, reachable states are bounded by s_num_states, one (k,c) is fixed up front, execution uses the exact polynomial budget, and the machine must have halted. The former Boolean-tape Blank=false relation is preserved only as legacy_poly_reduces because word_reduce is proven trailing-false-sensitive.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityReductions.v":"4a137b28fa9992d113c488a4d63dd9b135942fcbc7b0eb820175be6162bb6763"},"files":{"coq_file":"proofs/coq/ComplexityReductions.v"},"id":"CUB-COMPLEXITY-003","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"canonical contract repair; canonical_poly_reduces_is_strict is reflexive; no semantic erasure bridge","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"","source_completeness":"full (CSV-sourced)","statement":"Canonical polynomial-time many-one reduction relation poly_reduces over the faithful finite STM: TapeSym has distinct Blank and Bit bool constructors, reachable states are bounded by s_num_states, one (k,c) is fixed up front, execution uses the exact polynomial budget, and the machine must have halted. The former Boolean-tape Blank=false relation is preserved only as legacy_poly_reduces because word_reduce is proven trailing-false-sensitive.","status":"definition","use_cases":["admission","complexity"],"verification_state":"NOT_VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: 3-CNF syntax/semantics/total binary parser and the 3-SAT decision language L_3SAT. Definition only.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/Complexity3SatLanguage.v":"3a8ae31ac86fb28fbb9c5c21387bf64acfcf889fa52b1e29cb2dcb172b73fb32"},"files":{"coq_file":"proofs/coq/Complexity3SatLanguage.v"},"id":"CUB-COMPLEXITY-004","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"","source_completeness":"full (CSV-sourced)","statement":"3-CNF syntax/semantics/total binary parser and the 3-SAT decision language L_3SAT. Definition only.","status":"definition","use_cases":["complexity"],"verification_state":"NOT_VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: NP_Hard/NP_Complete DEFINITIONS over the real L_3SAT/L_TSP. Cook-Levin and TSP-completeness are STATED as open; the sole THEOREM is conditional (L_TSP NP-complete IF poly_reduces is transitive). No Admitted; 0 axioms.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityNpComplete.v":"c0c757b93c4ec7b78b0db61332ffbda5f154c89361e05eaa30fb152f523a9e7e"},"files":{"coq_file":"proofs/coq/ComplexityNpComplete.v"},"id":"CUB-COMPLEXITY-005","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"open-obligation","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"","source_completeness":"full (CSV-sourced)","statement":"NP_Hard/NP_Complete DEFINITIONS over the real L_3SAT/L_TSP. Cook-Levin and TSP-completeness are STATED as open; the sole THEOREM is conditional (L_TSP NP-complete IF poly_reduces is transitive). No Admitted; 0 axioms.","status":"open","use_cases":["admission","TSP","complexity"],"verification_state":"NOT_VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Boundary marker separating easy-sub-family from P vs NP. PROVEN (0 axioms): all-accepting and all-rejecting languages are in Class_P -- so Class_P membership of a restricted/finite/structured TSP variant says NOTHING about the general L_TSP. tsp_in_P_open := Class_P L_TSP is STATED open (a P=NP resolution is exactly its proof; its negation is P<>NP). Refutes the wreath/RG easy-sub-family = P=NP error inside the kernel.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityBoundary.v":"186e58d0b1e6978f6b4c0455589d5ade16a8b6ec06d974950c5dcb2088b8d56c"},"files":{"coq_file":"proofs/coq/ComplexityBoundary.v"},"id":"CUB-COMPLEXITY-BOUNDARY","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"boundary-lemma","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"","source_completeness":"full (CSV-sourced)","statement":"Boundary marker separating easy-sub-family from P vs NP. PROVEN (0 axioms): all-accepting and all-rejecting languages are in Class_P -- so Class_P membership of a restricted/finite/structured TSP variant says NOTHING about the general L_TSP. tsp_in_P_open := Class_P L_TSP is STATED open (a P=NP resolution is exactly its proof; its negation is P<>NP). Refutes the wreath/RG easy-sub-family = P=NP error inside the kernel.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Binary serialization + syntax/semantics of the Directed Hamiltonian Cycle decision language L_DHC (structural mirror of L_TSP). Infrastructure for the Karp chain L_3SAT <=p L_DHC <=p L_UHC <=p L_TSP. Definition only; the reductions (NP-hardness Karp 1972) are in progress. Not P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityDhcLanguage.v":"979a6259bdaca52712201eaf27a2e7d81f1414a6f65ee1d5422dc64242353598"},"files":{"coq_file":"proofs/coq/ComplexityDhcLanguage.v"},"id":"CUB-COMPLEXITY-DHC","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"","source_completeness":"full (CSV-sourced)","statement":"Binary serialization + syntax/semantics of the Directed Hamiltonian Cycle decision language L_DHC (structural mirror of L_TSP). Infrastructure for the Karp chain L_3SAT <=p L_DHC <=p L_UHC <=p L_TSP. Definition only; the reductions (NP-hardness Karp 1972) are in progress. Not P vs NP.","status":"definition","use_cases":["TSP","complexity"],"verification_state":"NOT_VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Karp Phase 2 node-tripling DHC->UHC PROVEN as a 0-axiom IFF (dhc_to_uhc_correct: dhc_instance_solvable d <-> uhc_instance_solvable (dhc_to_uhc_instance d); v -> in=3v mid=3v+1 out=3v+2; directed edge u->v -> undirected out_u--in_v). FORWARD (dhc_to_uhc_forward) via tripled_path (removelast p). BACKWARD (dhc_to_uhc_backward): traversal-forcing FULLY MECHANISED -- mid degree-2 inversions (mid_neighbor_inv/'), mid_flanked + junction_next_mid force each block, front-peel induction forward_reconstruct proves a forward-started valid UHC walk IS a tripled walk, orientation dispatched (mid0_dispatch + is_valid_uhc_rev via matrix symmetry), tripled_edges_to_chain + chain->nth bridges + project yield is_valid_dhc. NP-hardness (Karp 1972) not P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityDhcToUhc.v":"927d5e9e9892099a70023bd26fae5816c9bedd95404518b5cda7e310e5973bb2"},"files":{"coq_file":"proofs/coq/ComplexityDhcToUhc.v"},"id":"CUB-COMPLEXITY-DHC-UHC","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"dhc_to_uhc_correct (forward+backward)","source_completeness":"full (CSV-sourced)","statement":"Karp Phase 2 node-tripling DHC->UHC PROVEN as a 0-axiom IFF (dhc_to_uhc_correct: dhc_instance_solvable d <-> uhc_instance_solvable (dhc_to_uhc_instance d); v -> in=3v mid=3v+1 out=3v+2; directed edge u->v -> undirected out_u--in_v). FORWARD (dhc_to_uhc_forward) via tripled_path (removelast p). BACKWARD (dhc_to_uhc_backward): traversal-forcing FULLY MECHANISED -- mid degree-2 inversions (mid_neighbor_inv/'), mid_flanked + junction_next_mid force each block, front-peel induction forward_reconstruct proves a forward-started valid UHC walk IS a tripled walk, orientation dispatched (mid0_dispatch + is_valid_uhc_rev via matrix symmetry), tripled_edges_to_chain + chain->nth bridges + project yield is_valid_dhc. NP-hardness (Karp 1972) not P vs NP.","status":"proven","use_cases":["complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: many_one reduction algebra (poly_bound output-length + membership-preserving map): reflexivity; non-vacuity; TRANSITIVITY with the composed budget (k1*k2; c2*(c1+1)^k2) -- discharging UNCONDITIONALLY the reduction-transitivity that CUB-COMPLEXITY-005 leaves as a hypothesis; at the many_one (output-length) level which is STRICTLY WEAKER than poly_reduces (no TM required). Capstone tsp_nphard_via_many_one derives L_TSP NP-completeness from the concrete reduction with NO transitivity assumption. The stronger poly_reduces/s_poly_reduces transitivity stays gated on the item-4 word_reduce machine. 0 axioms; coqchk Axioms: .","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityGenericReduction.v":"ba7432601bf84aa9bd2603ac9c963e6ac30a682006f20b3f993bf132c5562c7b"},"files":{"coq_file":"proofs/coq/ComplexityGenericReduction.v"},"id":"CUB-COMPLEXITY-GENERIC-REDUCTION","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"many-one-level","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"many_one_trans + tsp_nphard_via_many_one","source_completeness":"full (CSV-sourced)","statement":"many_one reduction algebra (poly_bound output-length + membership-preserving map): reflexivity; non-vacuity; TRANSITIVITY with the composed budget (k1*k2; c2*(c1+1)^k2) -- discharging UNCONDITIONALLY the reduction-transitivity that CUB-COMPLEXITY-005 leaves as a hypothesis; at the many_one (output-length) level which is STRICTLY WEAKER than poly_reduces (no TM required). Capstone tsp_nphard_via_many_one derives L_TSP NP-completeness from the concrete reduction with NO transitivity assumption. The stronger poly_reduces/s_poly_reduces transitivity stays gated on the item-4 word_reduce machine. 0 axioms; coqchk Axioms: .","status":"proven","use_cases":["admission","TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Capstone composing the Karp chain at instance-solvability level. PROVEN (0 axioms): threesat_to_dhc_reduction, dhc_to_uhc_reduction, uhc_to_tsp_reduction, and karp_chain_solvability_closed discharge all three instance phases. word_reduce_correct packages the total membership-preserving Word map. The canonical finite-machine Phase-4 wrapper is discharged downstream by CUB-COMPLEXITY-STRICT-ENCODE-TSP. NP-hardness (Karp 1972), not P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityKarpChain.v":"abe9aaa192f9d156faf285381141aa9980346e1a5f2387b55baa03942b5609c7"},"files":{"coq_file":"proofs/coq/ComplexityKarpChain.v"},"id":"CUB-COMPLEXITY-KARP-CHAIN","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"instance chain closed in this module; canonical poly_reduces close is phase4_poly_reduces in proofs/coq/ComplexityStrictEncodeTsp.v","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"karp_chain_solvability_closed + threesat_to_dhc_reduction + word_reduce_correct","source_completeness":"full (CSV-sourced)","statement":"Capstone composing the Karp chain at instance-solvability level. PROVEN (0 axioms): threesat_to_dhc_reduction, dhc_to_uhc_reduction, uhc_to_tsp_reduction, and karp_chain_solvability_closed discharge all three instance phases. word_reduce_correct packages the total membership-preserving Word map. The canonical finite-machine Phase-4 wrapper is discharged downstream by CUB-COMPLEXITY-STRICT-ENCODE-TSP. NP-hardness (Karp 1972), not P vs NP.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: concrete instantiation of the many_one algebra: many_one L_3SAT L_TSP is now a 0-axiom THEOREM via word_reduce. The content is poly_bound 4 (7*72*72) word_reduce -- output length <= 36288*(|w|+1)^4 -- proven from the UNARY-parser size lemmas (split_clauses_length; decode_len; formula_maxvar via trues-conservation -> num_clauses/num_vars <= O(|w|)) chained through karp_g_size_poly + word_reduce_length. Discharges the reduction premise of tsp_nphard_via_many_one; the premise-lighter capstone tsp_nphard_via_many_one_concrete needs ONLY Cook-Levin + TSP-in-NP (both open). LENGTH side only -- poly-TIME poly_reduces/s_poly_reduces still needs the item-4 machine. 0 axioms; coqchk Axioms: .","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityManyOneInstance.v":"d5d686fb30b3e7ecc1d9bc60e0d546ab01273b02be539ece6256d8e783605dc6"},"files":{"coq_file":"proofs/coq/ComplexityManyOneInstance.v"},"id":"CUB-COMPLEXITY-MANY-ONE-INSTANCE","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"many-one-level","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"many_one_3sat_tsp + tsp_nphard_via_many_one_concrete","source_completeness":"full (CSV-sourced)","statement":"concrete instantiation of the many_one algebra: many_one L_3SAT L_TSP is now a 0-axiom THEOREM via word_reduce. The content is poly_bound 4 (7*72*72) word_reduce -- output length <= 36288*(|w|+1)^4 -- proven from the UNARY-parser size lemmas (split_clauses_length; decode_len; formula_maxvar via trues-conservation -> num_clauses/num_vars <= O(|w|)) chained through karp_g_size_poly + word_reduce_length. Discharges the reduction premise of tsp_nphard_via_many_one; the premise-lighter capstone tsp_nphard_via_many_one_concrete needs ONLY Cook-Levin + TSP-in-NP (both open). LENGTH side only -- poly-TIME poly_reduces/s_poly_reduces still needs the item-4 machine. 0 axioms; coqchk Axioms: .","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Resolution propositional proof system (literals/clauses/CNF + the resolution rule) with a PROVEN soundness theorem (a refutation deriving the empty clause => the CNF is unsatisfiable; 0 axioms). Soundness is a CORRECTNESS property NOT a lower bound. Haken 1985 (Resolution refutations of PHP_{N+1,N} have size 2^Omega(N)) is STATED over the concrete generator generate_PHP_CNF and the resolution_size metric as open obligation haken_resolution_lower_bound_open NOT proven. Proof-complexity infrastructure; does not approach P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityProofSystem.v":"4711afe41a7925574f9cbb1a06d29292e07dc1a200e7e66b4274cdd4fb05edac"},"files":{"coq_file":"proofs/coq/ComplexityProofSystem.v"},"id":"CUB-COMPLEXITY-PROOFSYS","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"infrastructure","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"","source_completeness":"full (CSV-sourced)","statement":"Resolution propositional proof system (literals/clauses/CNF + the resolution rule) with a PROVEN soundness theorem (a refutation deriving the empty clause => the CNF is unsatisfiable; 0 axioms). Soundness is a CORRECTNESS property NOT a lower bound. Haken 1985 (Resolution refutations of PHP_{N+1,N} have size 2^Omega(N)) is STATED over the concrete generator generate_PHP_CNF and the resolution_size metric as open obligation haken_resolution_lower_bound_open NOT proven. Proof-complexity infrastructure; does not approach P vs NP.","status":"architectural","use_cases":["complexity"],"verification_state":"NOT_VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: first brick toward Haken 1985 over generate_PHP_CNF. php_unsatisfiable: PHP_N unsatisfiable for every N (constructive finite pigeonhole no_injection + hole-function extraction). php_refutation_contains_every_axiom: minimal unsatisfiability -- every Resolution refutation of PHP_N contains every axiom clause (derivation_avoid filtering + resolution_soundness + explicit matching-assignment witnesses php_minus_pigeon_sat/php_minus_hole_sat). php_resolution_cubic_lower_bound: 2*size >= 4 + 2(N+1) + N^2(N+1), an Omega(N^3) size lower bound for all N>=1. php1_refutation_min_size: PHP_1 refutations need >= 5 lines (tight). HONEST SCOPE: Omega(N^3) is polynomial -- haken_resolution_lower_bound_open (exponential) remains OPEN; next brick = width bound via matching-restricted entailment measure (Ben-Sasson--Wigderson route).","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityProofSystemHaken1.v":"1dad280668fab6e2a526e1961d4dffb9fc07eed111ba8aff8d182ac4a575691d"},"files":{"coq_file":"proofs/coq/ComplexityProofSystemHaken1.v"},"id":"CUB-COMPLEXITY-PROOFSYS-HAKEN1","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; 34 Qed; coq-only proof-complexity corpus, no Lean/Verus mirror","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"php_unsatisfiable + php_refutation_contains_every_axiom + php_resolution_cubic_lower_bound + php1_refutation_min_size","source_completeness":"full (CSV-sourced)","statement":"first brick toward Haken 1985 over generate_PHP_CNF. php_unsatisfiable: PHP_N unsatisfiable for every N (constructive finite pigeonhole no_injection + hole-function extraction). php_refutation_contains_every_axiom: minimal unsatisfiability -- every Resolution refutation of PHP_N contains every axiom clause (derivation_avoid filtering + resolution_soundness + explicit matching-assignment witnesses php_minus_pigeon_sat/php_minus_hole_sat). php_resolution_cubic_lower_bound: 2*size >= 4 + 2(N+1) + N^2(N+1), an Omega(N^3) size lower bound for all N>=1. php1_refutation_min_size: PHP_1 refutations need >= 5 lines (tight). HONEST SCOPE: Omega(N^3) is polynomial -- haken_resolution_lower_bound_open (exponential) remains OPEN; next brick = width bound via matching-restricted entailment measure (Ben-Sasson--Wigderson route).","status":"proven","use_cases":["complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Haken chain brick 1/4: matching-assignment layer over generate_PHP_CNF. pmatching + pm_wf (partial injection pigeons->holes, total on holes: |M|=N) + pm_assign (induced assignment via phi encoding) + entails_m (matching-restricted entailment). Lemmas: total_matching_exists (id_matching wf), hole_axioms_entailed, entails_m_weaken, pm_assign_true_iff.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityProofSystemHaken2a.v":"5d4ec79367fc72b80f0d6aeef85ba9f031258f3061f1ef65b5bdf44631931003"},"files":{"coq_file":"proofs/coq/ComplexityProofSystemHaken2a.v"},"id":"CUB-COMPLEXITY-PROOFSYS-HAKEN2A","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only proof-complexity corpus","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"pmatching + pm_assign + entails_m + hole_axioms_entailed","source_completeness":"full (CSV-sourced)","statement":"Haken chain brick 1/4: matching-assignment layer over generate_PHP_CNF. pmatching + pm_wf (partial injection pigeons->holes, total on holes: |M|=N) + pm_assign (induced assignment via phi encoding) + entails_m (matching-restricted entailment). Lemmas: total_matching_exists (id_matching wf), hole_axioms_entailed, entails_m_weaken, pm_assign_true_iff.","status":"proven","use_cases":["complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Haken chain brick 2/4: the mu measure in predicate form. covers N S C (every wf matching satisfying pigeon axioms of S satisfies C) + mu_at_most N k C (exists covering pigeon-set of size <= k). mu_hole_axiom (<=0), mu_pigeon_axiom (<=1), mu_subadditive (resolvent covered by S1++S2, deduped), mu_empty_clause_hard (~mu_at_most N N empty_clause via skip_matching construction).","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityProofSystemHaken2b.v":"fa6b06aa4aaec40b6aa9c48007f824e94824b948f1d1af6a3d2e123168203628"},"files":{"coq_file":"proofs/coq/ComplexityProofSystemHaken2b.v"},"id":"CUB-COMPLEXITY-PROOFSYS-HAKEN2B","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only proof-complexity corpus","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"covers + mu_at_most + mu_subadditive + mu_empty_clause_hard","source_completeness":"full (CSV-sourced)","statement":"Haken chain brick 2/4: the mu measure in predicate form. covers N S C (every wf matching satisfying pigeon axioms of S satisfies C) + mu_at_most N k C (exists covering pigeon-set of size <= k). mu_hole_axiom (<=0), mu_pigeon_axiom (<=1), mu_subadditive (resolvent covered by S1++S2, deduped), mu_empty_clause_hard (~mu_at_most N N empty_clause via skip_matching construction).","status":"proven","use_cases":["complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Haken chain brick 3a/4: decidability by finite enumeration -- the constructive excluded-middle the IVT walk needs (repo forbids classical axioms). sublists (2^n) + sublists_complete; covers_b + covers_b_iff (full two-directional reflection); mu_at_most_b + mu_at_most_b_iff; mu_at_most_dec.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityProofSystemHaken2c.v":"44c3b24f7afd2d7ff3ba661644e358ecee3326f1cea2c00d8ad6564540c0dda1"},"files":{"coq_file":"proofs/coq/ComplexityProofSystemHaken2c.v"},"id":"CUB-COMPLEXITY-PROOFSYS-HAKEN2C","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only proof-complexity corpus","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"covers_b_iff + mu_at_most_b_iff + mu_at_most_dec","source_completeness":"full (CSV-sourced)","statement":"Haken chain brick 3a/4: decidability by finite enumeration -- the constructive excluded-middle the IVT walk needs (repo forbids classical axioms). sublists (2^n) + sublists_complete; covers_b + covers_b_iff (full two-directional reflection); mu_at_most_b + mu_at_most_b_iff; mu_at_most_dec.","status":"proven","use_cases":["complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Haken chain brick 3b/4: the IVT walk. derivation_first_failure (generic decidable first-failure over a derivation: failing line is axiom or resolvent of two passing lines) + ivt_medium_mu: every refutation of PHP_N (N>=3) contains a clause C with ~mu_at_most N (N/3) C and mu_at_most N (2*(N/3)) C -- exact constant 2*(N/3), tighter than 2*(N/3)+1.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityProofSystemHaken2d.v":"e2ca9c15efafaedd4355134f3586f58969a68e988aa2a4bd808709d7f5812f5d"},"files":{"coq_file":"proofs/coq/ComplexityProofSystemHaken2d.v"},"id":"CUB-COMPLEXITY-PROOFSYS-HAKEN2D","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only proof-complexity corpus","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"ivt_medium_mu + derivation_first_failure + mu_at_most_mono_k","source_completeness":"full (CSV-sourced)","statement":"Haken chain brick 3b/4: the IVT walk. derivation_first_failure (generic decidable first-failure over a derivation: failing line is axiom or resolvent of two passing lines) + ivt_medium_mu: every refutation of PHP_N (N>=3) contains a clause C with ~mu_at_most N (N/3) C and mu_at_most N (2*(N/3)) C -- exact constant 2*(N/3), tighter than 2*(N/3)+1.","status":"proven","use_cases":["complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Haken chain brick 4/4 -- THE WIDTH LOWER BOUND (Ben-Sasson--Wigderson stepping stone to Haken 1985). php_width_lower_bound: every resolution refutation of generate_PHP_CNF N (N>=3) contains a clause of width > N/3 (strict; K=3, the full textbook constant). Engine: minimize_cover (constructive minimal covering set via covers_b reflection), witness_unmatched, swap_flip_literal (total-matching swap flip), dichotomy count (every p in S0 mentioned => width >= |S0| > N/3; some p unmentioned => every eligible swap edge yields a distinct literal => width >= N-|S0|+1 > N/3). HONEST SCOPE: the exponential haken_resolution_lower_bound_open remains OPEN -- the missing step is the size-width tradeoff.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityProofSystemHaken2e.v":"db0a9a02aba0e5cb36d6b66f78f24938191befca010b7cadc60e555341e45aaf"},"files":{"coq_file":"proofs/coq/ComplexityProofSystemHaken2e.v"},"id":"CUB-COMPLEXITY-PROOFSYS-HAKEN2E","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only proof-complexity corpus; 351 lines","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"php_width_lower_bound + minimize_cover + swap_flip_literal","source_completeness":"full (CSV-sourced)","statement":"Haken chain brick 4/4 -- THE WIDTH LOWER BOUND (Ben-Sasson--Wigderson stepping stone to Haken 1985). php_width_lower_bound: every resolution refutation of generate_PHP_CNF N (N>=3) contains a clause of width > N/3 (strict; K=3, the full textbook constant). Engine: minimize_cover (constructive minimal covering set via covers_b reflection), witness_unmatched, swap_flip_literal (total-matching swap flip), dichotomy count (every p in S0 mentioned => width >= |S0| > N/3; some p unmentioned => every eligible swap edge yields a distinct literal => width >= N-|S0|+1 > N/3). HONEST SCOPE: the exponential haken_resolution_lower_bound_open remains OPEN -- the missing step is the size-width tradeoff.","status":"proven","use_cases":["TEP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: single-polynomial BUDGET WRAPPER closing the composition layer (the item-(i) gap bricks 6/7 left open): machine-intrinsic output bound (clean_output_length -- tape grows <=1 cell per step via s_step_tsize; s_extract <= tape; s_init <= |w|+1 cells; so |f w| <= |w|+1+budget with NO poly_bound hypothesis); explicit budget algebra seq_K=(k1+1)*(k2+1) and seq_C=2*(c1+c2+c2*(2c1+1)^k2)*2^seq_K (seq_budget; (n+1)-power basis + pow_base_succ_le conversion keep nia on small symbolic terms); stm_seq_clean_computes_poly (clean o computes = genuine s_computes_in_poly_strict at the explicit budget -- brick 6 upgraded); stm_seq_clean_preserves_poly (clean o clean = clean at the explicit budget; composite halt time pinned <=t1+t2 by never-halts-early minimality -- brick 7 upgraded); s_bounded_halt_has_first derives the least/never-early halt witness from any bounded halt; s_clean_implies_computes; capstone s_phase4_from_stage_machines: two clean transducers g1 g2 + a computer g3 with g3(g2(g1 w)) = word_reduce w discharge s_poly_reduces L_3SAT L_TSP outright. Does NOT build any stage machine; strict wrapper remains OPEN reduced to exactly the three stage machines. NP-hardness (Karp 1972) not P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictBudget.v":"95fbaf90dab398d455969c5d123d5507ff59b3611352fa8349239a554ecadfa3"},"files":{"coq_file":"proofs/coq/ComplexityStrictBudget.v"},"id":"CUB-COMPLEXITY-STRICT-BUDGET","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_phase4_from_stage_machines + stm_seq_clean_computes_poly + stm_seq_clean_preserves_poly + s_bounded_halt_has_first","source_completeness":"full (CSV-sourced)","statement":"single-polynomial BUDGET WRAPPER closing the composition layer (the item-(i) gap bricks 6/7 left open): machine-intrinsic output bound (clean_output_length -- tape grows <=1 cell per step via s_step_tsize; s_extract <= tape; s_init <= |w|+1 cells; so |f w| <= |w|+1+budget with NO poly_bound hypothesis); explicit budget algebra seq_K=(k1+1)*(k2+1) and seq_C=2*(c1+c2+c2*(2c1+1)^k2)*2^seq_K (seq_budget; (n+1)-power basis + pow_base_succ_le conversion keep nia on small symbolic terms); stm_seq_clean_computes_poly (clean o computes = genuine s_computes_in_poly_strict at the explicit budget -- brick 6 upgraded); stm_seq_clean_preserves_poly (clean o clean = clean at the explicit budget; composite halt time pinned <=t1+t2 by never-halts-early minimality -- brick 7 upgraded); s_bounded_halt_has_first derives the least/never-early halt witness from any bounded halt; s_clean_implies_computes; capstone s_phase4_from_stage_machines: two clean transducers g1 g2 + a computer g3 with g3(g2(g1 w)) = word_reduce w discharge s_poly_reduces L_3SAT L_TSP outright. Does NOT build any stage machine; strict wrapper remains OPEN reduced to exactly the three stage machines. NP-hardness (Karp 1972) not P vs NP.","status":"proven","use_cases":["TEP","admission","TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Ten-state total fused unary halve-plus-successor. s_ceilhalve_clean_pad computes repeat true (S (halve (bit_to_nat w))) for every word with first-halt minimality, canonical blank padding, and budget 6*|w|^2+6; unary specialization is the terminal num_vars arithmetic.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictCeilHalve.v":"bf9840cea33ab32205c69066b0db7ff085d21177f6c24561fbc4a812fd8dd16a"},"files":{"coq_file":"proofs/coq/ComplexityStrictCeilHalve.v"},"id":"CUB-COMPLEXITY-STRICT-CEIL-HALVE","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; wrong-halving and missing-successor Fail controls included","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_ceilhalve_run + ch_total_fuel_quadratic + s_ceilhalve_clean_pad","source_completeness":"full (CSV-sourced)","statement":"Ten-state total fused unary halve-plus-successor. s_ceilhalve_clean_pad computes repeat true (S (halve (bit_to_nat w))) for every word with first-halt minimality, canonical blank padding, and budget 6*|w|^2+6; unary specialization is the terminal num_vars arithmetic.","status":"proven","use_cases":["admission","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: {1,2}-cell reduction of strict Phase-4: word_reduce_stream's grid cells are 1 (edge) or 2 (non-edge) per the UHC->TSP cost gadget, budget B=N. word_reduce_stream_bit restates the emission as enc_nat N (twice) ++ an N*N grid of edge-bit-selected 2/3-bit constants; strict_phase4_reduced_to_edge_decision shows a strict machine for that form closes s_poly_reduces (via s_phase4_from_stream). Narrows the SOLE open residual from 'compute an arbitrary nat per cell' to 'decide one edge bit karp_edge = uhc_matrix(dhc_to_uhc(threesat_to_dhc2(parse_3sat w))) u v'. This module does NOT build that decider. CLOSED by proofs/coq/ComplexityStrictCellClose.v (2026-08-12): word_reduce IS the {1,2}-cell emission (word_reduce_bit_form), so the s_encode_tsp witness of CUB-COMPLEXITY-STRICT-ENCODE-TSP discharges the exact existential premise (strict_cell_premise) and strict_cell_residual_closed derives strict s_poly_reduces L_3SAT L_TSP through strict_phase4_reduced_to_edge_decision itself. NP-hardness (Karp 1972), not P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictCell.v":"7d345ff6c267d7d0694f5458c1906e67435cc0c8e850e4371ef52cbdf1d8d69c"},"files":{"coq_file":"proofs/coq/ComplexityStrictCell.v"},"id":"CUB-COMPLEXITY-STRICT-CELL","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror; closure theorems live in proofs/coq/ComplexityStrictCellClose.v (ComplexityStrictCell.v itself byte-unchanged)","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"word_reduce_bit_form + s_encode_tsp_computes_bit_form + strict_cell_premise + strict_cell_residual_closed + strict_cell_residual_closed_canonical","source_completeness":"full (CSV-sourced)","statement":"{1,2}-cell reduction of strict Phase-4: word_reduce_stream's grid cells are 1 (edge) or 2 (non-edge) per the UHC->TSP cost gadget, budget B=N. word_reduce_stream_bit restates the emission as enc_nat N (twice) ++ an N*N grid of edge-bit-selected 2/3-bit constants; strict_phase4_reduced_to_edge_decision shows a strict machine for that form closes s_poly_reduces (via s_phase4_from_stream). Narrows the SOLE open residual from 'compute an arbitrary nat per cell' to 'decide one edge bit karp_edge = uhc_matrix(dhc_to_uhc(threesat_to_dhc2(parse_3sat w))) u v'. This module does NOT build that decider. CLOSED by proofs/coq/ComplexityStrictCellClose.v (2026-08-12): word_reduce IS the {1,2}-cell emission (word_reduce_bit_form), so the s_encode_tsp witness of CUB-COMPLEXITY-STRICT-ENCODE-TSP discharges the exact existential premise (strict_cell_premise) and strict_cell_residual_closed derives strict s_poly_reduces L_3SAT L_TSP through strict_phase4_reduced_to_edge_decision itself. NP-hardness (Karp 1972), not P vs NP.","status":"proven","use_cases":["admission","TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Canonical clean-word packaging for the total parser-faithful literal-table machine. The canonical bit-only record is false :: sat_N_frame(w) ++ [false] ++ true^i ++ [false] ++ true^j ++ [false;pos;acc], whose exact length is clause_seek_span(w,i,j). A well-formed 9-state physical unpacker converts only its marker and three serialized separators to distinct Blank cells, preserving arbitrary metadata behind the frame/base sentinel and landing at the existing selector-ready raw layout. The unchanged well-formed 252-state total raw machine executes, and a well-formed 8-state physical packer restores every serialized separator and the leading marker. Their well-formed 269-state composition has a least halt within 70*(clause_seek_span w i j)^2 for every w,i,j,pos,acc and arbitrary TapeSym base, preserves the complete frame/query/base, and changes only acc to acc OR serialized_literal_table(sat_N_frame w,i,j,pos). For base=[] the result is exactly blank_padded and extracts to the canonical output word. Controls execute default and in-range branches, polarity mutation, partial-clause parsing, nonzero fields, exact early nonhalt, arbitrary mixed base preservation, and rejected wrong accumulator/marker/separator layouts. This is an indexed canonical-record theorem, not a decoder or acceptance claim for arbitrary malformed Words. Finite descriptor encoding/comparison, karp_edge, grid emission, encode_tsp, and the strict reduction capstone remain OPEN.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictClauseClean.v":"5f6c0568cc4994435dbd9215d61f1fb1ff173658d71150864ae833077ced202c"},"files":{"coq_file":"proofs/coq/ComplexityStrictClauseClean.v"},"id":"CUB-COMPLEXITY-STRICT-CLAUSE-CLEAN","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk Axioms:; exact 269-state product and 70*span^2 least-halt bound; malformed-record semantics intentionally unspecified; descriptor/edge stage remains open","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"sat_literal_query_word_span + s_literal_query_unpack_state_bound + s_literal_query_unpack_well_formed + literal_query_unpack_exact_run + literal_query_unpack_first_halt + s_literal_query_pack_state_bound + s_literal_query_pack_well_formed + literal_query_pack_exact_run + literal_query_pack_first_halt + s_sat_literal_table_clean_state_bound + s_sat_literal_table_clean_well_formed + sat_literal_table_clean_first_halt_span_base + sat_literal_table_clean_first_halt_span + sat_literal_table_clean_extract","source_completeness":"full (CSV-sourced)","statement":"Canonical clean-word packaging for the total parser-faithful literal-table machine. The canonical bit-only record is false :: sat_N_frame(w) ++ [false] ++ true^i ++ [false] ++ true^j ++ [false;pos;acc], whose exact length is clause_seek_span(w,i,j). A well-formed 9-state physical unpacker converts only its marker and three serialized separators to distinct Blank cells, preserving arbitrary metadata behind the frame/base sentinel and landing at the existing selector-ready raw layout. The unchanged well-formed 252-state total raw machine executes, and a well-formed 8-state physical packer restores every serialized separator and the leading marker. Their well-formed 269-state composition has a least halt within 70*(clause_seek_span w i j)^2 for every w,i,j,pos,acc and arbitrary TapeSym base, preserves the complete frame/query/base, and changes only acc to acc OR serialized_literal_table(sat_N_frame w,i,j,pos). For base=[] the result is exactly blank_padded and extracts to the canonical output word. Controls execute default and in-range branches, polarity mutation, partial-clause parsing, nonzero fields, exact early nonhalt, arbitrary mixed base preservation, and rejected wrong accumulator/marker/separator layouts. This is an indexed canonical-record theorem, not a decoder or acceptance claim for arbitrary malformed Words. Finite descriptor encoding/comparison, karp_edge, grid emission, encode_tsp, and the strict reduction capstone remain OPEN.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: the FIRST machine-to-parse bridge, closing the Div3 brick's recorded honest-scope gap: split_len_terminated (on delimiter-terminated encodings -- last w false = false, [] included via the default -- #parts = #false exactly; the dangling-true divergence is precisely what termination excludes), decode_len_div3 (clauses consume three parts at a time = floor division, fuel-indexed depth-3 induction), num_clauses_parse (num_clauses (parse_3sat w) = #false(w)/3 on terminated w). HEADLINE clause_counter_counts_clauses: on every delimiter-terminated encoding the strict machine clause_counter HALTS within its proven polynomial budget with s_extract = repeat true (num_clauses (parse_3sat w)) -- a strict finite machine provably producing a parameter of the PARSED formula. Two Symbol-vs-bool elaboration traps resolved (forall w : Word annotation; conversion-change over rewrite for mixed @cons elaborations). Stage bodies num_vars/N/grid remain; strict wrapper OPEN. NP-hardness (Karp 1972) not P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictClauseCount.v":"5176a3d74b81ba6818317816e161b64255b2b5de4c98f02b1df34e5579f857e6"},"files":{"coq_file":"proofs/coq/ComplexityStrictClauseCount.v"},"id":"CUB-COMPLEXITY-STRICT-CLAUSE-COUNT","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"clause_counter_counts_clauses + num_clauses_parse","source_completeness":"full (CSV-sourced)","statement":"the FIRST machine-to-parse bridge, closing the Div3 brick's recorded honest-scope gap: split_len_terminated (on delimiter-terminated encodings -- last w false = false, [] included via the default -- #parts = #false exactly; the dangling-true divergence is precisely what termination excludes), decode_len_div3 (clauses consume three parts at a time = floor division, fuel-indexed depth-3 induction), num_clauses_parse (num_clauses (parse_3sat w) = #false(w)/3 on terminated w). HEADLINE clause_counter_counts_clauses: on every delimiter-terminated encoding the strict machine clause_counter HALTS within its proven polynomial budget with s_extract = repeat true (num_clauses (parse_3sat w)) -- a strict finite machine provably producing a parameter of the PARSED formula. Two Symbol-vs-bool elaboration traps resolved (forall w : Word annotation; conversion-change over rewrite for mixed @cons elaborations). Stage bodies num_vars/N/grid remain; strict wrapper OPEN. NP-hardness (Karp 1972) not P vs NP.","status":"proven","use_cases":["admission","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Standalone parser-default clause-query cycle. The well-formed 10-state s_clause_default_scan_raw walks the selector-ready SAT frame and unary i/j query fields, preserves every cell, and computes sticky acc OR (i=0 AND pos) at the far-right Blank in exactly |sat_N_frame w|+i+j+5 steps. Hstate0 is the exact existing qrf_start_cfg; composition with the 8-state reframe gives the well-formed 18-state s_sat_clause_default_cycle_raw. Its whole-product first halt returns the exact selector-ready layout within 2*clause_seek_span for every i and j. Under num_clauses(parse_3sat w)<=j, the output is exactly acc OR serialized_literal_table(sat_N_frame w,i,j,pos). Executable controls cover empty/default-positive, one-step-early nonhalt, sticky accumulator, and a rejected wrong output. This remains the standalone default branch body; the parser-faithful range marker and physical router now compose it with the in-range product as a total raw machine. No |w|-only bound is claimed for arbitrary external unary j. Canonical clean padding, karp_edge, grid emission, encode_tsp, and the strict capstone remain OPEN.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictClauseDefault.v":"a5d4a7eb4bcc14feb94fcbc8e0bbec2ea3f9be91371e6cc9529e028b0f77b495"},"files":{"coq_file":"proofs/coq/ComplexityStrictClauseDefault.v"},"id":"CUB-COMPLEXITY-STRICT-CLAUSE-DEFAULT","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; exact 18-state default body; total raw routing closed in CUB-COMPLEXITY-STRICT-CLAUSE-ROUTER; clean-pad interface remains open","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"tally_bits_right_same + s_clause_default_scan_raw_state_bound + s_clause_default_scan_raw_well_formed + clause_default_scan_exact_run + clause_default_scan_first_halt + s_sat_clause_default_cycle_raw_state_bound + s_sat_clause_default_cycle_raw_well_formed + sat_clause_default_cycle_first_halt_span + sat_clause_default_cycle_literal_table_first_halt_span","source_completeness":"full (CSV-sourced)","statement":"Standalone parser-default clause-query cycle. The well-formed 10-state s_clause_default_scan_raw walks the selector-ready SAT frame and unary i/j query fields, preserves every cell, and computes sticky acc OR (i=0 AND pos) at the far-right Blank in exactly |sat_N_frame w|+i+j+5 steps. Hstate0 is the exact existing qrf_start_cfg; composition with the 8-state reframe gives the well-formed 18-state s_sat_clause_default_cycle_raw. Its whole-product first halt returns the exact selector-ready layout within 2*clause_seek_span for every i and j. Under num_clauses(parse_3sat w)<=j, the output is exactly acc OR serialized_literal_table(sat_N_frame w,i,j,pos). Executable controls cover empty/default-positive, one-step-early nonhalt, sticky accumulator, and a rejected wrong output. This remains the standalone default branch body; the parser-faithful range marker and physical router now compose it with the in-range product as a total raw machine. No |w|-only bound is claimed for arbitrary external unary j. Canonical clean padding, karp_edge, grid emission, encode_tsp, and the strict capstone remain OPEN.","status":"proven","use_cases":["TEP","TSP","complexity","topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Total payload-preserving clause-field appender and parser-safe joint-frame specification. The 28-state s_clauseframe_raw preserves every input bit and appends enc_nat(count_false(w)/3), with first-halt minimality, canonical blank padding, and budget 24*|w|^2+24 on every word. The 41-state s_clauseframe precomposes normalization and emits normalize_complete_clauses(w) ++ enc_nat(num_clauses(parse_3sat w)) under one seq_K/seq_C budget. sat_parameter_frame proves that exactly two suffix fields, num_vars then num_clauses, preserve parse_3sat and are physically recoverable; appending a third field is an executable negative control. The payload-preserving num_vars machine needed to compute that two-field target remains open.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictClauseFrame.v":"e3a5fb8257902ab86ca47c0d85907bda22ad7b5e5eeab761e8503fcfa446937f"},"files":{"coq_file":"proofs/coq/ComplexityStrictClauseFrame.v"},"id":"CUB-COMPLEXITY-STRICT-CLAUSE-FRAME","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; total formula-plus-clause machine closed; two-field joint-frame semantics pinned; payload-preserving num_vars/N/grid/final reduction open","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_clauseframe_raw_clean_pad + s_clauseframe_clean_pad + sat_parameter_frame_parse + sat_parameter_fields_exact","source_completeness":"full (CSV-sourced)","statement":"Total payload-preserving clause-field appender and parser-safe joint-frame specification. The 28-state s_clauseframe_raw preserves every input bit and appends enc_nat(count_false(w)/3), with first-halt minimality, canonical blank padding, and budget 24*|w|^2+24 on every word. The 41-state s_clauseframe precomposes normalization and emits normalize_complete_clauses(w) ++ enc_nat(num_clauses(parse_3sat w)) under one seq_K/seq_C budget. sat_parameter_frame proves that exactly two suffix fields, num_vars then num_clauses, preserve parse_3sat and are physically recoverable; appending a third field is an executable negative control. The payload-preserving num_vars machine needed to compute that two-field target remains open.","status":"proven","use_cases":["admission","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Thirteen-state total parser-preserving complete-clause normalizer. normalize_mod3_correct identifies the executable machine specification with normalize_complete_clauses; s_clause_normalize_clean_pad proves first-halt minimality, canonical blank padding, and budget 3*|w|+3 for every word.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictClauseNormalize.v":"8d3a02273eb83f80e4be2979fe9fae0df54da6c137f2346a0e915fc5165033b8"},"files":{"coq_file":"proofs/coq/ComplexityStrictClauseNormalize.v"},"id":"CUB-COMPLEXITY-STRICT-CLAUSE-NORMALIZE","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; Route B total normalizer; negative mutation control included","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"normalize_mod3_correct + s_clause_normalize_clean_pad","source_completeness":"full (CSV-sourced)","statement":"Thirteen-state total parser-preserving complete-clause normalizer. normalize_mod3_correct identifies the executable machine specification with normalize_complete_clauses; s_clause_normalize_clean_pad proves first-halt minimality, canonical blank padding, and budget 3*|w|+3 for every word.","status":"proven","use_cases":["admission","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: IN-RANGE first-literal operational composition. The 61-state s_sat_clause_first_query_raw is the finite product of the 22-state preservation-safe clause selector and the 39-state arbitrary-middle query. The exact selector halt is physically identical to the query start; the whole product has a least halt within 20*(frame+i+j+6)^2, and under grid-range premises within the explicit strict quartic constant (20*900*16)*|w|^4+(20*900*16). Its final tapes exactly encode acc OR the selected clause's first tally. A checked negative control proves direct query reentry halts on the far-right Blank, so a real reframe/reselect adapter is required before later tallies. The complete in-range three-tally product is closed separately; total out-of-range behavior, clean padding, karp_edge, grid emission, encode_tsp, and the strict capstone remain OPEN.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictClauseQuery.v":"868f73287485dbc6d6792a809fd166182ecf7445f6be0315af8eb6b0283aa46b"},"files":{"coq_file":"proofs/coq/ComplexityStrictClauseQuery.v"},"id":"CUB-COMPLEXITY-STRICT-CLAUSE-QUERY","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; pinned Coq compile; whole-product halt minimality and explicit quartic input budget; one-tally in-range raw brick","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_sat_clause_first_query_raw_state_bound + s_sat_clause_first_query_raw_well_formed + sat_clause_seek_literal_init + sat_clause_first_query_first_halt_span + sat_clause_first_query_first_halt_strict_quartic + slm_done_direct_reentry_halted","source_completeness":"full (CSV-sourced)","statement":"IN-RANGE first-literal operational composition. The 61-state s_sat_clause_first_query_raw is the finite product of the 22-state preservation-safe clause selector and the 39-state arbitrary-middle query. The exact selector halt is physically identical to the query start; the whole product has a least halt within 20*(frame+i+j+6)^2, and under grid-range premises within the explicit strict quartic constant (20*900*16)*|w|^4+(20*900*16). Its final tapes exactly encode acc OR the selected clause's first tally. A checked negative control proves direct query reentry halts on the far-right Blank, so a real reframe/reselect adapter is required before later tallies. The complete in-range three-tally product is closed separately; total out-of-range behavior, clean padding, karp_edge, grid emission, encode_tsp, and the strict capstone remain OPEN.","status":"proven","use_cases":["admission","TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Complete IN-RANGE three-literal table query product. The well-formed 212-state s_sat_clause_three_query_raw composes three selector/query/reframe cycles: 69 states for tally one, 71 for tally two after one delimiter, and 72 for tally three after two delimiters. Its whole-product least halt returns the exact selector-ready SAT frame within 63*(clause_seek_span)^2, with the sticky accumulator equal to acc OR serialized_literal_table(sat_N_frame w,i,j,pos). Under grid-range premises the explicit strict quartic constant is 63*900*16 = 907200. Third-prefix reconstruction proves the physical Blank frame/base sentinel remains load-bearing. A checked halted-machine counterexample at j=num_clauses directly disagrees with the serialized parser table, so this standalone selector cannot decide range. The parser-default body, range marker, and physical router are closed separately as the total raw literal-table product. This theorem remains the raw internal-layout, j-in-range branch result; canonical clean padding, finite karp_edge, grid emission, encode_tsp, and the strict capstone remain OPEN.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictClauseQueryAll.v":"3d22b6e08ce4dc9ebdfff5204853d02904b52bed0b0422cc55b6d1b3d1630035"},"files":{"coq_file":"proofs/coq/ComplexityStrictClauseQueryAll.v"},"id":"CUB-COMPLEXITY-STRICT-CLAUSE-QUERY-ALL","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; exact 212-state in-range product; total raw routing closed in CUB-COMPLEXITY-STRICT-CLAUSE-ROUTER; clean-pad stage remains open","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"ci_third_query_frame_reconstruct + s_sat_clause_third_cycle_raw_state_bound + s_sat_clause_three_query_raw_state_bound + s_sat_clause_three_query_raw_well_formed + sat_clause_three_query_out_correct + sat_clause_three_query_literal_table_first_halt_span + sat_clause_three_query_literal_table_first_halt_strict_quartic","source_completeness":"full (CSV-sourced)","statement":"Complete IN-RANGE three-literal table query product. The well-formed 212-state s_sat_clause_three_query_raw composes three selector/query/reframe cycles: 69 states for tally one, 71 for tally two after one delimiter, and 72 for tally three after two delimiters. Its whole-product least halt returns the exact selector-ready SAT frame within 63*(clause_seek_span)^2, with the sticky accumulator equal to acc OR serialized_literal_table(sat_N_frame w,i,j,pos). Under grid-range premises the explicit strict quartic constant is 63*900*16 = 907200. Third-prefix reconstruction proves the physical Blank frame/base sentinel remains load-bearing. A checked halted-machine counterexample at j=num_clauses directly disagrees with the serialized parser table, so this standalone selector cannot decide range. The parser-default body, range marker, and physical router are closed separately as the total raw literal-table product. This theorem remains the raw internal-layout, j-in-range branch result; canonical clean padding, finite karp_edge, grid emission, encode_tsp, and the strict capstone remain OPEN.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Complete in-range second-literal query cycle. The reusable stm_seq_first_halt_layout theorem composes arbitrary internal-layout stages from least-halt and exact Hstate0 contracts without pretending they are clean s_init transducers. The well-formed 71-state s_sat_clause_second_cycle_raw is selector -> one-delimiter skip -> 39-state literal query -> 8-state reframe. Its whole-product first halt returns the exact selector-ready SAT frame with accumulator updated by tally two within 21*(clause_seek_span)^2. The second-query prefix/base reconstruction proves the Blank sentinel remains load-bearing and recovers the original sat_N_frame exactly. A sticky-accumulator control and false dropped-accumulator statement are checked. This cycle remains explicitly j-in-range; the combined in-range first/second/third product is closed separately. The total out-of-range default branch, clean padding, karp_edge, grid emission, encode_tsp, and the strict capstone remain OPEN.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictClauseQueryNext.v":"369b40419625876ac3a7f9bd5b9bd353a2c87bda49a728cf8260367514f08485"},"files":{"coq_file":"proofs/coq/ComplexityStrictClauseQueryNext.v"},"id":"CUB-COMPLEXITY-STRICT-CLAUSE-QUERY-NEXT","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk; exact 71-state cycle; in-range three-query product closed separately","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"stm_seq_first_halt_layout + ci_second_query_frame_reconstruct + sat_clause_second_query_reframe_start + s_sat_clause_second_cycle_raw_state_bound + s_sat_clause_second_cycle_raw_well_formed + sat_clause_second_cycle_first_halt_span","source_completeness":"full (CSV-sourced)","statement":"Complete in-range second-literal query cycle. The reusable stm_seq_first_halt_layout theorem composes arbitrary internal-layout stages from least-halt and exact Hstate0 contracts without pretending they are clean s_init transducers. The well-formed 71-state s_sat_clause_second_cycle_raw is selector -> one-delimiter skip -> 39-state literal query -> 8-state reframe. Its whole-product first halt returns the exact selector-ready SAT frame with accumulator updated by tally two within 21*(clause_seek_span)^2. The second-query prefix/base reconstruction proves the Blank sentinel remains load-bearing and recovers the original sat_N_frame exactly. A sticky-accumulator control and false dropped-accumulator statement are checked. This cycle remains explicitly j-in-range; the combined in-range first/second/third product is closed separately. The total out-of-range default branch, clean padding, karp_edge, grid emission, encode_tsp, and the strict capstone remain OPEN.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Total parser-faithful range marker for canonical SAT clause queries. The well-formed 19-state s_clause_range_raw counts Bit-false delimiters modulo three across the exact sat_N_frame, cancels one unary j bit per complete clause, restores every temporary frame and query mark, and replaces only the frame-boundary Blank with Bit(j < num_clauses(parse_3sat w)). The exact theorem quantifies over every w, i, and j; the least halt is bounded by 5*(clause_seek_span w i j)^2. The two enc_nat suffix fields are load-bearing and independently cross-checked by count_false(sat_N_frame w)/3 = num_clauses(parse_3sat w). Executable controls cover empty input, equality and greater-than bounds, multiple clauses, a partial clause, a one-bit completion that flips the flag, full restoration with a nonempty base, one-step-early nonhalting, and a rejected wrong flag. This remains the standalone internal-layout marker; the physical router and total raw literal-table product are closed separately. Canonical padding, karp_edge, grid emission, encode_tsp, and the strict capstone remain OPEN.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictClauseRange.v":"44dc70504faf6700b75d909297a40a1611f90888f7b5c70612be9ca04253d482"},"files":{"coq_file":"proofs/coq/ComplexityStrictClauseRange.v"},"id":"CUB-COMPLEXITY-STRICT-CLAUSE-RANGE","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; exact 19-state total range marker and 5*span^2 internal-layout budget; total raw router closed in CUB-COMPLEXITY-STRICT-CLAUSE-ROUTER","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_clause_range_raw_state_bound + s_clause_range_raw_well_formed + clause_range_core_exact_run + sat_clause_range_exact_run + sat_clause_range_exact_first_halt + sat_clause_range_fuel_span_quadratic + sat_clause_range_first_halt_span + clause_range_done_Hstate0","source_completeness":"full (CSV-sourced)","statement":"Total parser-faithful range marker for canonical SAT clause queries. The well-formed 19-state s_clause_range_raw counts Bit-false delimiters modulo three across the exact sat_N_frame, cancels one unary j bit per complete clause, restores every temporary frame and query mark, and replaces only the frame-boundary Blank with Bit(j < num_clauses(parse_3sat w)). The exact theorem quantifies over every w, i, and j; the least halt is bounded by 5*(clause_seek_span w i j)^2. The two enc_nat suffix fields are load-bearing and independently cross-checked by count_false(sat_N_frame w)/3 = num_clauses(parse_3sat w). Executable controls cover empty input, equality and greater-than bounds, multiple clauses, a partial clause, a one-bit completion that flips the flag, full restoration with a nonempty base, one-step-early nonhalting, and a rejected wrong flag. This remains the standalone internal-layout marker; the physical router and total raw literal-table product are closed separately. Canonical padding, karp_edge, grid emission, encode_tsp, and the strict capstone remain OPEN.","status":"proven","use_cases":["TEP","admission","TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: IN-RANGE first-query reframe brick. The well-formed 8-state s_clause_query_reframe_raw starts at the literal-query far-right Blank, preserves every tape cell while crossing the flag, metadata, index, and serialized-frame regions, then uses the explicit frame/base Blank sentinel to turn right and halt in the selector-ready layout with the updated OR accumulator. Its exact fuel is |sat_N_frame w|+i+j+7 = S(clause_seek_span), with least-halt/no-early evidence and the explicit bound 31*(|w|+1)^2 under grid-range premises. The sentinel is load-bearing because generic slm_done_cfg base/k parameters are not uniquely recoverable. A checked wrong-accumulator negative control prevents restoration of the stale input accumulator. Delimiter skips and all three in-range cycles are closed separately; the total out-of-range branch, clean padding, karp_edge, grid emission, encode_tsp, and the strict capstone remain OPEN.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictClauseReframe.v":"0713666924060c3ae7a2de9ad23c6169cdac0d9e359933863bb3bec0cc7032cf"},"files":{"coq_file":"proofs/coq/ComplexityStrictClauseReframe.v"},"id":"CUB-COMPLEXITY-STRICT-CLAUSE-REFRAME","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; pinned Coq compile; exact physical reframe and selector-ready handoff; in-range internal-layout brick","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_clause_query_reframe_raw_state_bound + s_clause_query_reframe_raw_well_formed + qrf_exact_run + qrf_first_halt + qrf_slm_done_start + sat_clause_first_query_reframe_selector_ready + sat_clause_first_query_reframe_fuel_grid_quadratic + sat_clause_first_query_reframe_first_halt_span","source_completeness":"full (CSV-sourced)","statement":"IN-RANGE first-query reframe brick. The well-formed 8-state s_clause_query_reframe_raw starts at the literal-query far-right Blank, preserves every tape cell while crossing the flag, metadata, index, and serialized-frame regions, then uses the explicit frame/base Blank sentinel to turn right and halt in the selector-ready layout with the updated OR accumulator. Its exact fuel is |sat_N_frame w|+i+j+7 = S(clause_seek_span), with least-halt/no-early evidence and the explicit bound 31*(|w|+1)^2 under grid-range premises. The sentinel is load-bearing because generic slm_done_cfg base/k parameters are not uniquely recoverable. A checked wrong-accumulator negative control prevents restoration of the stale input accumulator. Delimiter skips and all three in-range cycles are closed separately; the total out-of-range branch, clean padding, karp_edge, grid emission, encode_tsp, and the strict capstone remain OPEN.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Total parser-faithful raw serialized-literal-table machine. The 19-state range marker writes the physical Boolean j output := b + o; counter consumed to Blanks). Proven 0-axiom by the fold-over-the-counter induction s_copy_run (recursive-fuel shadow of the run) built on copy_cycle (one full cycle: consume + copy_out output round-trip + refind frontier) reusing four march-folds copy_m1-4. s_copy_run/extract: s_extract = repeat true (S k + o). UNARY MULTIPLY is this nested with a source-preserving s_emit body. coqchk Axioms: .","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictCopy.v":"35bcc94ff0ab2f6efe7c50fe42a6761d0ba18ec105cc8c9c11f900ca9aa66fdf"},"files":{"coq_file":"proofs/coq/ComplexityStrictCopy.v"},"id":"CUB-COMPLEXITY-STRICT-COPY","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"iter-emit-handoff","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_copy_run + s_copy_extract","source_completeness":"full (CSV-sourced)","statement":"item-4 the s_iter x s_emit HANDOFF: s_copy (5-state) drives an s_emit-style output write once per counter unit -- UNARY ADDITION across a gap (counter b | gap | output o -> output := b + o; counter consumed to Blanks). Proven 0-axiom by the fold-over-the-counter induction s_copy_run (recursive-fuel shadow of the run) built on copy_cycle (one full cycle: consume + copy_out output round-trip + refind frontier) reusing four march-folds copy_m1-4. s_copy_run/extract: s_extract = repeat true (S k + o). UNARY MULTIPLY is this nested with a source-preserving s_emit body. coqchk Axioms: .","status":"proven","use_cases":["crypto","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: unary FLOOR-DIVISION BY 3 as a single right scan: s_div3 (3-state; the finite control IS the mod-3 counter via the explicit finite match st3 -- no Nat.modulo in the machine) keeps the true completing each triple, erases other trues + every false to Blank, halts on Blank. Proven via the spec fold div3_cells + the 6-case value lemma div3_cells_value: s_div3_computes = w -> repeat true (bit_to_nat w / 3), k=1 c=1, |w|+1 steps. Composed through the closed stack: clause_counter := stm_seq (s_map_prepend negb) s_div3 computes repeat true (#false(w)/3) at the explicit (seq_K 1 1, seq_C 1 4 1 1) budget (clause_counter_computes) -- on the false-terminated 3SAT literal encoding that is NUM_CLAUSES IN UNARY: the first full parse-parameter machine. Honest scope: computes #false/3 of the RAW input; the #parts-vs-#false trailing-true adjustment lemma equating it to num_clauses(parse_3sat w) is a pure-Coq successor, not claimed. Design falsifiers div3_check1/2 committed. Strict wrapper OPEN. NP-hardness (Karp 1972) not P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictDiv3.v":"73f3589dc8d3b5f0720270c3ce937c2609e458bd0a7c8c9262d308710f60fcea"},"files":{"coq_file":"proofs/coq/ComplexityStrictDiv3.v"},"id":"CUB-COMPLEXITY-STRICT-DIV3","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_div3_computes + clause_counter_computes","source_completeness":"full (CSV-sourced)","statement":"unary FLOOR-DIVISION BY 3 as a single right scan: s_div3 (3-state; the finite control IS the mod-3 counter via the explicit finite match st3 -- no Nat.modulo in the machine) keeps the true completing each triple, erases other trues + every false to Blank, halts on Blank. Proven via the spec fold div3_cells + the 6-case value lemma div3_cells_value: s_div3_computes = w -> repeat true (bit_to_nat w / 3), k=1 c=1, |w|+1 steps. Composed through the closed stack: clause_counter := stm_seq (s_map_prepend negb) s_div3 computes repeat true (#false(w)/3) at the explicit (seq_K 1 1, seq_C 1 4 1 1) budget (clause_counter_computes) -- on the false-terminated 3SAT literal encoding that is NUM_CLAUSES IN UNARY: the first full parse-parameter machine. Honest scope: computes #false/3 of the RAW input; the #parts-vs-#false trailing-true adjustment lemma equating it to num_clauses(parse_3sat w) is a pure-Coq successor, not claimed. Design falsifiers div3_check1/2 committed. Strict wrapper OPEN. NP-hardness (Karp 1972) not P vs NP.","status":"proven","use_cases":["TEP","admission","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Division-free semantic bridge for the physical edge handlers. Valid exit/entry operands reduce cyclic successor to ordinary successor or the unique nv wrap; the last row is the physically measurable false tally of sat_N_frame; clause slots are three unary copies of j plus fixed two/three-cell suffixes; and edge_program_machine_eval contains neither mod nor edge_row_len. Under valid operands and the exact frame tally it equals edge_program_eval and therefore edge_unode_adj. This row is a proof specification for later finite handlers, not a tape machine.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeArithmetic.v":"f52dcaa9b075f106650ca0489191f572d29c40fd0d6b6aa449d1703c5e3ebde2"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeArithmetic.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-ARITHMETIC","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; division/modulo eliminated from the machine-facing evaluator; pure semantic bridge only","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"edge_exit_entry_successor_short_circuit + edge_row_last_from_sat_N_frame + edge_clause_positive_slot_unary + edge_clause_negative_slot_unary + edge_program_machine_eval_correct + edge_program_machine_eval_sat_correct","source_completeness":"full (CSV-sourced)","statement":"Division-free semantic bridge for the physical edge handlers. Valid exit/entry operands reduce cyclic successor to ordinary successor or the unique nv wrap; the last row is the physically measurable false tally of sat_N_frame; clause slots are three unary copies of j plus fixed two/three-cell suffixes; and edge_program_machine_eval contains neither mod nor edge_row_len. Under valid operands and the exact frame tally it equals edge_program_eval and therefore edge_unode_adj. This row is a proof specification for later finite handlers, not a tape machine.","status":"proven","use_cases":["complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Physical marker handoff around preservation-safe unary equality. The two-state s_edge_compare_finish moves from the restored first operand to the equality marker without altering tape data. Its exact well-formed composition with the 11-state comparator has 13 states, preserves arbitrary mixed base, header, both canonical unary operands, separators, and arbitrary mixed metadata, and halts with the head directly on Bit(Nat.eqb a b) so a later finite router can branch on the physical tape. Exact least-halt and bounded-run theorems give unary_eq_fuel(a,b)+1 <= (a+b+2)^2+1, including both zero and mismatch. Operand preparation, handler routing, finite karp_edge, grid emission, encode_tsp, and the strict capstone remain OPEN.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeCompareCall.v":"63836e2efd02cd27907116a5c40f5ecf5c2d9ec91c0e4d49c3884365d7f9b333"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeCompareCall.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-COMPARE-CALL","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk; exact 2-state finisher and 13-state product; arbitrary base/header/meta preserved","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_edge_compare_finish_state_bound + s_edge_compare_finish_well_formed + edge_compare_finish_exact_run + s_edge_compare_call_state_bound + s_edge_compare_call_well_formed + edge_compare_call_first_halt + edge_compare_call_exact_bounded_run + edge_compare_call_bound_square + edge_compare_call_first_halt_square","source_completeness":"full (CSV-sourced)","statement":"Physical marker handoff around preservation-safe unary equality. The two-state s_edge_compare_finish moves from the restored first operand to the equality marker without altering tape data. Its exact well-formed composition with the 11-state comparator has 13 states, preserves arbitrary mixed base, header, both canonical unary operands, separators, and arbitrary mixed metadata, and halts with the head directly on Bit(Nat.eqb a b) so a later finite router can branch on the physical tape. Exact least-halt and bounded-run theorems give unary_eq_fuel(a,b)+1 <= (a+b+2)^2+1, including both zero and mismatch. Operand preparation, handler routing, finite karp_edge, grid emission, encode_tsp, and the strict capstone remain OPEN.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Finite terminal destruction of compared unary operands. The exact well-formed 12-state machine reads the physical equality marker, stores only that Boolean in finite control, erases both unary fields and separators to Blank cells, restores the marker, and halts on it in 2*a+2*b+6 steps with least-halt semantics. Blank at dispatch refuses rather than selecting a branch.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeCompareCleanup.v":"f2eaeabfd5d1defff18c2c7b02823ebad509973b6a6d59be4c6e26ba9d274acc"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeCompareCleanup.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-COMPARE-CLEANUP","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk; exact 12 states; physical marker dispatch and malformed refusal","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_edge_compare_cleanup_state_bound + s_edge_compare_cleanup_well_formed + edge_compare_cleanup_exact_run + edge_compare_cleanup_first_halt + edge_compare_cleanup_blank_refuses","source_completeness":"full (CSV-sourced)","statement":"Finite terminal destruction of compared unary operands. The exact well-formed 12-state machine reads the physical equality marker, stores only that Boolean in finite control, erases both unary fields and separators to Blank cells, restores the marker, and halts on it in 2*a+2*b+6 steps with least-halt semantics. Blank at dispatch refuses rather than selecting a branch.","status":"proven","use_cases":["TDX","TEP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Finite reusable recycling of compared unary operands. The exact well-formed 10-state machine reads the physical equality marker, rewrites both unary fields and both separators into Bit-false frame cells, physically rewinds, restores the marker, and halts on it in 2*a+2*b+6 steps with least-halt semantics. Unlike terminal Blank cleanup, the resulting all-bit suffix can be incorporated into another canonical edge frame; Blank dispatch fails closed.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeCompareRecycle.v":"79a8fd8a845358c3669727478830dbca1840d7e83b80d1088ef24fa1e6d688a3"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeCompareRecycle.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-COMPARE-RECYCLE","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk; exact 10-state physical recycling; arbitrary base/header/meta preserved","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_edge_compare_recycle_state_bound + s_edge_compare_recycle_well_formed + edge_compare_recycle_exact_run + edge_compare_recycle_first_halt + edge_compare_recycle_blank_refuses","source_completeness":"full (CSV-sourced)","statement":"Finite reusable recycling of compared unary operands. The exact well-formed 10-state machine reads the physical equality marker, rewrites both unary fields and both separators into Bit-false frame cells, physically rewinds, restores the marker, and halts on it in 2*a+2*b+6 steps with least-halt semantics. Unlike terminal Blank cleanup, the resulting all-bit suffix can be incorporated into another canonical edge frame; Blank dispatch fails closed.","status":"proven","use_cases":["TDX","TEP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Canonical bit-only serialization contract for division-free edge descriptor pairs. edge_pair_word emits the fixed header 01;role(a);role(b);kind(a);kind(b), followed by four delimiter-terminated unary coordinates. The strict partial decoder rejects invalid role 11, truncated/missing unary terminators, noncanonical non-row y coordinates, and trailing cells. It has both roundtrip and canonical inverse theorems, hence injectivity, an exact length 14+xa+ya+xb+yb, reflected descriptor-range validity, bounded numbered IDs, an evaluator-success iff theorem exposing canonicality plus validity, and a validity-scoped bridge showing evaluation over sat_N_frame equals the existing numbered karp_edge. This file claims a serialization/specification layer only; it does not claim a decoder machine or finite edge machine. The physical selected-field stager, frame false-tally builder, nv-suffix stager, literal-query adapter, finite karp_edge, grid emission, encode_tsp, and strict reduction capstone remain OPEN.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeEncoding.v":"c8d5f78f844f3652c4743c00afb2aa671bc094cd2a3a03690d8d7c53cca227d0"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeEncoding.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-ENCODING","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk; pure canonical encoding/decoder contract; no finite edge machine claimed","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"edge_take_unary_enc_nat + edge_take_unary_sound + edge_decode_pair_encode + edge_decode_pair_canonical + edge_pair_encode_injective + edge_pair_word_length + edge_dnode_validb_spec + edge_pair_validb_spec + edge_pair_ids_bound + edge_pair_word_valid_length + edge_pair_eval_some_iff + edge_pair_eval_sat_N_frame","source_completeness":"full (CSV-sourced)","statement":"Canonical bit-only serialization contract for division-free edge descriptor pairs. edge_pair_word emits the fixed header 01;role(a);role(b);kind(a);kind(b), followed by four delimiter-terminated unary coordinates. The strict partial decoder rejects invalid role 11, truncated/missing unary terminators, noncanonical non-row y coordinates, and trailing cells. It has both roundtrip and canonical inverse theorems, hence injectivity, an exact length 14+xa+ya+xb+yb, reflected descriptor-range validity, bounded numbered IDs, an evaluator-success iff theorem exposing canonicality plus validity, and a validity-scoped bridge showing evaluation over sat_N_frame equals the existing numbered karp_edge. This file claims a serialization/specification layer only; it does not claim a decoder machine or finite edge machine. The physical selected-field stager, frame false-tally builder, nv-suffix stager, literal-query adapter, finite karp_edge, grid emission, encode_tsp, and strict reduction capstone remain OPEN.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Finite physical equality products for any compile-time pair of xa/ya/xb/yb descriptor fields. The reusable pre-cleanup product stages the first coordinate, freezes and rewinds, stages the second, rearms the exact unary comparison layout, and halts on the physical equality marker while retaining both operands. Its state count is selector1+selector2+20 and its least halt is bounded by 13*span^2. The terminal product adds exact operand erasure, has selector1+selector2+32 states, returns the marker with Blank cleanup, and is bounded by 15*span^2. Arbitrary base/frame/work bits and zero operands are preserved.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeFieldPair.v":"be42937f7e130ed87e2392683998aa4c474219529d3fe72d179d59d07775fd5a"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeFieldPair.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-FIELD-PAIR","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk; reusable physical comparison and terminal cleanup products","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_edge_field_selector_state_bound + s_edge_field_selector_well_formed + s_edge_field_pair_compare_raw_state_bound + s_edge_field_pair_compare_raw_well_formed + edge_field_pair_compare_raw_first_halt_polynomial + s_edge_field_pair_state_bound + s_edge_field_pair_well_formed + edge_field_pair_first_halt_polynomial","source_completeness":"full (CSV-sourced)","statement":"Finite physical equality products for any compile-time pair of xa/ya/xb/yb descriptor fields. The reusable pre-cleanup product stages the first coordinate, freezes and rewinds, stages the second, rearms the exact unary comparison layout, and halts on the physical equality marker while retaining both operands. Its state count is selector1+selector2+20 and its least halt is bounded by 13*span^2. The terminal product adds exact operand erasure, has selector1+selector2+32 states, returns the marker with Blank cleanup, and is bounded by 15*span^2. Arbitrary base/frame/work bits and zero operands are preserved.","status":"proven","use_cases":["complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Reusable finite physical equality of any compile-time pair of xa/ya/xb/yb descriptor fields. The product stages and compares both coordinates, reads the physical equality marker, rewrites both operands and separators into false frame cells, resets the marker, and physically rewinds to descriptor cell zero. Its exact state count is selector1+selector2+35; the two distinct final states decode exactly to Nat.eqb of the tape-selected coordinates; the frame grows by exactly x+y+2 false cells; and its least halt is bounded by 16*span^2 for arbitrary base/frame/work bits. Blank marker dispatch fails closed.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeFieldPairRecycle.v":"0d5402634939b8d7557dc7a43a11e9db3c5a5fb57ddec62b7645958304f35e68"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeFieldPairRecycle.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-FIELD-PAIR-RECYCLE","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk; exact physical result-state handoff and recyclable frame extension; handler work-bit folds remain separate","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_edge_field_pair_recycle_state_bound + s_edge_field_pair_recycle_well_formed + edge_field_pair_recycle_first_halt_terminal + edge_field_pair_recycle_terminal_states_last + edge_field_pair_recycle_terminal_state_decodes + edge_field_pair_recycle_first_halt_polynomial + edge_field_pair_recycle_malformed_refuses","source_completeness":"full (CSV-sourced)","statement":"Reusable finite physical equality of any compile-time pair of xa/ya/xb/yb descriptor fields. The product stages and compares both coordinates, reads the physical equality marker, rewrites both operands and separators into false frame cells, resets the marker, and physically rewinds to descriptor cell zero. Its exact state count is selector1+selector2+35; the two distinct final states decode exactly to Nat.eqb of the tape-selected coordinates; the frame grows by exactly x+y+2 false cells; and its least halt is bounded by 16*span^2 for arbitrary base/frame/work bits. Blank marker dispatch fails closed.","status":"proven","use_cases":["TDX","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Finite physical descriptor-coordinate appenders for the canonical bit-only edge workspace. Four well-formed machines start on the ten-bit descriptor header, locate xa/ya/xb/yb by physical scans, preserve the exact descriptor, arbitrary mixed base, arbitrary bit-only frame, work cells, and existing scratch, and append the selected unary coordinate at the far right. xa uses a 30-state router that reads the physical kb1 predecessor and selects one of two finite clean-stager slices; malformed Blank fails closed. The ya/xb/yb products have 22/23/24 states. Every path handles zero, proves exact least-halt/no-early-halt semantics, normalizes the scratch boundary to Blank, returns a common scratch-head layout, and is bounded by 4*edge_field_span^2. Frame-derived operands, handler Boolean routing, finite karp_edge, grid emission, encode_tsp, and the strict capstone remain OPEN.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeFieldStage.v":"8957dc31e960dfd10f217bd4c1e4c1b5f13adbdac448c55cd21c846718ece52d"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeFieldStage.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-FIELD-STAGE","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk; exact state counts 30/22/23/24; physical kb1 branch; arbitrary base/frame/scratch preserved","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_edge_xa_stage_state_bound + s_edge_xa_stage_well_formed + s_edge_ya_stage_state_bound + s_edge_ya_stage_well_formed + s_edge_xb_stage_state_bound + s_edge_xb_stage_well_formed + s_edge_yb_stage_state_bound + s_edge_yb_stage_well_formed + edge_xa_stage_exact_run + edge_xa_stage_first_halt + edge_ya_stage_exact_run + edge_ya_stage_first_halt + edge_xb_stage_exact_run + edge_xb_stage_first_halt + edge_yb_stage_exact_run + edge_yb_stage_first_halt","source_completeness":"full (CSV-sourced)","statement":"Finite physical descriptor-coordinate appenders for the canonical bit-only edge workspace. Four well-formed machines start on the ten-bit descriptor header, locate xa/ya/xb/yb by physical scans, preserve the exact descriptor, arbitrary mixed base, arbitrary bit-only frame, work cells, and existing scratch, and append the selected unary coordinate at the far right. xa uses a 30-state router that reads the physical kb1 predecessor and selects one of two finite clean-stager slices; malformed Blank fails closed. The ya/xb/yb products have 22/23/24 states. Every path handles zero, proves exact least-halt/no-early-halt semantics, normalizes the scratch boundary to Blank, returns a common scratch-head layout, and is bounded by 4*edge_field_span^2. Frame-derived operands, handler Boolean routing, finite karp_edge, grid emission, encode_tsp, and the strict capstone remain OPEN.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Finite physical adapter from frame-derived operands back to the canonical unpadded edge workspace. The exact well-formed six-state machine starts on the first frame cell, scans an arbitrary bit-only frame and scratch, converts the prefix/frame, frame/scratch, and virtual-right Blank boundaries into Bit-false cells, and physically rewinds an arbitrary bit-only descriptor/work prefix to its outer Blank sentinel. It has exact least-halt/no-early-halt semantics and runs within twice the local span (hence twice its square). Exact specializations connect both the false-frame tally and encoded-nv stager outputs to edge_field_stage_start_cfg while preserving arbitrary base and every bit. Interior malformed layouts do not satisfy the canonical handoff.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeFrameScratchFreeze.v":"09593fdfceb657b314aadd21bc61151522e363af9b1019db194c9a3935eea1ee"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeFrameScratchFreeze.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-FRAME-SCRATCH-FREEZE","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk Axioms:; exact six-state unpadded physical reentry for frame-derived scratch","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_edge_frame_scratch_freeze_raw_state_bound + s_edge_frame_scratch_freeze_raw_well_formed + edge_frame_scratch_freeze_exact_run + edge_frame_scratch_freeze_first_halt_polynomial + edge_false_tally_done_freeze_exact_run + edge_false_tally_done_freeze_first_halt + edge_nv_stage_done_freeze_exact_run + edge_nv_stage_done_freeze_first_halt + edge_frame_scratch_freeze_refuses_unchanged","source_completeness":"full (CSV-sourced)","statement":"Finite physical adapter from frame-derived operands back to the canonical unpadded edge workspace. The exact well-formed six-state machine starts on the first frame cell, scans an arbitrary bit-only frame and scratch, converts the prefix/frame, frame/scratch, and virtual-right Blank boundaries into Bit-false cells, and physically rewinds an arbitrary bit-only descriptor/work prefix to its outer Blank sentinel. It has exact least-halt/no-early-halt semantics and runs within twice the local span (hence twice its square). Exact specializations connect both the false-frame tally and encoded-nv stager outputs to edge_field_stage_start_cfg while preserving arbitrary base and every bit. Interior malformed layouts do not satisfy the canonical handoff.","status":"proven","use_cases":["TDX","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Finite physical classifier for the canonical ten-bit edge descriptor header. The exact well-formed 3073-state machine validates magic 01, reads eight role/kind bits into bounded finite control, validates the first coordinate cell, preserves every tape cell, physically rewinds to descriptor cell zero, and halts in one of 256 code-specific states after exactly 20 steps. Pure decoding the terminal state agrees with the constructor tag of edge_program_classify; invalid or malformed Blank header cells fail closed. No coordinate, parser, literal table, or semantic edge predicate appears in the transition function. Handler products, finite karp_edge, grid emission, encode_tsp, and the strict capstone remain OPEN.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeHeaderRouter.v":"c7a870301847786af687e3dc5d1abe740743178d147930a8e71cbc757f4b44c6"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeHeaderRouter.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-HEADER-ROUTER","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk; exact 3073 finite states and 20 physical steps; malformed headers refuse","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_edge_header_router_state_bound + s_edge_header_router_well_formed + edge_header_router_exact_run + edge_header_router_first_halt + edge_header_code_tag_classify + edge_header_router_run_program_tag","source_completeness":"full (CSV-sourced)","statement":"Finite physical classifier for the canonical ten-bit edge descriptor header. The exact well-formed 3073-state machine validates magic 01, reads eight role/kind bits into bounded finite control, validates the first coordinate cell, preserves every tape cell, physically rewinds to descriptor cell zero, and halts in one of 256 code-specific states after exactly 20 steps. Pure decoding the terminal state agrees with the constructor tag of edge_program_classify; invalid or malformed Blank header cells fail closed. No coordinate, parser, literal table, or semantic edge predicate appears in the transition function. Handler products, finite karp_edge, grid emission, encode_tsp, and the strict capstone remain OPEN.","status":"proven","use_cases":["TDX","TEP","TSP","complexity","gateway"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Exact support boundary and finite constant accumulation for edge operands. Explicit single-tape support is monotone, proving that a field-stage halt with a represented trailing Blank cannot equal the original virtual-Blank start layout. The replacement well-formed four-state padded rearm has exact least-halt semantics and one-step operational convergence; the well-formed seven-state freeze-plus family uses a four-constructor finite-control parameter k in {0,1,2,3}, incorporates the operand plus k into an ordinary bit-only extended frame, and returns the exact unpadded canonical workspace. This closes the representational gap without an axiom or hidden RAM.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeOperandAccumulate.v":"650e133334cea0008cbf13e7995a63c81f661e7eb37c7ef4b8c9b276659687bd"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeOperandAccumulate.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-OPERAND-ACCUMULATE","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk; formal impossibility result plus exact 4-state padded and 7-state freeze-plus replacements","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"edge_operand_exact_unpadded_rearm_impossible + s_edge_operand_rearm_padded_state_bound + edge_operand_rearm_padded_first_halt + s_edge_operand_freeze_plus_state_bound + s_edge_operand_freeze_plus_well_formed + edge_operand_freeze_plus_exact_unpadded + edge_operand_freeze_plus_first_halt","source_completeness":"full (CSV-sourced)","statement":"Exact support boundary and finite constant accumulation for edge operands. Explicit single-tape support is monotone, proving that a field-stage halt with a represented trailing Blank cannot equal the original virtual-Blank start layout. The replacement well-formed four-state padded rearm has exact least-halt semantics and one-step operational convergence; the well-formed seven-state freeze-plus family uses a four-constructor finite-control parameter k in {0,1,2,3}, incorporates the operand plus k into an ordinary bit-only extended frame, and returns the exact unpadded canonical workspace. This closes the representational gap without an axiom or hidden RAM.","status":"proven","use_cases":["TEP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Finite physical preparation of two selected descriptor coordinates for unary equality. A well-formed three-state freeze adapter turns the first live scratch boundaries into false frame bits and rewinds to descriptor cell zero; a well-formed four-state rearm adapter reconstructs exactly the two Blank-separated unary operands required by the existing comparator. Exact and least-halt theorems preserve arbitrary base, descriptor, frame, work bits, and zero/nonzero operands.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeOperandPair.v":"3f092e5f1ca8b7d544bdbbc215b22b2f8dde708e62d9f99cdc9854e02527fdea"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeOperandPair.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-OPERAND-PAIR","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk; exact 3-state freeze and 4-state compare rearm","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_edge_operand_freeze_raw_state_bound + s_edge_operand_freeze_raw_well_formed + edge_operand_freeze_first_halt + s_edge_compare_rearm_raw_state_bound + s_edge_compare_rearm_raw_well_formed + edge_compare_rearm_first_halt","source_completeness":"full (CSV-sourced)","statement":"Finite physical preparation of two selected descriptor coordinates for unary equality. A well-formed three-state freeze adapter turns the first live scratch boundaries into false frame bits and rewinds to descriptor cell zero; a well-formed four-state rearm adapter reconstructs exactly the two Blank-separated unary operands required by the existing comparator. Exact and least-halt theorems preserve arbitrary base, descriptor, frame, work bits, and zero/nonzero operands.","status":"proven","use_cases":["complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Finite semantic instruction classification for edge handlers. edge_program_classify selects one of nine constructor tags solely from the two node kinds and two role tags, while edge_program_eval states the requested Boolean arithmetic and literal queries. Valid descriptors prove edge_program_eval_correct against edge_unode_adj. This is deliberately a pure specification and does not claim that host-language evaluation is a tape transition; the finite physical header router and handler machines are separate rows.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeProgram.v":"609ffff98e14abceb6e06cb23460c64224667feab11a690f5bb8eeca2f50dd9c"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeProgram.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-PROGRAM","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; pure classifier/evaluator contract only; no machine claim","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"edge_dnode_id_eqb_decompose + edge_program_eval_correct","source_completeness":"full (CSV-sourced)","statement":"Finite semantic instruction classification for edge handlers. edge_program_classify selects one of nine constructor tags solely from the two node kinds and two role tags, while edge_program_eval states the requested Boolean arithmetic and literal queries. Valid descriptors prove edge_program_eval_correct against edge_unode_adj. This is deliberately a pure specification and does not claim that host-language evaluation is a tape transition; the finite physical header router and handler machines are separate rows.","status":"proven","use_cases":["complexity","gateway"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Finite physical Boolean branch handoff after a recycled edge comparison. The exact well-formed five-state machine reads and resets the result marker to Bit false, remembers only that Boolean in finite control, rewinds the complete arbitrary bit word to its explicit Blank sentinel, and halts on word cell zero in distinct true/false terminal states. Its least halt is within |word|+2, the terminal state decodes exactly to the tape-read flag, and normalizing it yields the exact canonical field-stage start with recycled cells appended to the frame. Blank dispatch refuses.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeResultRewind.v":"bc75d49271b13d044eb6745c174b8b23f4722f11b7cdda3c29df8fb39a808a0b"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeResultRewind.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-RESULT-REWIND","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk; exact 5 states; physical result reset and descriptor rewind","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_edge_result_rewind_state_bound + s_edge_result_rewind_well_formed + edge_result_rewind_exact_run + edge_result_rewind_first_halt + edge_result_rewind_state_decodes + edge_result_rewind_field_handoff + edge_result_rewind_blank_refuses","source_completeness":"full (CSV-sourced)","statement":"Finite physical Boolean branch handoff after a recycled edge comparison. The exact well-formed five-state machine reads and resets the result marker to Bit false, remembers only that Boolean in finite control, rewinds the complete arbitrary bit word to its explicit Blank sentinel, and halts on word cell zero in distinct true/false terminal states. Its least halt is within |word|+2, the terminal state decodes exactly to the tape-read flag, and normalizing it yields the exact canonical field-stage start with recycled cells appended to the frame. Blank dispatch refuses.","status":"proven","use_cases":["TDX","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Pure edge-oracle, descriptor, and row-major grid specification. serialized_literal_table_parse proves the parser-faithful serialized literal table, including the default-clause fallback. edge_dnode_adj_correct and edge_unode_adj_correct prove valid division-free descriptors equal the numbered Karp adjacency relation. The canonical descriptor enumeration is valid, duplicate-free, and maps exactly to seq 0 N; edge_descriptor_grid_correct proves the outer-u/inner-v descriptor painter equals the numbered N-by-N grid. No finite serialized-query, edge, or grid machine is claimed; the strict reduction remains OPEN.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeSpec.v":"c2bf6184dfe456325bbadc4c7ce9ac33db26ba8199f690e3afc0f9530b29a019"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeSpec.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-SPEC","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; coqchk Axioms:; pure specification only; executable query/edge/grid stages open","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"serialized_literal_table_parse + edge_dnode_adj_correct + edge_unode_adj_correct + edge_unode_descriptors_ids_closed + edge_descriptor_grid_correct","source_completeness":"full (CSV-sourced)","statement":"Pure edge-oracle, descriptor, and row-major grid specification. serialized_literal_table_parse proves the parser-faithful serialized literal table, including the default-clause fallback. edge_dnode_adj_correct and edge_unode_adj_correct prove valid division-free descriptors equal the numbered Karp adjacency relation. The canonical descriptor enumeration is valid, duplicate-free, and maps exactly to seq 0 N; edge_descriptor_grid_correct proves the outer-u/inner-v descriptor painter equals the numbered N-by-N grid. No finite serialized-query, edge, or grid machine is claimed; the strict reduction remains OPEN.","status":"proven","use_cases":["complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Finite physical updater for the two Boolean work cells in the canonical edge workspace. The exact well-formed 18-state machine validates descriptor magic 01, crosses the remaining eight header bits and four delimiter-terminated unary coordinates, applies one compile-time finite set/and/or fold to either out or lit, validates the other work cell, and physically rewinds to descriptor cell zero. It preserves every other cell, has least-halt/no-early-halt semantics, and runs in exactly 32+2*(xa+ya+xb+yb) steps, at most twice the local edge-field span. Blank or malformed magic fails closed. No semantic edge predicate occurs in the transition function.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeWorkStore.v":"d02b2e6bca9ec648b0ccafb3db02c5707e3d666bf560e43353499fd7db43b5e6"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeWorkStore.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-WORK-STORE","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk Axioms:; exact 18-state physical work-bit fold; handler sequencing remains separate","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_edge_work_store_state_bound + s_edge_work_store_well_formed + edge_work_store_exact_run + edge_work_store_least_halt + edge_work_store_done_reentry + edge_work_store_preserves_other + edge_work_store_fuel_linear + edge_work_store_blank_refuses","source_completeness":"full (CSV-sourced)","statement":"Finite physical updater for the two Boolean work cells in the canonical edge workspace. The exact well-formed 18-state machine validates descriptor magic 01, crosses the remaining eight header bits and four delimiter-terminated unary coordinates, applies one compile-time finite set/and/or fold to either out or lit, validates the other work cell, and physically rewinds to descriptor cell zero. It preserves every other cell, has least-halt/no-early-halt semantics, and runs in exactly 32+2*(xa+ya+xb+yb) steps, at most twice the local edge-field span. Blank or malformed magic fails closed. No semantic edge predicate occurs in the transition function.","status":"proven","use_cases":["TDX","TEP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Bit-only physical workspace contract for finite edge handlers. edge_workspace_seed places the canonical descriptor, two fixed work bits, the clean literal-query marker, an arbitrary frame, and the first false scratch separator in one exact word. edge_workspace_query proves that after physical coordinate staging the suffix beginning at that marker is exactly sat_literal_query_word, so the existing 269-state clean literal product can preserve the descriptor/work prefix as arbitrary base. Exact seed/query lengths and marker-level SConfig identities are proved. This is layout algebra only; finite descriptor-field locators, nv staging, the edge router, grid emission, encode_tsp, and the strict capstone remain OPEN.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeWorkspace.v":"65c02ba09263cdfbae00d2d01373d314adf2aeb84c5d258843c3a004b81d2d9e"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeWorkspace.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-WORKSPACE","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; targeted pinned Coq compile; pure physical-layout contract only; no edge machine claimed","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"edge_workspace_seed_explicit + edge_workspace_query_payload + edge_workspace_marker_cfg_exact + edge_workspace_query_length","source_completeness":"full (CSV-sourced)","statement":"Bit-only physical workspace contract for finite edge handlers. edge_workspace_seed places the canonical descriptor, two fixed work bits, the clean literal-query marker, an arbitrary frame, and the first false scratch separator in one exact word. edge_workspace_query proves that after physical coordinate staging the suffix beginning at that marker is exactly sat_literal_query_word, so the existing 269-state clean literal product can preserve the descriptor/work prefix as arbitrary base. Exact seed/query lengths and marker-level SConfig identities are proved. This is layout algebra only; finite descriptor-field locators, nv staging, the edge router, grid emission, encode_tsp, and the strict capstone remain OPEN.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: item-4 travel-write-return primitive (single-region core): s_emit1 travels to the data-dependent far end of a unary block, WRITES a new true there (block grows S m -> S (S m)), and RETURNS the head to the start -- the write-at-a-distant-growing-output + return piece that s_iter (monotone march) and s_rewind (content-preserving round trip) do not by themselves provide. Proven 0-axiom by the same march-fold induction as s_rewind plus a writing turn (s_emit1_march_right/left, s_emit1_run/halted/extract; s_extract grows by one). HONEST: single-region; the source-preserving gap-crossing 4-phase variant (invariant Compute-verified) is next, and unary multiply = s_iter counter with an s_emit-across body. coqchk Axioms: .","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEmit.v":"c19c567cc6de31684551762326120eb424a13e8841693e89fde26d929190c3be"},"files":{"coq_file":"proofs/coq/ComplexityStrictEmit.v"},"id":"CUB-COMPLEXITY-STRICT-EMIT","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"travel-write-return","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_emit1_run + s_emit1_extract","source_completeness":"full (CSV-sourced)","statement":"item-4 travel-write-return primitive (single-region core): s_emit1 travels to the data-dependent far end of a unary block, WRITES a new true there (block grows S m -> S (S m)), and RETURNS the head to the start -- the write-at-a-distant-growing-output + return piece that s_iter (monotone march) and s_rewind (content-preserving round trip) do not by themselves provide. Proven 0-axiom by the same march-fold induction as s_rewind plus a writing turn (s_emit1_march_right/left, s_emit1_run/halted/extract; s_extract grows by one). HONEST: single-region; the source-preserving gap-crossing 4-phase variant (invariant Compute-verified) is next, and unary multiply = s_iter counter with an s_emit-across body. coqchk Axioms: .","status":"proven","use_cases":["complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: item-4 SOURCE-PRESERVING travel-write-return: s_emit (4-state) crosses a gap from a source region to a DISTANT output region; appends one true at the output far end; returns the head to the source start leaving the SOURCE INTACT. Proven 0-axiom by four march-fold phases (emit_r0 source-right; emit_r1 output-right; emit_l2 output-left; emit_l3 source-left) glued through the two gap crossings and the writing turn (emit_cross_r1; emit_write_l2_cross; emit_middle handles o=0). s_emit_run: source(S s)|gap|output(o) -> source(S s)|gap|output(S o), head home, in 2*S s + 2*o + 3 steps; s_emit_halted/extract (s_extract = repeat true (S s) ++ repeat true (S o)). This is exactly the body unary multiply drives S b times. coqchk Axioms: .","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEmitGap.v":"3c6010114f0864372e8625fea331beb8ddc9ea3d662ecd06159e3adaae9da814"},"files":{"coq_file":"proofs/coq/ComplexityStrictEmitGap.v"},"id":"CUB-COMPLEXITY-STRICT-EMIT-GAP","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"gap-travel-write-return","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_emit_run + s_emit_extract","source_completeness":"full (CSV-sourced)","statement":"item-4 SOURCE-PRESERVING travel-write-return: s_emit (4-state) crosses a gap from a source region to a DISTANT output region; appends one true at the output far end; returns the head to the source start leaving the SOURCE INTACT. Proven 0-axiom by four march-fold phases (emit_r0 source-right; emit_r1 output-right; emit_l2 output-left; emit_l3 source-left) glued through the two gap crossings and the writing turn (emit_cross_r1; emit_write_l2_cross; emit_middle handles o=0). s_emit_run: source(S s)|gap|output(o) -> source(S s)|gap|output(S o), head home, in 2*S s + 2*o + 3 steps; s_emit_halted/extract (s_extract = repeat true (S s) ++ repeat true (S o)). This is exactly the body unary multiply drives S b times. coqchk Axioms: .","status":"proven","use_cases":["TEP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Finite 11689-state faithful machine computes word_reduce from every s_init w within one fixed degree-110 budget and establishes both s_poly_reduces and canonical ComplexityReductions.poly_reduces L_3SAT L_TSP. The canonical relation is now definitionally the finite-state distinct-Blank contract; the retired Boolean-tape relation remains available only as legacy_poly_reduces. NP-completeness, arbitrary-layout rejection, and a stronger clean-empty-left transducer remain unclaimed.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEncodeTsp.v":"22bad3aaec4e75fad0f6bdd598f2db8b76dd94f48e7dbcd559e0198aa5c586bf"},"files":{"coq_file":"proofs/coq/ComplexityStrictEncodeTsp.v"},"id":"CUB-COMPLEXITY-STRICT-ENCODE-TSP","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Coq-only faithful finite-TM theorem; first-halt correctness is modulo existential output padding, with no padding lower/minimality claim; canonical Phase 4 closed without erasing Blank to false; coqchk Axioms: required by the live proof gate","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_encode_tsp_state_bound + s_encode_tsp_well_formed + s_encode_tsp_first_halt + encode_tsp_total_bound_strict + s_encode_tsp_computes_strict + s_encode_tsp_poly_reduces + encode_tsp_poly_reduces + phase4_poly_reduces","source_completeness":"full (CSV-sourced)","statement":"Finite 11689-state faithful machine computes word_reduce from every s_init w within one fixed degree-110 budget and establishes both s_poly_reduces and canonical ComplexityReductions.poly_reduces L_3SAT L_TSP. The canonical relation is now definitionally the finite-state distinct-Blank contract; the retired Boolean-tape relation remains available only as legacy_poly_reduces. NP-completeness, arbitrary-layout rejection, and a stronger clean-empty-left transducer remain unclaimed.","status":"proven","use_cases":["admission","TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: s_maxerode run lemmas PART 1 -- all phase-local march folds proven (the s_rewind/s_copy discipline): M1 erode_mfalse (A-phase skid over delimiters/eroded cells, state 0/1 preserved), M2 erode_mtrue (B-phase true-run), M3/M3' erode_dance/_end (the 3-step C/D back-up-erode-resume at a group's right edge, pure reflexivity -- interior + final-delimiter variants), M4 erode_rewind (E-phase left march over arbitrary Bits to the gap), M5 erode_emit (full F/G output round trip with erode_mF/mG sub-folds, EXACT 2m+3 budget; a draft 2m+4 miscount was compiler-caught). Parts 2/3 remain: single-pass composition (tallies l -> zero-interleaved map pred l), multi-pass induction to EROSION_IS_MAX, s_maxerode_computes -- the machine is still NOT claimed to compute anything. Strict wrapper OPEN. NP-hardness (Karp 1972) not P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun.v":"12ddb2cb94259f96b2d057a20afdf5ecfe3539633d48462bc446382791d5fded"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"erode_mfalse + erode_dance + erode_rewind + erode_emit","source_completeness":"full (CSV-sourced)","statement":"s_maxerode run lemmas PART 1 -- all phase-local march folds proven (the s_rewind/s_copy discipline): M1 erode_mfalse (A-phase skid over delimiters/eroded cells, state 0/1 preserved), M2 erode_mtrue (B-phase true-run), M3/M3' erode_dance/_end (the 3-step C/D back-up-erode-resume at a group's right edge, pure reflexivity -- interior + final-delimiter variants), M4 erode_rewind (E-phase left march over arbitrary Bits to the gap), M5 erode_emit (full F/G output round trip with erode_mF/mG sub-folds, EXACT 2m+3 budget; a draft 2m+4 miscount was compiler-caught). Parts 2/3 remain: single-pass composition (tallies l -> zero-interleaved map pred l), multi-pass induction to EROSION_IS_MAX, s_maxerode_computes -- the machine is still NOT claimed to compute anything. Strict wrapper OPEN. NP-hardness (Karp 1972) not P vs NP.","status":"proven","use_cases":["TEP","admission","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: erode_scan -- the GENERAL A-phase scan over a MIXED group list (zeros allowed), advisor-reviewed. Drops erode_scan_pos's all-positive assumption; the scan every round >=2 needs (next_ts injects empty groups). Over group_word ts followed by a nonempty suffix (the trailing Blank), one sweep: t>0 -> erode_group_interior shaves one true (t+3 steps, state->1); t=0 -> erode_mfalse skids the lone delimiter (1 step, state preserved). Ends at hd suf, deposits map Bit (scan_bits_gen ts) on the left, state = if has_pos ts then 1 else s. Every nonempty group is interior (the suffix guarantees a following cell, so erode_group_final is unneeded). New scan_fuel_gen (empty=1, nonempty=t+3) + scan_state. Feeds E2 canonical pass + E3 fold. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun10.v":"6d90a3b0e04c5877fe2dc9fc72e3efdf61d0f66ecd16c4f1e15af73365eb59ea"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun10.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN10","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"erode_scan + scan_fuel_gen + scan_state","source_completeness":"full (CSV-sourced)","statement":"erode_scan -- the GENERAL A-phase scan over a MIXED group list (zeros allowed), advisor-reviewed. Drops erode_scan_pos's all-positive assumption; the scan every round >=2 needs (next_ts injects empty groups). Over group_word ts followed by a nonempty suffix (the trailing Blank), one sweep: t>0 -> erode_group_interior shaves one true (t+3 steps, state->1); t=0 -> erode_mfalse skids the lone delimiter (1 step, state preserved). Ends at hd suf, deposits map Bit (scan_bits_gen ts) on the left, state = if has_pos ts then 1 else s. Every nonempty group is interior (the suffix guarantees a following cell, so erode_group_final is unneeded). New scan_fuel_gen (empty=1, nonempty=t+3) + scan_state. Feeds E2 canonical pass + E3 fold. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","status":"proven","use_cases":["TEP","crypto","TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: erode_pass_canon -- ONE canonical erosion pass from the mid-computation shape (any output count m, any tally list, zeros allowed), advisor-reviewed. Multi-round invariant (Compute-confirmed): tape = [gap Blank][m output trues] | group_word ts | [one trailing Blank], head at first cell, state 0; one pass maps it to the same shape with m->m+1 and ts->next_ts ts; exactly one trailing Blank throughout (no accumulation). Composes erode_scan (E1) + state-1-on-Blank entry + erode_rewind_to_gap (leftsuf = the m output trues) + erode_emit m; the eroded left reversed = group_word (next_ts ts) via the general bridge. pass_fuel_canon = scan_fuel_gen ts + length(scan_bits_gen ts) + 2m + 4. erode_pass1_pos (m=0) matches this canonical form, so E3's fold chains round 1 into it. Only E3 (tmax-fold to s_maxerode_computes + false-tail conservation) remains for the erosion capstone. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun11.v":"f21bf149f0759aef8350e7f5d503550583294a32cffafe30be3a6d7be6e81726"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun11.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN11","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"erode_pass_canon + pass_fuel_canon","source_completeness":"full (CSV-sourced)","statement":"erode_pass_canon -- ONE canonical erosion pass from the mid-computation shape (any output count m, any tally list, zeros allowed), advisor-reviewed. Multi-round invariant (Compute-confirmed): tape = [gap Blank][m output trues] | group_word ts | [one trailing Blank], head at first cell, state 0; one pass maps it to the same shape with m->m+1 and ts->next_ts ts; exactly one trailing Blank throughout (no accumulation). Composes erode_scan (E1) + state-1-on-Blank entry + erode_rewind_to_gap (leftsuf = the m output trues) + erode_emit m; the eroded left reversed = group_word (next_ts ts) via the general bridge. pass_fuel_canon = scan_fuel_gen ts + length(scan_bits_gen ts) + 2m + 4. erode_pass1_pos (m=0) matches this canonical form, so E3's fold chains round 1 into it. Only E3 (tmax-fold to s_maxerode_computes + false-tail conservation) remains for the erosion capstone. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","status":"proven","use_cases":["crypto","TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: cell-count conservation for the erosion capstone's false tail (advisor-recommended smallest first E3 sub-brick, pure list arithmetic). L1 group_word_length: length (group_word ts) = fold_right Nat.add 0 ts + length ts (sum of tallies + number of groups). L2 group_word_length_next_ts: length (group_word (next_ts ts)) = length (group_word ts) -- erosion preserves tape cell count across every pass (t>0 expands to [t-1;0] contributing t+1 cells = same; t=0 stays [0] = 1 cell). These make the final s_maxerode tape's false-tail length = |w| (with the round-1 anchor length (group_word (tallies w)) = |w| for delimiter-terminated w, next). Feeds E3 s_maxerode_computes. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun12.v":"3507d07a45755dc5f2fd06e1115d27d93ab1d628e982e924c36437645fdad428"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun12.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN12","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"group_word_length + group_word_length_next_ts","source_completeness":"full (CSV-sourced)","statement":"cell-count conservation for the erosion capstone's false tail (advisor-recommended smallest first E3 sub-brick, pure list arithmetic). L1 group_word_length: length (group_word ts) = fold_right Nat.add 0 ts + length ts (sum of tallies + number of groups). L2 group_word_length_next_ts: length (group_word (next_ts ts)) = length (group_word ts) -- erosion preserves tape cell count across every pass (t>0 expands to [t-1;0] contributing t+1 cells = same; t=0 stays [0] = 1 cell). These make the final s_maxerode tape's false-tail length = |w| (with the round-1 anchor length (group_word (tallies w)) = |w| for delimiter-terminated w, next). Feeds E3 s_maxerode_computes. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: the round-1 length anchor for the erosion capstone's false tail. group_word_tallies_length: for delimiter-terminated w (last w false = false), length (group_word (tallies w)) = length w. With L2 (ErodeRun12) the eroded tape's cell count stays |w| across every pass, so the final s_extract false tail is exactly repeat false |w|. Via L1: length = sum(tallies) + #groups = #trues + #falses = |w|. Helpers sum_tallies_bit_to_nat (sum of per-group tally counts = total trues) + trues_plus_falses (#trues + #falses = length); #groups = #falses via the existing split_len_terminated. Feeds E3 s_maxerode_computes. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun13.v":"48f0e8eadd6172a4af57dd6b194e077a3046450ca3a4ae2e419ab3ad7db5748d"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun13.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN13","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"group_word_tallies_length + sum_tallies_bit_to_nat + trues_plus_falses","source_completeness":"full (CSV-sourced)","statement":"the round-1 length anchor for the erosion capstone's false tail. group_word_tallies_length: for delimiter-terminated w (last w false = false), length (group_word (tallies w)) = length w. With L2 (ErodeRun12) the eroded tape's cell count stays |w| across every pass, so the final s_extract false tail is exactly repeat false |w|. Via L1: length = sum(tallies) + #groups = #trues + #falses = |w|. Helpers sum_tallies_bit_to_nat (sum of per-group tally counts = total trues) + trues_plus_falses (#trues + #falses = length); #groups = #falses via the existing split_len_terminated. Feeds E3 s_maxerode_computes. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: the round-1 tape identity: group_word_tallies -- for delimiter-terminated w (last w false = false), group_word (tallies w) = map Bit w: the initial tape IS the group_word of its tallies, the content twin of the Run13 length anchor. Puts s_init w into the erosion machine's canonical group_word shape for pass 1. Helpers: split_clauses_true/split_clauses_false reduction equations pinned at @cons Symbol (the Symbol-vs-bool elaboration trap makes bare true::tl rewrites fail), split_clauses_nonempty, tallies_cons_ne. Feeds the s_maxerode_computes assembly. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun14.v":"6399f70e96c35a9217be560c032cf0d3244714b5be6e304aac77358a7a3776a9"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun14.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN14","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"group_word_tallies + split_clauses_nonempty + tallies_cons_ne","source_completeness":"full (CSV-sourced)","statement":"the round-1 tape identity: group_word_tallies -- for delimiter-terminated w (last w false = false), group_word (tallies w) = map Bit w: the initial tape IS the group_word of its tallies, the content twin of the Run13 length anchor. Puts s_init w into the erosion machine's canonical group_word shape for pass 1. Helpers: split_clauses_true/split_clauses_false reduction equations pinned at @cons Symbol (the Symbol-vs-bool elaboration trap makes bare true::tl rewrites fail), split_clauses_nonempty, tallies_cons_ne. Feeds the s_maxerode_computes assembly. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","status":"proven","use_cases":["crypto","TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: erode_scan_end -- the GENERAL (mixed-group) A-phase scan ending at the PHYSICAL tape end (no materialized trailing Blank), the round-1 twin of erode_scan. One sweep over group_word ts (ts <> [], zeros allowed) from state s in {0,1} deposits map Bit (scan_bits_gen ts) and lands on the fresh end Blank (right tape empty) in state scan_state s ts, with the SAME fuel scan_fuel_gen ts. No new machine induction: snoc-split ts = ts' ++ [tlast], drive ts' with erode_scan (suffix = the last group's word, never empty), finish with erode_group_final (t>0) or the 1-step skid (t=0). Pure-list glue: scan_fuel_gen_app, scan_bits_gen_app, has_pos_app. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun15.v":"aad0c07ec4b6d555d6ae7c5066a1e43759b6d50d9d667eaff1d30e48a3ef06a5"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun15.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN15","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"erode_scan_end + erode_scan_last + scan_bits_gen_app + has_pos_app","source_completeness":"full (CSV-sourced)","statement":"erode_scan_end -- the GENERAL (mixed-group) A-phase scan ending at the PHYSICAL tape end (no materialized trailing Blank), the round-1 twin of erode_scan. One sweep over group_word ts (ts <> [], zeros allowed) from state s in {0,1} deposits map Bit (scan_bits_gen ts) and lands on the fresh end Blank (right tape empty) in state scan_state s ts, with the SAME fuel scan_fuel_gen ts. No new machine induction: snoc-split ts = ts' ++ [tlast], drive ts' with erode_scan (suffix = the last group's word, never empty), finish with erode_group_final (t>0) or the 1-step skid (t=0). Pure-list glue: scan_fuel_gen_app, scan_bits_gen_app, has_pos_app. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","status":"proven","use_cases":["TEP","TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: erode_pass1_canon -- the GENERAL (mixed-group) ROUND-1 pass from the initial tape shape (empty left tape, no trailing Blank) into the canonical mid-computation shape at m=1, in pass_fuel_canon ts 0 steps. Round 1 differs from erode_pass_canon at both boundaries: the physical left edge plays the gap Blank and the physical right edge materializes the trailing Blank; the machine mints both during the pass. Composes erode_scan_end -> state-1-on-Blank SL entry -> erode_rewind (boundary) -> erode_emit m=0 -> the Run9 general bridge (eroded tape reversed = group_word (next_ts ts)). Supersedes erode_pass1_pos's all-positive restriction. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun16.v":"e09b1712d942981ce46ef30859a946b351780df1f56e6fd6325447ef9d419acc"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun16.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN16","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"erode_pass1_canon","source_completeness":"full (CSV-sourced)","statement":"erode_pass1_canon -- the GENERAL (mixed-group) ROUND-1 pass from the initial tape shape (empty left tape, no trailing Blank) into the canonical mid-computation shape at m=1, in pass_fuel_canon ts 0 steps. Round 1 differs from erode_pass_canon at both boundaries: the physical left edge plays the gap Blank and the physical right edge materializes the trailing Blank; the machine mints both during the pass. Composes erode_scan_end -> state-1-on-Blank SL entry -> erode_rewind (boundary) -> erode_emit m=0 -> the Run9 general bridge (eroded tape reversed = group_word (next_ts ts)). Supersedes erode_pass1_pos's all-positive restriction. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","status":"proven","use_cases":["TEP","crypto","TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: erode_fold -- the multi-pass E3 fold over canonical configurations. From the canonical shape (m output trues, group_word ts, one trailing Blank) with pass budget n >= tmax ts, the machine reaches the HALT configuration (state 0 on the terminating Blank) having emitted exactly tmax ts further output trues -- EROSION_IS_MAX at the machine level -- over a final all-zero ts_fin with length (group_word ts_fin) = length (group_word ts) (L2 conservation threaded through every pass). Concrete fuel recursion erode_fold_fuel (one pass_fuel_canon per productive pass + one final unproductive scan). Induction on n glues erode_pass_canon through tmax_next_ts; unproductive tail = erode_scan at [Blank] where A0-on-Blank is SHalt (max_pos_iff exact). Helpers: has_pos_false_tmax, erode_fold_flat. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun17.v":"2feedc5c30416f71b1619f504bc416f83576059436a91ac3caed8da8cabacc2c"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun17.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN17","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"erode_fold + erode_fold_fuel + erode_fold_flat + has_pos_false_tmax","source_completeness":"full (CSV-sourced)","statement":"erode_fold -- the multi-pass E3 fold over canonical configurations. From the canonical shape (m output trues, group_word ts, one trailing Blank) with pass budget n >= tmax ts, the machine reaches the HALT configuration (state 0 on the terminating Blank) having emitted exactly tmax ts further output trues -- EROSION_IS_MAX at the machine level -- over a final all-zero ts_fin with length (group_word ts_fin) = length (group_word ts) (L2 conservation threaded through every pass). Concrete fuel recursion erode_fold_fuel (one pass_fuel_canon per productive pass + one final unproductive scan). Induction on n glues erode_pass_canon through tmax_next_ts; unproductive tail = erode_scan at [Blank] where A0-on-Blank is SHalt (max_pos_iff exact). Helpers: has_pos_false_tmax, erode_fold_flat. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","status":"proven","use_cases":["admission","crypto","TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: s_maxerode_computes -- THE EROSION CAPSTONE. On every delimiter-terminated w (last w false = false) the erosion machine run with the concrete fuel maxerode_fuel w HALTS with s_extract (final) = repeat true (max_tally w) ++ repeat false (length w): EROSION_IS_MAX at the machine level, the PART 2/3 target. Assembly: round-1 tape identity (Run14) -> productive round 1 (erode_pass1_canon, Run16) -> multi-pass fold (erode_fold, Run17); false tail = |w| by cell-count conservation (Run12 L1/L2 + Run13 anchor); unproductive round 1 (all tallies zero, me_check4 boundary) halts directly via erode_scan_end (Run15). Extraction helpers tape_to_bits_app/map_Bit/map_Bit_rev + final_extract/flat_extract + tmax_zero_sum/tmax_zero_scan_bits. NOT yet proven: the polynomial budget wrapper (max_tally_le_length hook) and the s_clean_transduces_pad wrap toward the num_vars stage machine. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun18.v":"95a4c6ecb7ddac65aec958e6c26cb603be26b568add051bf45e394c4f56d578b"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun18.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN18","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_maxerode_computes + maxerode_fuel + final_extract + flat_extract","source_completeness":"full (CSV-sourced)","statement":"s_maxerode_computes -- THE EROSION CAPSTONE. On every delimiter-terminated w (last w false = false) the erosion machine run with the concrete fuel maxerode_fuel w HALTS with s_extract (final) = repeat true (max_tally w) ++ repeat false (length w): EROSION_IS_MAX at the machine level, the PART 2/3 target. Assembly: round-1 tape identity (Run14) -> productive round 1 (erode_pass1_canon, Run16) -> multi-pass fold (erode_fold, Run17); false tail = |w| by cell-count conservation (Run12 L1/L2 + Run13 anchor); unproductive round 1 (all tallies zero, me_check4 boundary) halts directly via erode_scan_end (Run15). Extraction helpers tape_to_bits_app/map_Bit/map_Bit_rev + final_extract/flat_extract + tmax_zero_sum/tmax_zero_scan_bits. NOT yet proven: the polynomial budget wrapper (max_tally_le_length hook) and the s_clean_transduces_pad wrap toward the num_vars stage machine. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","status":"proven","use_cases":["admission","TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: the polynomial budget wrapper for the erosion capstone. maxerode_fuel_quad: for delimiter-terminated w, maxerode_fuel w <= 6*|w|^2 + 13*|w| + 4 (sharp). maxerode_fuel_poly: maxerode_fuel w <= 19*(length w)^2 + 19 -- exactly the c*n^k+c shape ComplexityStrictBudget consumes (k=2, c=19); maxerode_fuel_poly_ex for existential consumers. Route: <= |w| passes via max_tally_le_length, O(|w|) fuel per pass via cell-count conservation (Run12/13). Still open on this axis: the s_computes_in_poly_strict packaging wrap. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun19.v":"78f918c2d4f004022a30d367f1931e20cc10ee2bf8d104d3a1d265f66b1960b6"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun19.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN19","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"maxerode_fuel_poly + maxerode_fuel_quad","source_completeness":"full (CSV-sourced)","statement":"the polynomial budget wrapper for the erosion capstone. maxerode_fuel_quad: for delimiter-terminated w, maxerode_fuel w <= 6*|w|^2 + 13*|w| + 4 (sharp). maxerode_fuel_poly: maxerode_fuel w <= 19*(length w)^2 + 19 -- exactly the c*n^k+c shape ComplexityStrictBudget consumes (k=2, c=19); maxerode_fuel_poly_ex for existential consumers. Route: <= |w| passes via max_tally_le_length, O(|w|) fuel per pass via cell-count conservation (Run12/13). Still open on this axis: the s_computes_in_poly_strict packaging wrap. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","status":"proven","use_cases":["admission","crypto","TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: s_maxerode run lemmas PART 2 (first swing): erode_group_interior -- one A-phase traversal of a nonempty group at an INTERIOR delimiter (m+4 steps) erodes the group's last true to Bit false and advances the head to the next group's first cell in state 1, i.e. tally (m+1)->m = pred (the per-group action of ONE erosion pass; fold_max_pred). Composed 0-axiom purely from the PART 1 folds: the entry step (0/1,Bit true)->state 2, erode_mtrue over the true-run, erode_dance at the delimiter. NOT proven: final-group variant (erode_dance_end, right tape empty), the whole-pass induction over the group list, the multi-pass fold to EROSION_IS_MAX, s_maxerode_computes. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun2.v":"089167c637fb178dece8664a6f5c49415ae77f1822e9e2196745b6c552453abb"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun2.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN2","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"erode_group_interior","source_completeness":"full (CSV-sourced)","statement":"s_maxerode run lemmas PART 2 (first swing): erode_group_interior -- one A-phase traversal of a nonempty group at an INTERIOR delimiter (m+4 steps) erodes the group's last true to Bit false and advances the head to the next group's first cell in state 1, i.e. tally (m+1)->m = pred (the per-group action of ONE erosion pass; fold_max_pred). Composed 0-axiom purely from the PART 1 folds: the entry step (0/1,Bit true)->state 2, erode_mtrue over the true-run, erode_dance at the delimiter. NOT proven: final-group variant (erode_dance_end, right tape empty), the whole-pass induction over the group list, the multi-pass fold to EROSION_IS_MAX, s_maxerode_computes. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","status":"proven","use_cases":["TEP","TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: s_maxerode_budget -- delimiter-domain BUDGET capstone at 19*|w|^2+19, with exact raw output repeat true(max_tally w)++repeat false(length w). s_maxerode_budget_first_halt now derives the least halting time and never-halts-early clause. A kernel-checked equal-length, delimiter-terminated collision proves no_total_num_vars_postprocessor_from_run20_output: no terminal function of Run20's raw output can compute unary num_vars on every word, because parse_3sat drops incomplete part suffixes. Therefore direct Blank-ended totalization of raw erosion is insufficient; the parse-preserving complete-prefix normalizer from StrictVarMax needs a finite clean-pad machine. Run20's left-tape output canonicalization, physical halve/successor, total composition, and strict s_poly_reduces L_3SAT L_TSP remain OPEN. NP-hardness (Karp 1972), NOT P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun20.v":"78f199e52c2e9e37614146c29cb240029cf1f731c3b0b109e7dbb969c616daa4"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun20.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN20","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; exact scoped theorems proven; no total clean num_vars stage claimed; coq-only strict-TM corpus","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_maxerode_budget + s_maxerode_budget_first_halt + no_total_num_vars_postprocessor_from_run20_output","source_completeness":"full (CSV-sourced)","statement":"s_maxerode_budget -- delimiter-domain BUDGET capstone at 19*|w|^2+19, with exact raw output repeat true(max_tally w)++repeat false(length w). s_maxerode_budget_first_halt now derives the least halting time and never-halts-early clause. A kernel-checked equal-length, delimiter-terminated collision proves no_total_num_vars_postprocessor_from_run20_output: no terminal function of Run20's raw output can compute unary num_vars on every word, because parse_3sat drops incomplete part suffixes. Therefore direct Blank-ended totalization of raw erosion is insufficient; the parse-preserving complete-prefix normalizer from StrictVarMax needs a finite clean-pad machine. Run20's left-tape output canonicalization, physical halve/successor, total composition, and strict s_poly_reduces L_3SAT L_TSP remain OPEN. NP-hardness (Karp 1972), NOT P vs NP.","status":"proven","use_cases":["admission","TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: erosion PART 2 -- the FINAL-group pass step: erode_group_final, the right-tape-EMPTY mirror of erode_group_interior (via erode_dance_end). From A-phase state s in {0,1} at the first true of the LAST group ((m+1) trues + the terminating delimiter, nothing after), m+4 steps erode the group's last true to Bit false and step off the tape end onto the fresh Blank in state 1 -- tally (m+1)->m = pred. Composed 0-axiom from PART 1 folds (entry step (0/1,Bit true)->2, erode_mtrue, erode_dance_end). The single-pass composition (erode_pass), multi-pass fold to EROSION_IS_MAX, and s_maxerode_computes remain. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun3.v":"7ceb71e84a9e3f705dab64098e3d1fd8a06dc11e162c8de8cd50717dd3da59e9"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun3.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN3","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"erode_group_final","source_completeness":"full (CSV-sourced)","statement":"erosion PART 2 -- the FINAL-group pass step: erode_group_final, the right-tape-EMPTY mirror of erode_group_interior (via erode_dance_end). From A-phase state s in {0,1} at the first true of the LAST group ((m+1) trues + the terminating delimiter, nothing after), m+4 steps erode the group's last true to Bit false and step off the tape end onto the fresh Blank in state 1 -- tally (m+1)->m = pred. Composed 0-axiom from PART 1 folds (entry step (0/1,Bit true)->2, erode_mtrue, erode_dance_end). The single-pass composition (erode_pass), multi-pass fold to EROSION_IS_MAX, and s_maxerode_computes remain. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","status":"proven","use_cases":["TEP","TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: the tally-level pass recurrence (PART 3 arithmetic core): the s_maxerode per-pass tally transform is the EXPANSION next_ts = flat_map (fun t => if 0; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"tmax_next_ts + has_pos_next_ts + next_ts","source_completeness":"full (CSV-sourced)","statement":"the tally-level pass recurrence (PART 3 arithmetic core): the s_maxerode per-pass tally transform is the EXPANSION next_ts = flat_map (fun t => if 00) load-bearing), composition-ready for erode_rewind/erode_emit. The empty-group (mfalse) generalization, the rewind+emit tail, and the multi-pass fold to EROSION_IS_MAX (via tmax_next_ts) remain. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun5.v":"2c0ca47b4da16217e2b4c3df1e5846245a5167e4a7f77e17786fcecc63251588"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun5.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN5","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"erode_scan_pos + group_word_pos","source_completeness":"full (CSV-sourced)","statement":"erode_pass SCAN phase (all-positive groups): erode_scan_pos -- the A-phase scan of s_maxerode over a delimiter-terminated ALL-NONEMPTY group list, by induction composing erode_group_interior (every group but the last) + erode_group_final (last), eroding one true from EVERY group (map pred at the tally level) in scan_fuel = sum(t_i+3) steps, halting at the terminating Blank in state 1 (productive) and depositing scan_acc_pos (grp_dep per group = two falses over the surviving t-1 trues). group_word_pos exposes a positive group's leading Bit true. Advisor-reviewed: statement faithful, non-vacuous (Forall(>0) load-bearing), composition-ready for erode_rewind/erode_emit. The empty-group (mfalse) generalization, the rewind+emit tail, and the multi-pass fold to EROSION_IS_MAX (via tmax_next_ts) remain. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","status":"proven","use_cases":["TEP","TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: erode_rewind_to_gap (advisor-designed): erode_rewind generalized so state 5 marches the Bit prefix and HALTS at an INTERIOR gap Blank. Left tape map Bit bs ++ Blank :: leftsuf, S(length bs) steps, exposing the gap Blank as head in state 5 with leftsuf (the emitted output block) untouched below it and the marched cells prepended to rightsuf. THE rewind lemma that serves EVERY erosion pass (pass 1 boundary = leftsuf []; pass>=2 gap = leftsuf the output trues); erode_rewind_to_gap_boundary corollary recovers the boundary case. Same induction as erode_rewind; gap + suffixes inert. Unblocks the rewind+emit tail of the full pass. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun6.v":"7c9bc96a90149f32a0007a4bdf48592f19e5ea1f1eef07432e1fa6ba6e632cd9"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun6.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN6","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"erode_rewind_to_gap + erode_rewind_to_gap_boundary","source_completeness":"full (CSV-sourced)","statement":"erode_rewind_to_gap (advisor-designed): erode_rewind generalized so state 5 marches the Bit prefix and HALTS at an INTERIOR gap Blank. Left tape map Bit bs ++ Blank :: leftsuf, S(length bs) steps, exposing the gap Blank as head in state 5 with leftsuf (the emitted output block) untouched below it and the marched cells prepended to rightsuf. THE rewind lemma that serves EVERY erosion pass (pass 1 boundary = leftsuf []; pass>=2 gap = leftsuf the output trues); erode_rewind_to_gap_boundary corollary recovers the boundary case. Same induction as erode_rewind; gap + suffixes inert. Unblocks the rewind+emit tail of the full pass. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","status":"proven","use_cases":["TEP","TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: the two pure-list bridges for the full erosion pass (advisor-reviewed). B0 scan_acc_map_bit: scan_acc_pos ts acc = map Bit (scan_bits ts) ++ acc (generalized accumulator) -- the scan output is map Bit of a bool list, so erode_rewind can consume it. A rev_scan_bits_group_word: for all-positive ts, map Bit (rev (scan_bits ts)) = group_word (next_ts ts) -- the eroded left tape reversed IS the next pass's input encoding; feeds the multi-pass fold. all-positive load-bearing (ts=[1;0;1] gives a length mismatch). Helpers: map_Bit_repeat_true, rev_repeat_bool, repeat_snoc_bool, group_word_app (group_word homomorphism), grp_bits_rev_group_word. scan_bits/grp_bits are the bool twins of scan_acc_pos/grp_dep. s_maxerode_computes + the pass composition (erode_pass1_pos) remain. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun7.v":"8317a77f98a0d0c273c41024d2a38f58cbc83db3782bd211228333fed0efc794"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun7.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN7","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"scan_acc_map_bit + rev_scan_bits_group_word + group_word_app","source_completeness":"full (CSV-sourced)","statement":"the two pure-list bridges for the full erosion pass (advisor-reviewed). B0 scan_acc_map_bit: scan_acc_pos ts acc = map Bit (scan_bits ts) ++ acc (generalized accumulator) -- the scan output is map Bit of a bool list, so erode_rewind can consume it. A rev_scan_bits_group_word: for all-positive ts, map Bit (rev (scan_bits ts)) = group_word (next_ts ts) -- the eroded left tape reversed IS the next pass's input encoding; feeds the multi-pass fold. all-positive load-bearing (ts=[1;0;1] gives a length mismatch). Helpers: map_Bit_repeat_true, rev_repeat_bool, repeat_snoc_bool, group_word_app (group_word homomorphism), grp_bits_rev_group_word. scan_bits/grp_bits are the bool twins of scan_acc_pos/grp_dep. s_maxerode_computes + the pass composition (erode_pass1_pos) remain. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: erode_pass1_pos: ONE FULL erosion pass of s_maxerode over an all-positive delimiter-terminated encoding (m=0, the first pass). 0 axioms; advisor-reviewed plan. Composes the proven pieces end to end: erode_scan_pos (scan) -> B0 scan_acc_map_bit (left tape is map Bit) -> the state-1-on-Blank SL entry step -> erode_rewind (march the Bit prefix to the boundary) -> erode_emit m=0 (write one output true, return to cell 0 in state 0). Total fuel scan_fuel ts + length(scan_bits ts) + 4 (scan + 1 entry + rewind + 3 emit). Result stated RAW (scan_bits/rev); lemma A re-expresses it as group_word(next_ts ts) in the fold. THE FIRST full end-to-end erosion pass proven. pass>=2 (erode_rewind_to_gap), the empty-group generalization, and the multi-pass tmax-fold to s_maxerode_computes remain. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun8.v":"82ae78ef3e18f2105915935aaaec67df96820d8dc720723d0abcd48023befc5f"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun8.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN8","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"erode_pass1_pos","source_completeness":"full (CSV-sourced)","statement":"erode_pass1_pos: ONE FULL erosion pass of s_maxerode over an all-positive delimiter-terminated encoding (m=0, the first pass). 0 axioms; advisor-reviewed plan. Composes the proven pieces end to end: erode_scan_pos (scan) -> B0 scan_acc_map_bit (left tape is map Bit) -> the state-1-on-Blank SL entry step -> erode_rewind (march the Bit prefix to the boundary) -> erode_emit m=0 (write one output true, return to cell 0 in state 0). Total fuel scan_fuel ts + length(scan_bits ts) + 4 (scan + 1 entry + rewind + 3 emit). Result stated RAW (scan_bits/rev); lemma A re-expresses it as group_word(next_ts ts) in the fold. THE FIRST full end-to-end erosion pass proven. pass>=2 (erode_rewind_to_gap), the empty-group generalization, and the multi-pass tmax-fold to s_maxerode_computes remain. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","status":"proven","use_cases":["TEP","TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: the GENERAL (mixed-group) bridge, advisor-designed: rev_scan_bits_gen_group_word -- map Bit (rev (scan_bits_gen ts)) = group_word (next_ts ts) for ALL tally lists (zeros included), NO all-positive hypothesis. Unblocks the multi-pass fold: from round 2 on the machine's tape always contains empty groups (next_ts injects a 0 after every nonempty group), where the all-positive bridge A (ErodeRun7) is FALSE. grp_bits_gen: empty group t=0 deposits a lone delimiter [false] (not grp_bits' two falses), matching next_ts's expand1 0 = [0] collapse. Per-group grp_bits_gen_rev_group_word holds for all t (reuses grp_bits_rev_group_word for t>0). Prerequisite for E1 empty-group scan, E2 canonical pass, E3 fold. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun9.v":"e344322b3236173369fc866da1a1b88d3aa7d8791136a23f6f971711660576de"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun9.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN9","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"rev_scan_bits_gen_group_word + grp_bits_gen_rev_group_word","source_completeness":"full (CSV-sourced)","statement":"the GENERAL (mixed-group) bridge, advisor-designed: rev_scan_bits_gen_group_word -- map Bit (rev (scan_bits_gen ts)) = group_word (next_ts ts) for ALL tally lists (zeros included), NO all-positive hypothesis. Unblocks the multi-pass fold: from round 2 on the machine's tape always contains empty groups (next_ts injects a 0 after every nonempty group), where the all-positive bridge A (ErodeRun7) is FALSE. grp_bits_gen: empty group t=0 deposits a lone delimiter [false] (not grp_bits' two falses), matching next_ts's expand1 0 = [0] collapse. Per-group grp_bits_gen_rev_group_word holds for all t (reuses grp_bits_rev_group_word for t>0). Prerequisite for E1 empty-group scan, E2 canonical pass, E3 fold. Strict s_poly_reduces L_3SAT L_TSP remains OPEN. NP-hardness (Karp 1972), NOT P vs NP.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: emit ONE unary field enc_nat(counter) = (counter) trues ++ [false] at the end of an ARBITRARY bit-string output -- the reusable 'emit one field' primitive the tsp_stream body names (ComplexityStrictStream.v): the encode stage emits enc_nat(num_cities) ++ enc_nat(max_bound) ++ (n^2 grid of enc_nat(adj)), each a s_field emission. s_field (7-state) generalizes s_copy's all-trues emit to a MIXED output -- prior fields carry Bit-false delimiters so state 2/3 cross Bit _ not just Bit true (proven via the map-Bit round-trip lemmas gfield_m2/m3 with rev bookkeeping that cancels in gfield_out) -- then state 0 on Blank REDIRECTS SR 5 to the delimiter phase (gfield_m5 travels to the output end, writes the Bit-false delimiter, halts). Design Compute-verified on 3 mixed cases before proof. CLEAN extract (unlike s_mult): the counter fully consumes to Blanks (dropped by tape_to_bits), so s_field_extract = ob ++ enc_nat(S k) -- prior output bits with the new field appended. Proven 0-axiom via gfield_m1/m4 (counter marches), gfield_cycle/gfield_emit (fold), gfield_m5 (delimiter travel), and tape_to_bits_rev. coqchk Axioms: .","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictField.v":"10777b06ac2a9cbc115bdc6e7bfa84ddb7a1ab315a7651f1228ff246f76e29dd"},"files":{"coq_file":"proofs/coq/ComplexityStrictField.v"},"id":"CUB-COMPLEXITY-STRICT-FIELD","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"field-emitter-clean-extract","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_field_extract","source_completeness":"full (CSV-sourced)","statement":"emit ONE unary field enc_nat(counter) = (counter) trues ++ [false] at the end of an ARBITRARY bit-string output -- the reusable 'emit one field' primitive the tsp_stream body names (ComplexityStrictStream.v): the encode stage emits enc_nat(num_cities) ++ enc_nat(max_bound) ++ (n^2 grid of enc_nat(adj)), each a s_field emission. s_field (7-state) generalizes s_copy's all-trues emit to a MIXED output -- prior fields carry Bit-false delimiters so state 2/3 cross Bit _ not just Bit true (proven via the map-Bit round-trip lemmas gfield_m2/m3 with rev bookkeeping that cancels in gfield_out) -- then state 0 on Blank REDIRECTS SR 5 to the delimiter phase (gfield_m5 travels to the output end, writes the Bit-false delimiter, halts). Design Compute-verified on 3 mixed cases before proof. CLEAN extract (unlike s_mult): the counter fully consumes to Blanks (dropped by tape_to_bits), so s_field_extract = ob ++ enc_nat(S k) -- prior output bits with the new field appended. Proven 0-axiom via gfield_m1/m4 (counter marches), gfield_cycle/gfield_emit (fold), gfield_m5 (delimiter travel), and tape_to_bits_rev. coqchk Axioms: .","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Finite physical staging of the encoded num-vars suffix from an exact sat_N_frame. The well-formed 10-state s_frame_nv_stage_raw scans to the right edge, locates the penultimate unary field, copies it right-to-left into arbitrary scratch using only tape transitions, restores every source bit, and returns to the first frame cell. Separate physical handoff lemmas cover a Blank predecessor for an empty normalized formula and a false predecessor for a nonempty terminated formula; the machine transition never invokes parse_3sat, num_vars, or sat_N_value. The total sat_N_frame specialization preserves arbitrary base and the complete frame, appends exactly true^num_vars, proves least-halt/no-early-halt semantics, and is bounded by 8*frame_nv_stage_span^2. Finite handler composition, karp_edge, grid emission, encode_tsp, and the strict capstone remain OPEN.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictFrameNvStage.v":"ba59fa7bf4d6c44b0131635a35df40433d6455bf118c5d4d37a2821f93f26c9b"},"files":{"coq_file":"proofs/coq/ComplexityStrictFrameNvStage.v"},"id":"CUB-COMPLEXITY-STRICT-FRAME-NV-STAGE","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk; exact 10-state physical machine; empty/nonempty branch is tape-symbol driven; arbitrary base/frame/scratch preserved","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_frame_nv_stage_raw_state_bound + s_frame_nv_stage_raw_well_formed + frame_nv_empty_formula_handoff + frame_nv_nonempty_formula_handoff + frame_nv_stage_exact_run + frame_nv_stage_first_halt + sat_N_frame_nv_stage_exact_run + sat_N_frame_nv_stage_first_halt","source_completeness":"full (CSV-sourced)","statement":"Finite physical staging of the encoded num-vars suffix from an exact sat_N_frame. The well-formed 10-state s_frame_nv_stage_raw scans to the right edge, locates the penultimate unary field, copies it right-to-left into arbitrary scratch using only tape transitions, restores every source bit, and returns to the first frame cell. Separate physical handoff lemmas cover a Blank predecessor for an empty normalized formula and a false predecessor for a nonempty terminated formula; the machine transition never invokes parse_3sat, num_vars, or sat_N_value. The total sat_N_frame specialization preserves arbitrary base and the complete frame, appends exactly true^num_vars, proves least-halt/no-early-halt semantics, and is bounded by 8*frame_nv_stage_span^2. Finite handler composition, karp_edge, grid emission, encode_tsp, and the strict capstone remain OPEN.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Preservation-safe physical false tally over an indexed canonical bit-only frame. The well-formed 7-state s_frame_false_tally_raw temporarily blanks one false cell at a time, shuttles to the far scratch end, appends one unary true, restores the false cell, and finally rewinds to the first frame cell. It preserves arbitrary mixed base, the exact frame, and existing scratch; exact and least-halt theorems are bounded by 2*(|frame|+|scratch|+1)^2. The sat_N_frame specialization appends exactly true^(3*num_clauses(parse_3sat w)+2), and proves S(count_false frame)=edge_row_len. The separate encoded-nv suffix reframe remains OPEN, followed by finite karp_edge, grid emission, encode_tsp, and the strict capstone.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictFrameStage.v":"991cd23ea56ededbd0737417d2e46770efe79e899a7e55491fc77681a9969544"},"files":{"coq_file":"proofs/coq/ComplexityStrictFrameStage.v"},"id":"CUB-COMPLEXITY-STRICT-FRAME-STAGE","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk; exact 7-state physical tally; arbitrary base/frame/scratch preservation; nv wrapper intentionally not claimed","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_frame_false_tally_raw_state_bound + s_frame_false_tally_raw_well_formed + frame_false_tally_exact_run + frame_false_tally_first_halt + sat_N_frame_false_tally_exact_run + sat_N_frame_false_tally_first_halt + sat_N_frame_false_tally_successor_row_len","source_completeness":"full (CSV-sourced)","statement":"Preservation-safe physical false tally over an indexed canonical bit-only frame. The well-formed 7-state s_frame_false_tally_raw temporarily blanks one false cell at a time, shuttles to the far scratch end, appends one unary true, restores the false cell, and finally rewinds to the first frame cell. It preserves arbitrary mixed base, the exact frame, and existing scratch; exact and least-halt theorems are bounded by 2*(|frame|+|scratch|+1)^2. The sat_N_frame specialization appends exactly true^(3*num_clauses(parse_3sat w)+2), and proves S(count_false frame)=edge_row_len. The separate encoded-nv suffix reframe remains OPEN, followed by finite karp_edge, grid emission, encode_tsp, and the strict capstone.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Finite physical recycler for one already-emitted grid cost. From the documented nonempty-grid layout, the well-formed 19-state machine parses exactly the two legal grid_cell_bits encodings, erases the old suffix, preserves the arbitrary mixed base, counters, and nonempty source, consumes the physical reserve, appends the same cost to the emitted grid, and returns to counter cell zero. Exact-run, unique-success, least-halt/no-early-halt, linear fuel, and quadratic span results are proven; malformed or missing cost suffixes and the unsupported empty-grid layout do not reach the success state. This is one cell-recycling brick, not pair enumeration, complete grid emission, encode_tsp, or the strict reduction capstone.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictGridCostRecycle.v":"f27e87087a061b4dc938d39057811313ad92c68021c752dedf92b867050f2585"},"files":{"coq_file":"proofs/coq/ComplexityStrictGridCostRecycle.v"},"id":"CUB-COMPLEXITY-STRICT-GRID-COST-RECYCLE","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Coq-only strict-TM corpus convention; nonempty G and physical reserve premises are load-bearing; malformed-cost and empty-G controls included; Print Assumptions capstones present; coqchk Axioms: required by the live proof gate","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_grid_cost_recycle_state_bound + s_grid_cost_recycle_well_formed + grid_cost_recycle_exact_run + grid_cost_recycle_first_halt + grid_cost_recycle_exact_grid_append + grid_cost_recycle_first_halt_span","source_completeness":"full (CSV-sourced)","statement":"Finite physical recycler for one already-emitted grid cost. From the documented nonempty-grid layout, the well-formed 19-state machine parses exactly the two legal grid_cell_bits encodings, erases the old suffix, preserves the arbitrary mixed base, counters, and nonempty source, consumes the physical reserve, appends the same cost to the emitted grid, and returns to counter cell zero. Exact-run, unique-success, least-halt/no-early-halt, linear fuel, and quadratic span results are proven; malformed or missing cost suffixes and the unsupported empty-grid layout do not reach the success state. This is one cell-recycling brick, not pair enumeration, complete grid emission, encode_tsp, or the strict reduction capstone.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Finite initializer builds the canonical descriptor-counter banks from sat_N_frame and reaches the exact odometer start with least-halt and polynomial-span evidence. The capstone is specialized to the canonical frame; generic phases do not validate arbitrary frames.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictGridCounterInit.v":"8ee4d6aa715a09aa40bed299b15d927253fd83ed8b2f2336d1e44c03b945bc60"},"files":{"coq_file":"proofs/coq/ComplexityStrictGridCounterInit.v"},"id":"CUB-COMPLEXITY-STRICT-GRID-COUNTER-INIT","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Coq-only strict-TM theorem; canonical sat_N_frame specialization is load-bearing; full proof gate 284/284 and coqchk Axioms:","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_grid_counter_init_raw_state_bound + s_grid_counter_init_raw_well_formed + grid_counter_init_first_halt_fuel + grid_counter_init_odometer_handoff + grid_counter_init_first_halt_span","source_completeness":"full (CSV-sourced)","statement":"Finite initializer builds the canonical descriptor-counter banks from sat_N_frame and reaches the exact odometer start with least-halt and polynomial-span evidence. The capstone is specialized to the canonical frame; generic phases do not validate arbitrary frames.","status":"proven","use_cases":["complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Finite source-preserving materializer for one canonical edge descriptor. Given the producer-certified ten-bit gdm_header from typed nodes and roles plus four fixed-capacity unary banks satisfying value < capacity, the well-formed 138-state machine restores the complete source and emits exactly edge_pair_word, with exact-run, least-halt/no-early-halt, and quadratic span evidence. The raw ten-bit layout lemma copies header bits opaquely and does not validate arbitrary magic/role/kind patterns; the canonical CUB claim is deliberately limited to grid_descriptor_materialize_edge_pair_exact_run. Blank header cells, malformed bank predecessors/frontiers/guards, and a malformed final separator halt outside the unique success state. Pair enumeration, full grid emission, encode_tsp, and s_poly_reduces L_3SAT L_TSP remain OPEN.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictGridDescriptorMaterialize.v":"4d89a6ee8b4a549860a2fda82b9c11b2bd5aac5e98bb63ea8c4d200bb16f52fd"},"files":{"coq_file":"proofs/coq/ComplexityStrictGridDescriptorMaterialize.v"},"id":"CUB-COMPLEXITY-STRICT-GRID-DESCRIPTOR-MATERIALIZE","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Coq-only strict-TM corpus convention; canonical-header producer boundary and strict value required by the live proof gate","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_grid_descriptor_materialize_state_bound + s_grid_descriptor_materialize_well_formed + grid_descriptor_materialize_edge_pair_exact_run + grid_descriptor_materialize_canonical_no_early_halt + grid_descriptor_materialize_canonical_first_halt_span","source_completeness":"full (CSV-sourced)","statement":"Finite source-preserving materializer for one canonical edge descriptor. Given the producer-certified ten-bit gdm_header from typed nodes and roles plus four fixed-capacity unary banks satisfying value < capacity, the well-formed 138-state machine restores the complete source and emits exactly edge_pair_word, with exact-run, least-halt/no-early-halt, and quadratic span evidence. The raw ten-bit layout lemma copies header bits opaquely and does not validate arbitrary magic/role/kind patterns; the canonical CUB claim is deliberately limited to grid_descriptor_materialize_edge_pair_exact_run. Blank header cells, malformed bank predecessors/frontiers/guards, and a malformed final separator halt outside the unique success state. Pair enumeration, full grid emission, encode_tsp, and s_poly_reduces L_3SAT L_TSP remain OPEN.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Finite canonical descriptor odometer enumerates valid descriptor-role pairs exactly once in row-major order and reaches the decoded successor with exact-run, least-halt, and quadratic-span evidence. Valid canonical counter layouts and 0 < nv are load-bearing; this is not an arbitrary-word decoder or total malformed-layout validator.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictGridDescriptorOdometer.v":"896f19f288334f3a95aecf1f5321e2b54245abb6b67176b8dc8a1ec9ae83ce37"},"files":{"coq_file":"proofs/coq/ComplexityStrictGridDescriptorOdometer.v"},"id":"CUB-COMPLEXITY-STRICT-GRID-DESCRIPTOR-ODOMETER","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Coq-only strict-TM theorem; valid descriptor and canonical counter premises are explicit; full proof gate 284/284 and coqchk Axioms:","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"gdo_pair_descriptors_indexes + gdo_pair_step_row_major_successor + s_grid_descriptor_odometer_well_formed + grid_descriptor_odometer_exact_run + grid_descriptor_odometer_first_halt + grid_descriptor_odometer_first_halt_decodes","source_completeness":"full (CSV-sourced)","statement":"Finite canonical descriptor odometer enumerates valid descriptor-role pairs exactly once in row-major order and reaches the decoded successor with exact-run, least-halt, and quadratic-span evidence. Valid canonical counter layouts and 0 < nv are load-bearing; this is not an arbitrary-word decoder or total malformed-layout validator.","status":"proven","use_cases":["TEP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Thirteen-state finalizer removes the prepared workspace with exact-run, least-halt, and quadratic-span evidence. It preserves arbitrary outer base visibly; exact s_extract = word_reduce is claimed only for the nil-base end-to-end start.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictGridFinalize.v":"9f75d1790ed55fae2e47d066bc120a91b510898b17bd48b41fa174d4260c89fb"},"files":{"coq_file":"proofs/coq/ComplexityStrictGridFinalize.v"},"id":"CUB-COMPLEXITY-STRICT-GRID-FINALIZE","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Coq-only strict-TM theorem; nil-base boundary on the extraction capstone is explicit; full proof gate 284/284 and coqchk Axioms:","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_grid_finalize_state_bound + s_grid_finalize_well_formed + grid_finalize_exact_run + grid_finalize_first_halt_span + grid_finalize_sat_extract_word_reduce + grid_finalize_sat_first_halt","source_completeness":"full (CSV-sourced)","statement":"Thirteen-state finalizer removes the prepared workspace with exact-run, least-halt, and quadratic-span evidence. It preserves arbitrary outer base visibly; exact s_extract = word_reduce is claimed only for the nil-base end-to-end start.","status":"proven","use_cases":["complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Finite cleanup and tail-copy adapters transform the seeded canonical counter layout into the exact prepared-loop start, preserving source regions and proving least halt. Exact reserve equality is load-bearing; this module neither allocates reserve nor accepts arbitrary raw layouts.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictGridInit.v":"93f4124c53eb160d44f1d1b49ab6faf69d0d63d685dddf326a89601e81a700ff"},"files":{"coq_file":"proofs/coq/ComplexityStrictGridInit.v"},"id":"CUB-COMPLEXITY-STRICT-GRID-INIT","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Coq-only strict-TM theorem; exact reserve equality is explicit; full proof gate 284/284 and coqchk Axioms:","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_grid_init_cleanup_raw_state_bound + s_grid_init_cleanup_raw_well_formed + grid_init_cleanup_first_halt + s_grid_init_tail_raw_state_bound + s_grid_init_tail_raw_well_formed + grid_init_tail_first_halt_prepared + grid_counter_finalize_exact_loop_handoff","source_completeness":"full (CSV-sourced)","statement":"Finite cleanup and tail-copy adapters transform the seeded canonical counter layout into the exact prepared-loop start, preserving source regions and proving least halt. Exact reserve equality is load-bearing; this module neither allocates reserve nor accepts arbitrary raw layouts.","status":"proven","use_cases":["complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Pure finite schedule/index and reserve-accounting algebra for the row-major descriptor-pair stream. Claims apply only at bounded indices; no executable tape machine, grid emission, or runtime scheduling claim.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictGridPairSchedule.v":"d71204496794e68a30cf2cbdb2ec949709d55e3ee3be3caeed7069e0570bc446"},"files":{"coq_file":"proofs/coq/ComplexityStrictGridPairSchedule.v"},"id":"CUB-COMPLEXITY-STRICT-GRID-PAIR-SCHEDULE","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Coq-only pure schedule theorem; in-range index premise is load-bearing; full proof gate 284/284 and coqchk Axioms:","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"gdo_pair_schedule_nth_error + gdo_pair_schedule_step_nonlast + gdo_pair_schedule_step_last + gdo_pair_schedule_reserve_step","source_completeness":"full (CSV-sourced)","statement":"Pure finite schedule/index and reserve-accounting algebra for the row-major descriptor-pair stream. Claims apply only at bounded indices; no executable tape machine, grid emission, or runtime scheduling claim.","status":"proven","use_cases":["TEP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Pure quantitative bridge proving uniform degree-eight bounds for valid Karp cells and the canonical prepared-grid schedule. It starts from the prepared layout; the complete encoder's degree remains 110 because of the existing sat_N_frame stage.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictGridPoly.v":"10aff8064491b35b06eda8ecf751a598dbaece064122a0d44d39b9e7b50458e0"},"files":{"coq_file":"proofs/coq/ComplexityStrictGridPoly.v"},"id":"CUB-COMPLEXITY-STRICT-GRID-POLY","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Coq-only quantitative theorem; prepared-layout scope and complete-encoder degree are explicit; full proof gate 284/284 and coqchk Axioms:","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"karp_edge_machine_bound_uniform + grid_prepared_cell_bound_polynomial + grid_prepared_schedule_bound_polynomial + grid_prepared_schedule_bound_strict + grid_prepared_loop_first_halt_strict_octavic","source_completeness":"full (CSV-sourced)","statement":"Pure quantitative bridge proving uniform degree-eight bounds for valid Karp cells and the canonical prepared-grid schedule. It starts from the prepared layout; the complete encoder's degree remains 110 because of the existing sat_N_frame stage.","status":"proven","use_cases":["complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Finite 11265-state prepared-layout loop emits the exact row-major word_reduce grid stream with cell, prefix, and exact first-halt theorems. It assumes the canonical prepared layout and adequate reserve; no arbitrary-layout validation or raw-input polynomial capstone is claimed here.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictGridPreparedLoop.v":"e258dea0f35ac1b1d4d1481c31509c4f0e5f39daf7ddf893827229d4359acb50"},"files":{"coq_file":"proofs/coq/ComplexityStrictGridPreparedLoop.v"},"id":"CUB-COMPLEXITY-STRICT-GRID-PREPARED-LOOP","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Coq-only strict-TM theorem; prepared-layout and reserve premises are load-bearing; full proof gate 284/284 and coqchk Axioms:","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"sat_grid_stream_word_reduce_stream + s_grid_prepared_loop_state_bound + s_grid_prepared_loop_well_formed + grid_prepared_cell_reaches + grid_prepared_prefix_reaches + grid_prepared_loop_first_halt","source_completeness":"full (CSV-sourced)","statement":"Finite 11265-state prepared-layout loop emits the exact row-major word_reduce grid stream with cell, prefix, and exact first-halt theorems. It assumes the canonical prepared layout and adequate reserve; no arbitrary-layout validation or raw-input polynomial capstone is claimed here.","status":"proven","use_cases":["complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Finite physical reserve seeder specialized to canonical sat_N_frame, producing exactly 3*N^2 work cells with exact-run, least-halt, degree-eight fuel, and padded downstream handoff. This is not a host allocator or general malformed-input recognizer.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictGridSeed.v":"2aa7c8120827f9e2ce2f86eae196652cf6208fea30ae4955a7486a3cc8ff249b"},"files":{"coq_file":"proofs/coq/ComplexityStrictGridSeed.v"},"id":"CUB-COMPLEXITY-STRICT-GRID-SEED","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Coq-only strict-TM theorem; canonical frame and physical reserve semantics are explicit; full proof gate 284/284 and coqchk Axioms:","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_grid_seed_raw_state_bound + s_grid_seed_raw_well_formed + grid_seed_exact_run + grid_seed_sat_first_halt + grid_seed_sat_fuel_degree_eight + sat_N_frame_grid_seed_padded_handoff","source_completeness":"full (CSV-sourced)","statement":"Finite physical reserve seeder specialized to canonical sat_N_frame, producing exactly 3*N^2 work cells with exact-run, least-halt, degree-eight fuel, and padded downstream handoff. This is not a host allocator or general malformed-input recognizer.","status":"proven","use_cases":["complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Finite canonical workspace materializer preserves source regions, emits the exact descriptor workspace, and establishes the padded Karp-edge handoff with exact-run, least-halt, and quadratic-span evidence. It assumes producer-certified descriptor counters and is not a general external-workspace parser.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictGridWorkspaceMaterialize.v":"69127f2191b34ebd6006cd31aaa6ad0ef7093f2c341aab8ec108456158fb2388"},"files":{"coq_file":"proofs/coq/ComplexityStrictGridWorkspaceMaterialize.v"},"id":"CUB-COMPLEXITY-STRICT-GRID-WORKSPACE-MATERIALIZE","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Coq-only strict-TM theorem; producer-certified counter boundary is explicit; full proof gate 284/284 and coqchk Axioms:","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_grid_workspace_materialize_state_bound + s_grid_workspace_materialize_well_formed + grid_workspace_materialize_run + grid_workspace_materialize_first_halt_fuel + grid_workspace_materialize_first_halt_span","source_completeness":"full (CSV-sourced)","statement":"Finite canonical workspace materializer preserves source regions, emits the exact descriptor workspace, and establishes the padded Karp-edge handoff with exact-run, least-halt, and quadratic-span evidence. It assumes producer-certified descriptor counters and is not a general external-workspace parser.","status":"proven","use_cases":["complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: item-4 iterate controller: s_iter, a fixed finite STM that runs a body a DATA-DEPENDENT S n times off a unary tape counter with a genuine loop-back per pass (state 0 CHECK -> 1 OUT -> 2 BACK -> 0), halting when the counter is exhausted. Proven correct + content-preserving by the fold-over-the-counter induction: s_iter_onestep (one self-similar iteration = 3 steps), s_iter_run (S n iterations), s_iter_computes/halted/extract (halts; s_extract = repeat true (S n), the counter preserved). Body is the trivial excursion; the reduction's real n-times loops splice a real body machine into states 1-2 via stm_seq. 0 axioms; coqchk Axioms: .","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictIter.v":"8b9b78149dd90c3ddcb2a83ccfbcb53bbf83597b8b3ced4090362cb98c4e766e"},"files":{"coq_file":"proofs/coq/ComplexityStrictIter.v"},"id":"CUB-COMPLEXITY-STRICT-ITER","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"iterate-controller","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_iter_run + s_iter_extract","source_completeness":"full (CSV-sourced)","statement":"item-4 iterate controller: s_iter, a fixed finite STM that runs a body a DATA-DEPENDENT S n times off a unary tape counter with a genuine loop-back per pass (state 0 CHECK -> 1 OUT -> 2 BACK -> 0), halting when the counter is exhausted. Proven correct + content-preserving by the fold-over-the-counter induction: s_iter_onestep (one self-similar iteration = 3 steps), s_iter_run (S n iterations), s_iter_computes/halted/extract (halts; s_extract = repeat true (S n), the counter preserved). Body is the trivial excursion; the reduction's real n-times loops splice a real body machine into states 1-2 via stm_seq. 0 axioms; coqchk Axioms: .","status":"proven","use_cases":["TEP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Finite canonical descriptor-workspace Karp edge machine. The fixed well-formed 9284-state single-tape product physically reads the ten-bit descriptor header, dispatches into one of twelve non-fallthrough finite handler families, normalizes represented or virtual trailing Blank padding, and erases the workspace to one Boolean under the head with only trailing Blanks. karp_edge_machine_first_halt is total over every source word, typed descriptor/role pair, and arbitrary mixed-symbol base, with no-early-halt semantics and the explicit local bound karp_edge_machine_bound. Under the load-bearing descriptor-validity premises, karp_edge_machine_value_correct and karp_edge_first_halt identify that tape result with the existing numbered karp_edge at the two edge_unode_id values. No parser, coordinate projection, literal table, or semantic edge predicate selects a transition. Scope is the canonical descriptor workspace: this does not provide an independent decoder from arbitrary externally supplied numbered vertices. The four-state cost-cell adapter, eighteen-state workspace copier, and finite role/unary cycles are closed support bricks, not executable N-by-N descriptor materialization. Total grid emission, encode_tsp, and s_poly_reduces L_3SAT L_TSP remain OPEN.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictKarpEdge.v":"a0b6eb712ac92940f6d2db5e5a9c4843a5a41b1a32732f82c6de78aeb54a7df7"},"files":{"coq_file":"proofs/coq/ComplexityStrictKarpEdge.v"},"id":"CUB-COMPLEXITY-STRICT-KARP-EDGE","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions capstones present; exact 9254+3+27=9284 state partition; arbitrary-base and checked false-output controls; Coq-only strict-machine lane; live proof gate is the verification source of truth","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_karp_edge_state_bound + s_karp_edge_well_formed + karp_edge_machine_first_halt + karp_edge_machine_value_correct + karp_edge_first_halt","source_completeness":"full (CSV-sourced)","statement":"Finite canonical descriptor-workspace Karp edge machine. The fixed well-formed 9284-state single-tape product physically reads the ten-bit descriptor header, dispatches into one of twelve non-fallthrough finite handler families, normalizes represented or virtual trailing Blank padding, and erases the workspace to one Boolean under the head with only trailing Blanks. karp_edge_machine_first_halt is total over every source word, typed descriptor/role pair, and arbitrary mixed-symbol base, with no-early-halt semantics and the explicit local bound karp_edge_machine_bound. Under the load-bearing descriptor-validity premises, karp_edge_machine_value_correct and karp_edge_first_halt identify that tape result with the existing numbered karp_edge at the two edge_unode_id values. No parser, coordinate projection, literal table, or semantic edge predicate selects a transition. Scope is the canonical descriptor workspace: this does not provide an independent decoder from arbitrary externally supplied numbered vertices. The four-state cost-cell adapter, eighteen-state workspace copier, and finite role/unary cycles are closed support bricks, not executable N-by-N descriptor materialization. Total grid emission, encode_tsp, and s_poly_reduces L_3SAT L_TSP remain OPEN.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Terminal physical adapter around the total raw parser-faithful literal machine. The 9-state s_edge_literal_finish preserves an arbitrary mixed base and header, scans the exact returned frame/query layout, erases the temporary query block, writes the resulting accumulator into the frame/output separator, physically rewinds the complete frame, and halts on the header. Its exact fuel is 2*|frame|+2*i+2*j+10. Composing it with the existing 252-state total raw query gives the exact well-formed 261-state s_edge_literal_call, with a parser-faithful least halt bounded by 70*clause_seek_span^2 for every w,i,j,pos,acc and arbitrary base. This is a terminal call interface; descriptor coordinate preparation, encoded-nv staging, finite karp_edge, grid emission, encode_tsp, and the strict capstone remain OPEN.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictLiteralCall.v":"f8dcf50ad2d0dcc3480ef0ccc169e75d0b62f5c61f22b830cebc70f0a9b7b3e4"},"files":{"coq_file":"proofs/coq/ComplexityStrictLiteralCall.v"},"id":"CUB-COMPLEXITY-STRICT-LITERAL-CALL","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk; exact 9-state adapter and 261-state product; arbitrary base/header preserved","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_edge_literal_finish_state_bound + s_edge_literal_finish_well_formed + edge_literal_finish_exact_run + edge_literal_finish_first_halt + s_edge_literal_call_state_bound + s_edge_literal_call_well_formed + edge_literal_call_first_halt_span","source_completeness":"full (CSV-sourced)","statement":"Terminal physical adapter around the total raw parser-faithful literal machine. The 9-state s_edge_literal_finish preserves an arbitrary mixed base and header, scans the exact returned frame/query layout, erases the temporary query block, writes the resulting accumulator into the frame/output separator, physically rewinds the complete frame, and halts on the header. Its exact fuel is 2*|frame|+2*i+2*j+10. Composing it with the existing 252-state total raw query gives the exact well-formed 261-state s_edge_literal_call, with a parser-faithful least halt bounded by 70*clause_seek_span^2 for every w,i,j,pos,acc and arbitrary base. This is a terminal call interface; descriptor coordinate preparation, encoded-nv staging, finite karp_edge, grid emission, encode_tsp, and the strict capstone remain OPEN.","status":"proven","use_cases":["TSP","complexity","topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: RAW serialized-literal query machines. The 36-state adjacent core preserves its tally/index/polarity fields and OR-updates only the accumulator. The 39-state s_serialized_lit_middle_or_raw generalizes the exact run to every TapeSym left base, arbitrary Bit-only frame suffix between the tally delimiter and scratch, and arbitrary Bit-only post-index metadata; every surrounding cell is restored and the output is acc OR serialized_lit_is(repeat true k,i,pos). It is well formed, has a least halt/no-early witness, and runs within 16*(k+i+|middle|+|meta|+2)^2. This remains a raw internal-Blank brick. Clause positioning, the in-range three-tally product, the parser-default cycle, the range marker, and their total physical router are closed separately. Canonical clean padding, finite karp_edge/grid machines, encode_tsp, and the strict capstone remain open.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictLiteralQuery.v":"5e9bf79a14955a75f27c450b390f495bad0626e23cad0e9d04c088330a0da16e"},"files":{"coq_file":"proofs/coq/ComplexityStrictLiteralQuery.v"},"id":"CUB-COMPLEXITY-STRICT-LITERAL-QUERY","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; targeted coqchk exit 0; arbitrary context preservation closed; total raw literal-table product closed separately; clean-pad/edge/grid stages open","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_serialized_lit_or_raw_serialized_run + s_serialized_lit_middle_or_raw_state_bound + s_serialized_lit_middle_or_raw_well_formed + s_serialized_lit_middle_or_raw_serialized_run + slm_total_fuel_quadratic + s_serialized_lit_middle_or_raw_first_halt_poly","source_completeness":"full (CSV-sourced)","statement":"RAW serialized-literal query machines. The 36-state adjacent core preserves its tally/index/polarity fields and OR-updates only the accumulator. The 39-state s_serialized_lit_middle_or_raw generalizes the exact run to every TapeSym left base, arbitrary Bit-only frame suffix between the tally delimiter and scratch, and arbitrary Bit-only post-index metadata; every surrounding cell is restored and the output is acc OR serialized_lit_is(repeat true k,i,pos). It is well formed, has a least halt/no-early witness, and runs within 16*(k+i+|middle|+|meta|+2)^2. This remains a raw internal-Blank brick. Clause positioning, the in-range three-tally product, the parser-default cycle, the range marker, and their total physical router are closed separately. Canonical clean padding, finite karp_edge/grid machines, encode_tsp, and the strict capstone remain open.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: item-4 first loop-back brick: s_rewind, a genuine BIDIRECTIONAL finite STM (state 0 marches right over a unary block; on Blank turns; state 1 marches left back to the block start; on Blank halts) -- the head revisits earlier tape cells; unlike every prior single-pass 1-state scan atom. Correct on a DATA-DEPENDENT block length by the fold-over-count induction (s_run_plus + march_right/march_left): s_rewind_run (exact halt config), s_rewind_halted, s_rewind_extract (content preserved = repeat true (S m)). It is the rewind-to-start primitive the stage machines need. NOT yet the full iterate-body-k-times combinator. 0 axioms; coqchk Axioms: .","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictLoop.v":"52d960883de50e0349a50dc494d2a11e483933097ab04fd31723107a589e8ea1"},"files":{"coq_file":"proofs/coq/ComplexityStrictLoop.v"},"id":"CUB-COMPLEXITY-STRICT-LOOP","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"loop-back-primitive","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_rewind_run + s_rewind_extract","source_completeness":"full (CSV-sourced)","statement":"item-4 first loop-back brick: s_rewind, a genuine BIDIRECTIONAL finite STM (state 0 marches right over a unary block; on Blank turns; state 1 marches left back to the block start; on Blank halts) -- the head revisits earlier tape cells; unlike every prior single-pass 1-state scan atom. Correct on a DATA-DEPENDENT block length by the fold-over-count induction (s_run_plus + march_right/march_left): s_rewind_run (exact halt config), s_rewind_halted, s_rewind_extract (content preserved = repeat true (S m)). It is the rewind-to-start primitive the stage machines need. NOT yet the full iterate-body-k-times combinator. 0 axioms; coqchk Axioms: .","status":"proven","use_cases":["complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: FIRST real clean stage atom: s_map_prepend g (4-state, 2|w|+3 flat steps) computes w -> false :: map g w as a genuine s_clean_transduces_pad transducer (k=1 c=4), realizing the adopted stage architecture end to end -- scan-relabel (mp_scan, the s_scan_map invariant), rewind (mp_rewind left-march fold; the first Blank read IS cell -1, the left-edge corollary made to work), and the rewind-finish dance (write false delimiter at the probed cell, step back, halt blank-padded canonical). Never-halts-early via per-phase SHAPE invariants (mp_scan_state / mp_rewind_state existential-shape trick, state stays < 3). Design Compute-verified first (mp_check_cons / mp_check_nil committed regressions). Composes at a single polynomial budget via stm_seq_clean_pad_computes_poly / _preserves_poly. Stage BODIES (counting/max/grid) remain open; strict wrapper OPEN. NP-hardness (Karp 1972) not P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictMapPrepend.v":"113ddacf6426a59d423d3b0ff3a002679756ac5d54c91dde40da6218348dabc5"},"files":{"coq_file":"proofs/coq/ComplexityStrictMapPrepend.v"},"id":"CUB-COMPLEXITY-STRICT-MAP-PREPEND","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_map_prepend_clean_pad + mp_run + mp_no_early","source_completeness":"full (CSV-sourced)","statement":"FIRST real clean stage atom: s_map_prepend g (4-state, 2|w|+3 flat steps) computes w -> false :: map g w as a genuine s_clean_transduces_pad transducer (k=1 c=4), realizing the adopted stage architecture end to end -- scan-relabel (mp_scan, the s_scan_map invariant), rewind (mp_rewind left-march fold; the first Blank read IS cell -1, the left-edge corollary made to work), and the rewind-finish dance (write false delimiter at the probed cell, step back, halt blank-padded canonical). Never-halts-early via per-phase SHAPE invariants (mp_scan_state / mp_rewind_state existential-shape trick, state stays < 3). Design Compute-verified first (mp_check_cons / mp_check_nil committed regressions). Composes at a single polynomial budget via stm_seq_clean_pad_computes_poly / _preserves_poly. Stage BODIES (counting/max/grid) remain open; strict wrapper OPEN. NP-hardness (Karp 1972) not P vs NP.","status":"proven","use_cases":["TEP","admission","crypto","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Five-state canonicalizer for the exact Run18 halt layout. s_maxclean erases the false scratch tail and Blank gap, preserves the unary max, halts, and produces blank_padded output for both zero and positive maxima; s_maxerode_halt_layout exposes the physical handoff.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictMaxClean.v":"583cdfc4346984cfba48434f0ee725ee014ac609cade20a715dc24f2b23be8ad"},"files":{"coq_file":"proofs/coq/ComplexityStrictMaxClean.v"},"id":"CUB-COMPLEXITY-STRICT-MAX-CLEAN","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; finite state bound and exact runs","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_maxclean_layout + s_maxerode_halt_layout","source_completeness":"full (CSV-sourced)","statement":"Five-state canonicalizer for the exact Run18 halt layout. s_maxclean erases the false scratch tail and Blank gap, preserves the unary max, halts, and produces blank_padded output for both zero and positive maxima; s_maxerode_halt_layout exposes the physical handoff.","status":"proven","use_cases":["complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: EROSION MACHINE design brick (s_emit precedent: Compute-certified design first, march-fold proofs next brick): s_maxerode (8 states) defined + well-formedness PROVEN + behavior certified by FIVE kernel-checked full-run falsifiers (single group; tallies 2,1; empty groups; the all-empty zero-max boundary -- the no-true pass halts immediately, max_pos_iff's exactness in action; staggered exhaustion 3,2,1) -- each run halts with s_extract = repeat true (max_tally w) ++ repeat false (|w|), the target function, by reflexivity. State plan: A0/A1 pass scan with productivity bit, B true-run, C/D local back-up-erode-resume (eroded cells become Bit false never Blank -- Blank=end survives), E rewind to the -1 gap, F/G emit one output true per productive pass across the gap. NOT yet proven: pass invariant (one pass = map pred on tallies), march-folds, fold to EROSION_IS_MAX, budget wrapper -- s_maxerode is NOT yet claimed to compute anything. Strict wrapper OPEN. NP-hardness (Karp 1972) not P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictMaxErode.v":"3ef185baabd2ccc9aefea930627636378340a0dfa18a6da4f99e3417ba32dc1f"},"files":{"coq_file":"proofs/coq/ComplexityStrictMaxErode.v"},"id":"CUB-COMPLEXITY-STRICT-MAX-ERODE","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; the file's own content (definition + well-formedness + 5 kernel-checked Compute falsifiers) is proven; the run-level computes theorem landed later as s_maxerode_computes (Run14-18) + budget packaging (Run19-20); status normalized from non-schema 'design-compute-verified' 2026-07-13; coq-only strict-TM corpus","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_maxerode_well_formed + me_check1-5 (Compute)","source_completeness":"full (CSV-sourced)","statement":"EROSION MACHINE design brick (s_emit precedent: Compute-certified design first, march-fold proofs next brick): s_maxerode (8 states) defined + well-formedness PROVEN + behavior certified by FIVE kernel-checked full-run falsifiers (single group; tallies 2,1; empty groups; the all-empty zero-max boundary -- the no-true pass halts immediately, max_pos_iff's exactness in action; staggered exhaustion 3,2,1) -- each run halts with s_extract = repeat true (max_tally w) ++ repeat false (|w|), the target function, by reflexivity. State plan: A0/A1 pass scan with productivity bit, B true-run, C/D local back-up-erode-resume (eroded cells become Bit false never Blank -- Blank=end survives), E rewind to the -1 gap, F/G emit one output true per productive pass across the gap. NOT yet proven: pass invariant (one pass = map pred on tallies), march-folds, fold to EROSION_IS_MAX, budget wrapper -- s_maxerode is NOT yet claimed to compute anything. Strict wrapper OPEN. NP-hardness (Karp 1972) not P vs NP.","status":"proven","use_cases":["admission","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Thirteen-state product of delimiter-domain max erosion and the five-state cleaner. s_maxpipeline_clean_pad_on_terminated proves a whole-product least halt, canonical unary max_tally output, and explicit 23*|w|^2+23 budget while keeping the termination predicate load-bearing.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictMaxPipeline.v":"8b7b7d0a84d335127b0a608f91968b22063155d461393cbff5edd1bccde771f9"},"files":{"coq_file":"proofs/coq/ComplexityStrictMaxPipeline.v"},"id":"CUB-COMPLEXITY-STRICT-MAX-PIPELINE","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; honest range-restricted middle stage","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_maxpipeline_clean_pad_on_terminated + maxpipeline_budget_bound","source_completeness":"full (CSV-sourced)","statement":"Thirteen-state product of delimiter-domain max erosion and the five-state cleaner. s_maxpipeline_clean_pad_on_terminated proves a whole-product least halt, canonical unary max_tally output, and explicit 23*|w|^2+23 budget while keeping the termination predicate load-bearing.","status":"proven","use_cases":["admission","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: the EROSION = MAX spec pinning the num_vars machine (item-3 pattern: spec first, machine shaped by it; pure Coq, no TM built): EROSION_IS_MAX -- counting productive map-pred passes over group tallies computes exactly fold max -- with fold_max_pred (one pass = pred of the running max), max_pos_iff (the termination test is EXACT: a pass finds a true iff max still positive), max_le_sum + max_tally_le_length (fuel/budget hooks: max <= sum of tallies <= |w|), max_tally defined over split_clauses tallies. PINNED OBLIGATION (stated not built): the erosion-pass STM -- erode one true at each group's right edge per pass (local back-up-rewrite-continue, no interior Blanks so Blank=end survives), productivity in finite control, emit one output true per productive pass across a one-Blank left gap, fuel |w| passes. Strict wrapper OPEN. NP-hardness (Karp 1972) not P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictMaxSpec.v":"e610df1a64f84acb65e676b26399a4a657f4cad30d552986d880ae6bee6b1cdd"},"files":{"coq_file":"proofs/coq/ComplexityStrictMaxSpec.v"},"id":"CUB-COMPLEXITY-STRICT-MAX-SPEC","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"EROSION_IS_MAX + max_pos_iff + max_tally_le_length","source_completeness":"full (CSV-sourced)","statement":"the EROSION = MAX spec pinning the num_vars machine (item-3 pattern: spec first, machine shaped by it; pure Coq, no TM built): EROSION_IS_MAX -- counting productive map-pred passes over group tallies computes exactly fold max -- with fold_max_pred (one pass = pred of the running max), max_pos_iff (the termination test is EXACT: a pass finds a true iff max still positive), max_le_sum + max_tally_le_length (fuel/budget hooks: max <= sum of tallies <= |w|), max_tally defined over split_clauses tallies. PINNED OBLIGATION (stated not built): the erosion-pass STM -- erode one true at each group's right edge per pass (local back-up-rewrite-continue, no interior Blanks so Blank=end survives), productivity in finite control, emit one output true per productive pass across a one-Blank left gap, fuel |w| passes. Strict wrapper OPEN. NP-hardness (Karp 1972) not P vs NP.","status":"proven","use_cases":["admission","crypto","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: UNARY MULTIPLY: s_mult (8-state STM) = the s_copy-style outer counter loop nesting the s_padd source-preserving add (states 0-5) as its per-unit body, joined by the state-4->6 BACK-EDGE (no forward composition / stm_seq gives a data-dependent loop -- confirmed with an advisor). Layout counter(b)|gap|source(a)|gap|output(o), head at the counter frontier state 6; per counter unit (consumed right-to-left Bit true->Bit false), the inner add appends a copy of the PRESERVED source to the output; after b passes output := a*b + o. Design Compute-verified on 4 cases (2x3=6, 3x2=6, 4x1=4, 1x5+2=7) BEFORE proof. Proven 0-axiom: inner mult_m1/m2/m3/m5, mult_out, mult_cycle, mult_copy_phase transfer verbatim from s_padd; new mult_unmark (reframed to halt on the left-gap Blank), mult_add (=s_padd_run over a non-empty left frame), mult_m7/mult_m6skip (outer marches over Bit-false marks), mult_ostep (one outer cycle, unified via hd/tl for recurse+halt), recursive-fuel fold mult_orun. s_mult_run: config level, output region = (S k)*(S bp)+o; s_mult_halted. STATED AT CONFIG LEVEL not a clean whole-tape s_extract (source preserved + counter marks remain on tape); scratch-clearing deferred to the composition layer. coqchk Axioms: .","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictMult.v":"249d9f5255c48e0f18566438e19a03583d8a75c94525f2605084b182666cfdad"},"files":{"coq_file":"proofs/coq/ComplexityStrictMult.v"},"id":"CUB-COMPLEXITY-STRICT-MULT","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"unary-multiply-config-level","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_mult_run + s_mult_halted","source_completeness":"full (CSV-sourced)","statement":"UNARY MULTIPLY: s_mult (8-state STM) = the s_copy-style outer counter loop nesting the s_padd source-preserving add (states 0-5) as its per-unit body, joined by the state-4->6 BACK-EDGE (no forward composition / stm_seq gives a data-dependent loop -- confirmed with an advisor). Layout counter(b)|gap|source(a)|gap|output(o), head at the counter frontier state 6; per counter unit (consumed right-to-left Bit true->Bit false), the inner add appends a copy of the PRESERVED source to the output; after b passes output := a*b + o. Design Compute-verified on 4 cases (2x3=6, 3x2=6, 4x1=4, 1x5+2=7) BEFORE proof. Proven 0-axiom: inner mult_m1/m2/m3/m5, mult_out, mult_cycle, mult_copy_phase transfer verbatim from s_padd; new mult_unmark (reframed to halt on the left-gap Blank), mult_add (=s_padd_run over a non-empty left frame), mult_m7/mult_m6skip (outer marches over Bit-false marks), mult_ostep (one outer cycle, unified via hd/tl for recurse+halt), recursive-fuel fold mult_orun. s_mult_run: config level, output region = (S k)*(S bp)+o; s_mult_halted. STATED AT CONFIG LEVEL not a clean whole-tape s_extract (source preserved + counter marks remain on tape); scratch-clearing deferred to the composition layer. coqchk Axioms: .","status":"proven","use_cases":["TEP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: TOTAL parser-safe Karp city-count strict-machine stage. The 71-state s_nreplace_raw replaces the honest parameter frame's clause-count suffix with unary N, handles both the empty normalized formula and every nonempty delimiter-terminated formula without conflating physical Blank with Bit false, and has an exact run bounded by 376*|x|^4+376. Composition with the total 78-state s_parameter_frame yields the 149-state s_sat_N_frame, total over every input word with least-halt minimality, canonical blank padding, and one explicit seq_K/seq_C polynomial. The frame also instantiates the serialized literal oracle and descriptor painter: karp_descriptor_grid_frame_direct equals the direct row-major Karp grid and karp_direct_grid_length proves N squared cells. Those latter theorems are pure specifications; finite query/edge/grid machines, encode_tsp, and s_poly_reduces L_3SAT L_TSP remain OPEN.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictNFrame.v":"feb7aa28a170d892c67ba012f051fcf2bf326f5bf3cd91d0cc6d6ac57f69c518"},"files":{"coq_file":"proofs/coq/ComplexityStrictNFrame.v"},"id":"CUB-COMPLEXITY-STRICT-N-FRAME","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; coqchk Axioms:; total clean polynomial N stage closed; frame-to-grid pure spec closed; executable edge/grid/encode/final reduction open","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"nfp_raw_honest_run + s_nreplace_raw_clean_on + s_sat_N_frame_clean + s_sat_N_frame_computes_strict + s_sat_N_frame_stage_exists_with_state_bound + karp_edge_descriptors_from_sat_N_frame + karp_descriptor_grid_frame_direct + karp_direct_grid_length","source_completeness":"full (CSV-sourced)","statement":"TOTAL parser-safe Karp city-count strict-machine stage. The 71-state s_nreplace_raw replaces the honest parameter frame's clause-count suffix with unary N, handles both the empty normalized formula and every nonempty delimiter-terminated formula without conflating physical Blank with Bit false, and has an exact run bounded by 376*|x|^4+376. Composition with the total 78-state s_parameter_frame yields the 149-state s_sat_N_frame, total over every input word with least-halt minimality, canonical blank padding, and one explicit seq_K/seq_C polynomial. The frame also instantiates the serialized literal oracle and descriptor painter: karp_descriptor_grid_frame_direct equals the direct row-major Karp grid and karp_direct_grid_length proves N squared cells. Those latter theorems are pure specifications; finite query/edge/grid machines, encode_tsp, and s_poly_reduces L_3SAT L_TSP remain OPEN.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: TOTAL num_clauses strict-machine stage. The 13-state s_clausecount_clean counts false delimiters modulo three, compacts the unary result, and first-halts blank-padded for every word within 14*|w|^2+14. The 26-state s_numclauses precomposes the parser-preserving complete-clause normalizer and outputs repeat true (num_clauses (parse_3sat w)) for every input under one explicit seq_K/seq_C budget. A joint parameter frame retaining the normalized formula remains open before N/grid construction.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictNumClauses.v":"631baaf702a1447c720837f85523e3047bf742271b23015355c222fb3200bffd"},"files":{"coq_file":"proofs/coq/ComplexityStrictNumClauses.v"},"id":"CUB-COMPLEXITY-STRICT-NUM-CLAUSES","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; total clean polynomial num_clauses stage closed; joint nv/nc/formula frame and N/grid/final reduction open","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_clausecount_clean_pad + s_numclauses_clean_pad + s_numclauses_computes_strict + s_numclauses_stage_exists_with_state_bound","source_completeness":"full (CSV-sourced)","statement":"TOTAL num_clauses strict-machine stage. The 13-state s_clausecount_clean counts false delimiters modulo three, compacts the unary result, and first-halts blank-padded for every word within 14*|w|^2+14. The 26-state s_numclauses precomposes the parser-preserving complete-clause normalizer and outputs repeat true (num_clauses (parse_3sat w)) for every input under one explicit seq_K/seq_C budget. A joint parameter frame retaining the normalized formula remains open before N/grid construction.","status":"proven","use_cases":["admission","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: TOTAL num_vars strict-machine stage. The 36-state s_numvars composes the parser-preserving normalizer, range-scoped erosion/cleanup, and clean halve-successor. s_numvars_clean_pad quantifies over every word and outputs repeat true (num_vars (parse_3sat w)) with first-halt minimality and canonical blank padding under one fixed seq_K/seq_C polynomial; s_numvars_computes_strict proves the exact-budget strict predicate. The final L_3SAT-to-L_TSP reduction remains OPEN.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictNumVars.v":"3ea1e814f2cec1f27c9e1fba9fd7f43d6ec1d00298808780d30efc83579f8e73"},"files":{"coq_file":"proofs/coq/ComplexityStrictNumVars.v"},"id":"CUB-COMPLEXITY-STRICT-NUM-VARS","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; total clean polynomial num_vars stage closed; N/grid/encode_tsp/final reduction open","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_numvars_clean_pad + s_numvars_computes_strict + s_numvars_stage_exists_with_state_bound","source_completeness":"full (CSV-sourced)","statement":"TOTAL num_vars strict-machine stage. The 36-state s_numvars composes the parser-preserving normalizer, range-scoped erosion/cleanup, and clean halve-successor. s_numvars_clean_pad quantifies over every word and outputs repeat true (num_vars (parse_3sat w)) with first-halt minimality and canonical blank padding under one fixed seq_K/seq_C polynomial; s_numvars_computes_strict proves the exact-budget strict predicate. The final L_3SAT-to-L_TSP reduction remains OPEN.","status":"proven","use_cases":["admission","TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: H3 hazard FOUND + REPAIRED: exact output-canonicity (s_clean_transduces) is UNSATISFIABLE at the tape edges -- the tape never shrinks (s_step_tsize_mono) and every write moves, so from the 1-cell s_init [] no machine reaches the 1-cell s_init (f []); proven concretely by no_clean_append_false (the delimiter-append stage function w++[false] -- s_append_false's own function -- admits NO exact clean transducer). REPAIR: blank_padded / s_clean_transduces_pad (output exact up to trailing Blanks); pad_rel is a full BISIMULATION of s_step/s_run preserving halting + s_extract (pad_rel_step/run/halted/extract), so trailing Blanks are semantically inert. Budget-closed composition layer re-proven over the repaired predicate reusing seq_K/seq_C/seq_budget (stm_seq_clean_pad_computes_poly, stm_seq_clean_pad_preserves_poly, capstone s_phase4_from_stage_machines_pad); clean_implies_pad retains everything prior. FIRST nontrivial clean witness: s_prepend_false (4-state, 3-step overshoot-absorb) is s_clean_transduces_pad for false::w (k=1 c=3) -- the repaired road is WALKABLE. Stage machines NOT built; strict wrapper remains OPEN. NP-hardness (Karp 1972) not P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictPad.v":"0ea7505cff2eabb67dd55c195c5fd1aafd8aebdf21554a84de92af14413a0f3c"},"files":{"coq_file":"proofs/coq/ComplexityStrictPad.v"},"id":"CUB-COMPLEXITY-STRICT-PAD","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_phase4_from_stage_machines_pad + no_clean_append_false + s_prepend_false_clean_pad","source_completeness":"full (CSV-sourced)","statement":"H3 hazard FOUND + REPAIRED: exact output-canonicity (s_clean_transduces) is UNSATISFIABLE at the tape edges -- the tape never shrinks (s_step_tsize_mono) and every write moves, so from the 1-cell s_init [] no machine reaches the 1-cell s_init (f []); proven concretely by no_clean_append_false (the delimiter-append stage function w++[false] -- s_append_false's own function -- admits NO exact clean transducer). REPAIR: blank_padded / s_clean_transduces_pad (output exact up to trailing Blanks); pad_rel is a full BISIMULATION of s_step/s_run preserving halting + s_extract (pad_rel_step/run/halted/extract), so trailing Blanks are semantically inert. Budget-closed composition layer re-proven over the repaired predicate reusing seq_K/seq_C/seq_budget (stm_seq_clean_pad_computes_poly, stm_seq_clean_pad_preserves_poly, capstone s_phase4_from_stage_machines_pad); clean_implies_pad retains everything prior. FIRST nontrivial clean witness: s_prepend_false (4-state, 3-step overshoot-absorb) is s_clean_transduces_pad for false::w (k=1 c=3) -- the repaired road is WALKABLE. Stage machines NOT built; strict wrapper remains OPEN. NP-hardness (Karp 1972) not P vs NP.","status":"proven","use_cases":["TEP","admission","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: source-preserving unary ADD sub-machine for unary MULTIPLY: s_padd (6-state) appends a COPY of a unary source(a) block to a DISTANT output(o) -- output := o + a -- while PRESERVING the source, using Bit false as a temporary mark on each source true (flipped back in a final unmark pass). States 1-3 are identical to s_copy's output round-trip; state 5 marches source-left to the Bit-false mark; state 4 is the unmark. Proven 0-axiom: padd_m1/m2/m3/m5 march-folds, padd_out round-trip, padd_cycle (2c'+2o+5 per cycle), padd_copy_phase (fold over the source), padd_unmark_nil, ttb_run_gap. s_padd_run: source(S k)|gap|output(o) -> source(S k) INTACT | gap | output(S k + o); s_padd_halted; s_padd_extract = repeat true (S k) ++ repeat true (S k + o). This is exactly the source-preserving body unary multiply nests inside the s_copy counter loop. coqchk Axioms: .","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictPadd.v":"3db3061ddc828d6615d95d1912761b9341a2376fdd61b2ec01e116dd991b3135"},"files":{"coq_file":"proofs/coq/ComplexityStrictPadd.v"},"id":"CUB-COMPLEXITY-STRICT-PADD","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"source-preserving-add","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_padd_run + s_padd_extract","source_completeness":"full (CSV-sourced)","statement":"source-preserving unary ADD sub-machine for unary MULTIPLY: s_padd (6-state) appends a COPY of a unary source(a) block to a DISTANT output(o) -- output := o + a -- while PRESERVING the source, using Bit false as a temporary mark on each source true (flipped back in a final unmark pass). States 1-3 are identical to s_copy's output round-trip; state 5 marches source-left to the Bit-false mark; state 4 is the unmark. Proven 0-axiom: padd_m1/m2/m3/m5 march-folds, padd_out round-trip, padd_cycle (2c'+2o+5 per cycle), padd_copy_phase (fold over the source), padd_unmark_nil, ttb_run_gap. s_padd_run: source(S k)|gap|output(o) -> source(S k) INTACT | gap | output(S k + o); s_padd_halted; s_padd_extract = repeat true (S k) ++ repeat true (S k + o). This is exactly the source-preserving body unary multiply nests inside the s_copy counter loop. coqchk Axioms: .","status":"proven","use_cases":["complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: FIRST LIVE PIPELINE: delim_counter := stm_seq (s_map_prepend negb) s_erase_false -- a genuine two-stage product machine proven (delim_counter_computes) to compute the UNARY COUNT OF THE INPUT'S FALSE DELIMITERS (repeat true (length (filter negb w))) at the single explicit budget (seq_K 1 1, seq_C 1 4 1 1), via stm_seq_clean_pad_computes_poly + the value identity filter_id_map_negb, with zero further glue. Both a real parse-body sub-quantity (the #parts counter core; num_clauses = #parts/3 is the div-3 successor brick) and the end-to-end integration witness that the clean-pad atoms + padding bisimulation + budget algebra compose. Stage bodies remain open; strict wrapper OPEN. NP-hardness (Karp 1972) not P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictPipeline.v":"60d0f26712cbe87d15195e7f874cf8c551e25e6692fae73f189b1f7445155c3b"},"files":{"coq_file":"proofs/coq/ComplexityStrictPipeline.v"},"id":"CUB-COMPLEXITY-STRICT-PIPELINE","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"delim_counter_computes","source_completeness":"full (CSV-sourced)","statement":"FIRST LIVE PIPELINE: delim_counter := stm_seq (s_map_prepend negb) s_erase_false -- a genuine two-stage product machine proven (delim_counter_computes) to compute the UNARY COUNT OF THE INPUT'S FALSE DELIMITERS (repeat true (length (filter negb w))) at the single explicit budget (seq_K 1 1, seq_C 1 4 1 1), via stm_seq_clean_pad_computes_poly + the value identity filter_id_map_negb, with zero further glue. Both a real parse-body sub-quantity (the #parts counter core; num_clauses = #parts/3 is the div-3 successor brick) and the end-to-end integration witness that the clean-pad atoms + padding bisimulation + budget algebra compose. Stage bodies remain open; strict wrapper OPEN. NP-hardness (Karp 1972) not P vs NP.","status":"proven","use_cases":["admission","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Honest composition through a proved intermediate range: s_clean_transduces_pad_on keeps a following stage's domain predicate explicit; stm_seq_clean_pad_preserves_range_poly turns a total clean first stage plus a range proof into an ordinary total clean composite. s_clean_transduces_pad_computes_strict lifts any clean-pad package to the exact-budget strict computation predicate.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictRangeCompose.v":"f22be3d18a5852f3d3f063f46260ffb086be098ee115817979dc11ea2bd75c35"},"files":{"coq_file":"proofs/coq/ComplexityStrictRangeCompose.v"},"id":"CUB-COMPLEXITY-STRICT-RANGE-COMPOSE","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; reusable range/strict composition infrastructure","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_clean_transduces_pad_on + stm_seq_clean_pad_preserves_range_poly + s_clean_transduces_pad_computes_strict","source_completeness":"full (CSV-sourced)","statement":"Honest composition through a proved intermediate range: s_clean_transduces_pad_on keeps a following stage's domain predicate explicit; stm_seq_clean_pad_preserves_range_poly turns a total clean first stage plus a range proof into an ordinary total clean composite. s_clean_transduces_pad_computes_strict lifts any clean-pad package to the exact-budget strict computation predicate.","status":"proven","use_cases":["admission","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: item-3 streaming spec: re-expresses the OPEN strict obligation from compute-word_reduce to compute-word_reduce_stream -- an EXPLICIT doubly-nested count-n loop (outer u; inner v over 0..num_cities) whose body emits one unary field enc_nat(adj_matrix u v); preceded by enc_nat(num_cities) and enc_nat(max_bound). word_reduce_stream_eq proves it equals word_reduce; s_computes_in_poly_strict_ext + s_phase4_from_stream transfer a machine for the streaming form to s_poly_reduces L_3SAT L_TSP. Pure Coq (no TM built); pins the iteration the iterate combinator must realize. 0 axioms; coqchk Axioms: .","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictStream.v":"2efe3bf9b8c229c4c2fb589eeef69a7a3b259e05dfdb57842b059fc996b9e218"},"files":{"coq_file":"proofs/coq/ComplexityStrictStream.v"},"id":"CUB-COMPLEXITY-STRICT-STREAM","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"spec-pins-loop","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"word_reduce_stream_eq + s_phase4_from_stream","source_completeness":"full (CSV-sourced)","statement":"item-3 streaming spec: re-expresses the OPEN strict obligation from compute-word_reduce to compute-word_reduce_stream -- an EXPLICIT doubly-nested count-n loop (outer u; inner v over 0..num_cities) whose body emits one unary field enc_nat(adj_matrix u v); preceded by enc_nat(num_cities) and enc_nat(max_bound). word_reduce_stream_eq proves it equals word_reduce; s_computes_in_poly_strict_ext + s_phase4_from_stream transfer a machine for the streaming form to s_poly_reduces L_3SAT L_TSP. Pure Coq (no TM built); pins the iteration the iterate combinator must realize. 0 axioms; coqchk Axioms: .","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Preservation-safe equality over two indexed canonical unary fields. The well-formed 11-state s_unary_eq_marker_raw starts on Blank;base;true^a;Blank;true^b;Blank;meta, uses Bit false only as temporary crossing marks, restores both operands and every separator, preserves arbitrary TapeSym base and meta regions, and replaces only the left Blank sentinel with Bit(Nat.eqb a b). The exact run uses unary_eq_fuel(a,b)=2*a*m+m^2+2*a+5*m+4 for m=min(a,b), has a least halt/no-early-halt witness within (a+b+2)^2, and exposes exact state and transition-range proofs. Executable controls cover empty/equal/asymmetric operands, mixed base/meta preservation, one-step-early nonhalting, and rejected wrong marker/restoration layouts. This is an indexed canonical-unary theorem, not a validator for malformed fields containing false bits. Descriptor-field staging, frame tally staging, literal-query adaptation, finite karp_edge, grid emission, encode_tsp, and the strict reduction capstone remain OPEN.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictUnaryEq.v":"7b6379f43299246f1c7bf1735bf856db556f39e6802a05be0a6fa4a7f115f844"},"files":{"coq_file":"proofs/coq/ComplexityStrictUnaryEq.v"},"id":"CUB-COMPLEXITY-STRICT-UNARY-EQ","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk; exact 11-state machine; arbitrary base/meta preserved; malformed unary fields intentionally outside the indexed contract","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_unary_eq_marker_raw_state_bound + s_unary_eq_marker_raw_well_formed + ueq_one_round + ueq_match_n + ueq_finish_A + ueq_finish_B + unary_eq_marker_exact_run + unary_eq_fuel_square + unary_eq_marker_first_halt_square","source_completeness":"full (CSV-sourced)","statement":"Preservation-safe equality over two indexed canonical unary fields. The well-formed 11-state s_unary_eq_marker_raw starts on Blank;base;true^a;Blank;true^b;Blank;meta, uses Bit false only as temporary crossing marks, restores both operands and every separator, preserves arbitrary TapeSym base and meta regions, and replaces only the left Blank sentinel with Bit(Nat.eqb a b). The exact run uses unary_eq_fuel(a,b)=2*a*m+m^2+2*a+5*m+4 for m=min(a,b), has a least halt/no-early-halt witness within (a+b+2)^2, and exposes exact state and transition-range proofs. Executable controls cover empty/equal/asymmetric operands, mixed base/meta preservation, one-step-early nonhalting, and rejected wrong marker/restoration layouts. This is an indexed canonical-unary theorem, not a validator for malformed fields containing false bits. Descriptor-field staging, frame tally staging, literal-query adaptation, finite karp_edge, grid emission, encode_tsp, and the strict reduction capstone remain OPEN.","status":"proven","use_cases":["TEP","TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Source-preserving unary staging across an arbitrary bit-only middle. The explicit well-formed 6-state s_unary_stage_raw uses false marks and one temporary Blank delimiter to copy true^n to the far scratch end, restores the complete source/middle/boundary, preserves arbitrary mixed base, and halts at the source's left Blank sentinel with scratch length n+o. Exact execution and least-halt semantics include n=0 and are bounded by 3*(n+|middle|+o+2)^2. A separate finite cleanup restores a fixed predecessor and exposes the copied scratch. Descriptor locators, frame-derived nv staging, finite karp_edge, grid emission, encode_tsp, and the strict capstone remain OPEN.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictUnaryStage.v":"3d45b4123e9b12a09bc90410851f3a365771576089359c41f9dbffb47adbe8dc"},"files":{"coq_file":"proofs/coq/ComplexityStrictUnaryStage.v"},"id":"CUB-COMPLEXITY-STRICT-UNARY-STAGE","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk; exact 6-state machine; arbitrary base and bit-only middle preserved","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_unary_stage_raw_state_bound + s_unary_stage_raw_well_formed + unary_stage_cycle + unary_stage_copy_phase + unary_stage_exact_run + unary_stage_fuel_quadratic + unary_stage_first_halt","source_completeness":"full (CSV-sourced)","statement":"Source-preserving unary staging across an arbitrary bit-only middle. The explicit well-formed 6-state s_unary_stage_raw uses false marks and one temporary Blank delimiter to copy true^n to the far scratch end, restores the complete source/middle/boundary, preserves arbitrary mixed base, and halts at the source's left Blank sentinel with scratch length n+o. Exact execution and least-halt semantics include n=0 and are bounded by 3*(n+|middle|+o+2)^2. A separate finite cleanup restores a fixed predecessor and exposes the copied scratch. Descriptor locators, frame-derived nv staging, finite karp_edge, grid emission, encode_tsp, and the strict capstone remain OPEN.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Canonical cleanup around source-preserving unary staging. A fixed finite-control predecessor bit parameter drives the 4-state cleanup: restore the predecessor, scan to the virtual tail, find the copied scratch from the right, rewrite its false boundary to Blank, and halt on the scratch start, including zero. Composing it with the 6-state raw stager gives an exact well-formed 10-state product over arbitrary base and bit-only middle. It preserves the source and middle, produces true^(n+o), has exact least-halt semantics, and is bounded by 3*(n+|middle|+o+2)^2. Dynamic xa predecessor selection still requires an upstream finite physical kind branch; finite edge field locators, nv staging, karp_edge, grid emission, encode_tsp, and the strict capstone remain OPEN.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictUnaryStageClean.v":"1e0a344d9838af70c0450570fd065a2c81196b3b64521406dc4e66dcc6b5b147"},"files":{"coq_file":"proofs/coq/ComplexityStrictUnaryStageClean.v"},"id":"CUB-COMPLEXITY-STRICT-UNARY-STAGE-CLEAN","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk; exact 4-state cleanup and 10-state composition; fixed predecessor is finite-control data","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_unary_stage_cleanup_state_bound + s_unary_stage_cleanup_well_formed + unary_stage_cleanup_exact_run + unary_stage_cleanup_first_halt + s_unary_stage_clean_state_bound + s_unary_stage_clean_well_formed + unary_stage_clean_exact_run + unary_stage_clean_first_halt","source_completeness":"full (CSV-sourced)","statement":"Canonical cleanup around source-preserving unary staging. A fixed finite-control predecessor bit parameter drives the 4-state cleanup: restore the predecessor, scan to the virtual tail, find the copied scratch from the right, rewrite its false boundary to Blank, and halt on the scratch start, including zero. Composing it with the 6-state raw stager gives an exact well-formed 10-state product over arbitrary base and bit-only middle. It preserves the source and middle, produces true^(n+o), has exact least-halt semantics, and is bounded by 3*(n+|middle|+o+2)^2. Dynamic xa predecessor selection still requires an upstream finite physical kind branch; finite edge field locators, nv staging, karp_edge, grid emission, encode_tsp, and the strict capstone remain OPEN.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: total payload-preserving num_vars annotation and joint SAT parameter frame. The 37-state s_varframe_raw directly handles every word, including a final unterminated group at physical Blank, preserves w, appends enc_nat(S(halve(max_tally w))), halts first within 34*|w|^2+34, and finishes blank_padded with empty left tape. Precomposition with the parser-preserving 13-state normalizer gives the 50-state s_varframe computing nv_annotated w = normalize(w)++enc_nat(num_vars(parse_3sat w)). Composition with the 28-state raw clause appender gives the 78-state s_parameter_frame computing normalize(w)++enc_nat(nv)++enc_nat(nc). All packages are total, finite-state, least-halt minimal, canonical, and polynomial. N assembly, karp_edge, N-by-N grid emission, encode_tsp, and s_poly_reduces L_3SAT L_TSP remain OPEN.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictVarFrame.v":"b73cbc00376900d09ac8a1d2aaafc52d807dac39e460182bdb3240a2aa522c0a"},"files":{"coq_file":"proofs/coq/ComplexityStrictVarFrame.v"},"id":"CUB-COMPLEXITY-STRICT-VAR-FRAME","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Print Assumptions Closed; coqchk Axioms:; direct totalization plus semantic normalizer composition; coq-only strict-TM corpus","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_varframe_raw_clean_pad + s_varframe_clean_pad + s_parameter_frame_clean_pad + s_parameter_frame_stage_exists_with_state_bound","source_completeness":"full (CSV-sourced)","statement":"total payload-preserving num_vars annotation and joint SAT parameter frame. The 37-state s_varframe_raw directly handles every word, including a final unterminated group at physical Blank, preserves w, appends enc_nat(S(halve(max_tally w))), halts first within 34*|w|^2+34, and finishes blank_padded with empty left tape. Precomposition with the parser-preserving 13-state normalizer gives the 50-state s_varframe computing nv_annotated w = normalize(w)++enc_nat(num_vars(parse_3sat w)). Composition with the 28-state raw clause appender gives the 78-state s_parameter_frame computing normalize(w)++enc_nat(nv)++enc_nat(nc). All packages are total, finite-state, least-halt minimal, canonical, and polynomial. N assembly, karp_edge, N-by-N grid emission, encode_tsp, and s_poly_reduces L_3SAT L_TSP remain OPEN.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: TOTAL PARSED-PREFIX MAX contract plus the original aligned raw-max theorem (pure Coq, no TM): complete_clause_parts drops exactly the one- or two-part suffix ignored by decode_to_3sat_formula; normalize_complete_clauses canonically re-encodes that prefix and is parser-preserving, delimiter-terminated, 3-aligned, and tally/max preserving for every word. TOTAL HEADLINES: MAXVAR_IS_HALVED_PARSED_MAXTALLY and num_vars_from_normalized_maxtally prove num_vars(parse_3sat w)=S(halve(max_tally(normalize_complete_clauses w))) with no premise. The original MAXVAR_IS_HALVED_MAXTALLY/num_vars_from_maxtally remain scoped to 3-aligned words. The finite clean-pad normalization machine and terminal physical compaction remain OPEN; strict wrapper OPEN. NP-hardness (Karp 1972) not P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictVarMax.v":"bbd175876f1bbb3a032964f6f0234a9cb2626b1d81004f5e97d773bb9e6d4e49"},"files":{"coq_file":"proofs/coq/ComplexityStrictVarMax.v"},"id":"CUB-COMPLEXITY-STRICT-VAR-MAX","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; total pure specification only, no finite normalization machine claimed; coq-only strict-TM corpus","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"normalize_complete_clauses_parse + normalize_complete_clauses_terminated + normalize_complete_clauses_aligned + normalize_complete_clauses_max_tally + MAXVAR_IS_HALVED_PARSED_MAXTALLY + num_vars_from_normalized_maxtally","source_completeness":"full (CSV-sourced)","statement":"TOTAL PARSED-PREFIX MAX contract plus the original aligned raw-max theorem (pure Coq, no TM): complete_clause_parts drops exactly the one- or two-part suffix ignored by decode_to_3sat_formula; normalize_complete_clauses canonically re-encodes that prefix and is parser-preserving, delimiter-terminated, 3-aligned, and tally/max preserving for every word. TOTAL HEADLINES: MAXVAR_IS_HALVED_PARSED_MAXTALLY and num_vars_from_normalized_maxtally prove num_vars(parse_3sat w)=S(halve(max_tally(normalize_complete_clauses w))) with no premise. The original MAXVAR_IS_HALVED_MAXTALLY/num_vars_from_maxtally remain scoped to 3-aligned words. The finite clean-pad normalization machine and terminal physical compaction remain OPEN; strict wrapper OPEN. NP-hardness (Karp 1972) not P vs NP.","status":"proven","use_cases":["complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: the per-literal VARIABLE-INDEX transducer: s_varidx (3-state) rewrites every false-delimited group of k trues to (k-1)/2 trues -- decode_literal's OWN index arithmetic Nat.div2 (Nat.pred k) -- preserving delimiters, in one |w|+1-step scan (k=1 c=1). Finite control = per-group phase counter (drop 1st true, keep every 2nd), reset by each delimiter: the reset-on-false generalization of s_div3. Proven via spec fold vi_cells + scan invariant s_varidx_scan, joint closed forms kept1 k = k/2 & kept2 k = (S k)/2, kept0_is_varindex (phase 0 IS div2 (pred k)), group lemma vi_group (tail closes BY CONVERSION -- the false-branch ignores the phase, no tracking argument needed), s_varidx_computes. Produces ALL per-part var indices in one pass; the MAX over halved groups (num_vars = 1 + max) is the still-open overlay/erosion machine. Strict wrapper OPEN. NP-hardness (Karp 1972) not P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictVarIdx.v":"fd238a218b34eef258a7627c529e2b53de2c18a8c3ed61d9745bc7d2e9a122da"},"files":{"coq_file":"proofs/coq/ComplexityStrictVarIdx.v"},"id":"CUB-COMPLEXITY-STRICT-VARIDX","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"s_varidx_computes + kept0_is_varindex + vi_group","source_completeness":"full (CSV-sourced)","statement":"the per-literal VARIABLE-INDEX transducer: s_varidx (3-state) rewrites every false-delimited group of k trues to (k-1)/2 trues -- decode_literal's OWN index arithmetic Nat.div2 (Nat.pred k) -- preserving delimiters, in one |w|+1-step scan (k=1 c=1). Finite control = per-group phase counter (drop 1st true, keep every 2nd), reset by each delimiter: the reset-on-false generalization of s_div3. Proven via spec fold vi_cells + scan invariant s_varidx_scan, joint closed forms kept1 k = k/2 & kept2 k = (S k)/2, kept0_is_varindex (phase 0 IS div2 (pred k)), group lemma vi_group (tail closes BY CONVERSION -- the false-branch ignores the phase, no tracking argument needed), s_varidx_computes. Produces ALL per-part var indices in one pass; the MAX over halved groups (num_vars = 1 + max) is the still-open overlay/erosion machine. Strict wrapper OPEN. NP-hardness (Karp 1972) not P vs NP.","status":"proven","use_cases":["TEP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Binary serialization + syntax/semantics of the Undirected Hamiltonian Cycle decision language L_UHC (edges via a clean structural helper). Last language endpoint of the Karp chain. Definition only. Not P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityUhcLanguage.v":"225a15d028c1396d79796cfaac640b5aff37138936227dc578de693ced5b5ec9"},"files":{"coq_file":"proofs/coq/ComplexityUhcLanguage.v"},"id":"CUB-COMPLEXITY-UHC","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"","source_completeness":"full (CSV-sourced)","statement":"Binary serialization + syntax/semantics of the Undirected Hamiltonian Cycle decision language L_UHC (edges via a clean structural helper). Last language endpoint of the Karp chain. Definition only. Not P vs NP.","status":"definition","use_cases":["complexity"],"verification_state":"NOT_VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Karp Phase 3: PROVEN reduction L_UHC <=p L_TSP (uhc_to_tsp_correct -- an iff 0-axiom theorem). Cost gadget: edge=1 non-edge=2 budget B=N; a tour of cost <= N exists IFF the graph has a Hamiltonian cycle. Pure topological mapping (NO Turing-machine/poly_reduces wrapper -- that is Phase 4). NP-hardness (Karp 1972) not P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityUhcToTsp.v":"420047619dbc7b8d797c6fa633dee05d3a51147146a9279c240837bb4d9e5991"},"files":{"coq_file":"proofs/coq/ComplexityUhcToTsp.v"},"id":"CUB-COMPLEXITY-UHC-TSP","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"uhc_to_tsp_instance","source_completeness":"full (CSV-sourced)","statement":"Karp Phase 3: PROVEN reduction L_UHC <=p L_TSP (uhc_to_tsp_correct -- an iff 0-axiom theorem). Cost gadget: edge=1 non-edge=2 budget B=N; a tour of cost <= N exists IFF the graph has a Hamiltonian cycle. Pure topological mapping (NO Turing-machine/poly_reduces wrapper -- that is Phase 4). NP-hardness (Karp 1972) not P vs NP.","status":"proven","use_cases":["admission","TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: mixed-stream Page-CUSUM fire threshold for the deployed encoding S <- max(0, S + x - k), x in {0,1}, k=1/2 (integer-scaled T <- max(0, T + 2x - 1), fire at T >= 2h). Max-suffix identity cusum_maxsuffix_identity: T_t = max over windows of (2*denials - len). (A) subcritical_no_fire/subcritical_never_fires/halfrate_pins_zero: every-window denial density <= 1/2 => never fires. (B) supercritical_fires/denial_burst_fires (N=2h consecutive denials)/supercritical_rate_fires (any rate a/b > 1/2, bound 2hb <= N(2a-b)); detection_delay_ceil N = ceil(2hb/(2a-b)) Coq-only. (C) observed instance: 1272/4772 = 27% subcritical, never fires. CRITICAL RATE PROVED rho* = k = 1/2 -- REFUTES the erosion_e2e_flow.html sketch rho* = k/(1+k) ~ 33% (that formula belongs to a deny:+1/allow:-k encoding, not the deployed one); no-fire verdict unaffected (27% < both).","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/CubCusumMixed001.v":"8c3297eaad2e70c6e0c1a6888692c61793d3e6f55f6ab7b970f6af6a155c076d","proofs/lean4/CubCusumMixed001.lean":"4557d3bf865e688ee532a9081767686ce35a273eaaf6673507ba8592cece8fcb","proofs/verus/cub_cusum_mixed_001.rs":"fd0d13ef05051cd21d6088d45c4de877fe176c791da7eae28b1f338c510f663d"},"files":{"coq_file":"proofs/coq/CubCusumMixed001.v","lean_file":"proofs/lean4/CubCusumMixed001.lean","verus_file":"proofs/verus/cub_cusum_mixed_001.rs"},"id":"CUB-CUSUM-MIXED-001","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; Lean 4.31 core exit 0; Verus 21 verified 0 errors; detection_delay_ceil div-packaging Coq-only (Lean/Verus carry the bound as side condition)","proof_scope":"standalone","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"cusum_maxsuffix_identity + subcritical_never_fires + supercritical_rate_fires + observed_27pct_never_fires","source_completeness":"full (CSV-sourced)","statement":"mixed-stream Page-CUSUM fire threshold for the deployed encoding S <- max(0, S + x - k), x in {0,1}, k=1/2 (integer-scaled T <- max(0, T + 2x - 1), fire at T >= 2h). Max-suffix identity cusum_maxsuffix_identity: T_t = max over windows of (2*denials - len). (A) subcritical_no_fire/subcritical_never_fires/halfrate_pins_zero: every-window denial density <= 1/2 => never fires. (B) supercritical_fires/denial_burst_fires (N=2h consecutive denials)/supercritical_rate_fires (any rate a/b > 1/2, bound 2hb <= N(2a-b)); detection_delay_ceil N = ceil(2hb/(2a-b)) Coq-only. (C) observed instance: 1272/4772 = 27% subcritical, never fires. CRITICAL RATE PROVED rho* = k = 1/2 -- REFUTES the erosion_e2e_flow.html sketch rho* = k/(1+k) ~ 33% (that formula belongs to a deny:+1/allow:-k encoding, not the deployed one); no-fire verdict unaffected (27% < both).","status":"proven","use_cases":["TEP","admission"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Belnap four-value meet over 2-bit cells (PASS=0b10, FAIL=0b01, FLUID=0b11, TAMPER=0b00) is bitwise AND: idempotent, commutative, associative, FLUID is identity, TAMPER is absorbing; FAIL resists PASS evidence (meet(FAIL,PASS)=TAMPER), so a reroute witness can never upgrade a failed cell (proof family R1-R10, 18 proof fns by bit_vector).","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/verus/cubie_reroute_witness_spec.rs":"5b2362e8f7d65e04cf299f3b2f7f25393f2b90ab966c14529e0263b8e7635038"},"files":{"verus_file":"proofs/verus/cubie_reroute_witness_spec.rs"},"id":"CUB-MATH-CORE-3266","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"Verus-only single-kernel row: 18 verified 0 errors under pinned verus 0.2026.06.28, no axioms/assume/admit; Coq/Lean mirrors not yet authored; recovered 2026-08-13 from claude.ai-session Drive artifact (recovered/README.md); not invoked by product code yet - unwired is an integration status, not a validity defect (docs/RECOVERY_CLAUDE_EXPORT_2026-08-13.md).","proof_scope":"standalone","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"standalone spec, no product anchor yet (reroute witness calculus)","source_completeness":"full (CSV-sourced)","statement":"Belnap four-value meet over 2-bit cells (PASS=0b10, FAIL=0b01, FLUID=0b11, TAMPER=0b00) is bitwise AND: idempotent, commutative, associative, FLUID is identity, TAMPER is absorbing; FAIL resists PASS evidence (meet(FAIL,PASS)=TAMPER), so a reroute witness can never upgrade a failed cell (proof family R1-R10, 18 proof fns by bit_vector).","status":"proven","use_cases":["admission"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Coq motion calculus M1-M10 over the 54-cell/27-carrier duality: arity is sticker count (8*3+12*2+6*1+1*0=54 over 27 carriers), the core is nullary and the fixed frame, rotation preserves arity and grade, complete placements survive authorized motion, and re-placement is bounded by God's Number 20 (depth-3 bound 60).","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"recovered/CubieMotionV1.v":"ea68c9be7b773315e451a577133bd38ef9a21e0341867b56704f1e4afc32d8ba"},"files":{"coq_file":"recovered/CubieMotionV1.v"},"id":"CUB-MATH-CORE-3267","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"FLUID not PASS: compiles under pinned Coq 8.18 (coqc EXIT=0) but declares 3 Admitted (M1 arity_is_sticker_count, M2 core_is_nullary, M6 grade_invariant_under_motion; each with a vm_compute discharge plan) + 6 axioms (5 standard-cube table facts + Rokicki 2010 God's Number, cited not proved); deliberately does not claim Rubik legality; recovered byte-exact from claude.ai export 2026-08-13 (recovered/README.md); not gated - lives outside proofs/ until Admitted discharge.","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"not wired (motion calculus over CUB-TSP-034 placement)","source_completeness":"full (CSV-sourced)","statement":"Coq motion calculus M1-M10 over the 54-cell/27-carrier duality: arity is sticker count (8*3+12*2+6*1+1*0=54 over 27 carriers), the core is nullary and the fixed frame, rotation preserves arity and grade, complete placements survive authorized motion, and re-placement is bounded by God's Number 20 (depth-3 bound 60).","status":"partial","use_cases":["admission","TSP"],"verification_state":"NOT_VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Lean motion calculus closing audit P1 tautologies: freshHandoff is unconsumed by construction (non-tautological cub_3141), rotateOk forces an unconsumed handoff via the LeaseBound model invariant (non-tautological cub_3140), consumption revokes rotation authority, rotation preserves arity, completeness survives authorized motion, and depth-3 motion is bounded by 60.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"recovered/CubieMotionV2_1.lean":"55f9022a7a50078d63a5f4826e7f35bbc2d4322c5242c1dc43c67fbfef23ddcf"},"files":{"lean_file":"recovered/CubieMotionV2_1.lean"},"id":"CUB-MATH-CORE-3268","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"FLUID not PASS: V2_1 compiles under pinned Lean 4.31.0 (EXIT=0) with 14 closed theorems and 3 axioms (standard-cube table facts awaiting instantiation); recovered CubieMotionV2.lean retained byte-exact but does NOT compile (Nonempty synthesis failure at opaque act, EXIT=1) - V2_1 is the minimal fix, only the Placement declaration differs; Rubik legality and VRF properties deliberately not claimed; recovered 2026-08-13 (recovered/README.md); not gated - lives outside proofs/ until axiom discharge.","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"not wired (bridges CubieAuth.rotateOk to LinearHandoff)","source_completeness":"full (CSV-sourced)","statement":"Lean motion calculus closing audit P1 tautologies: freshHandoff is unconsumed by construction (non-tautological cub_3141), rotateOk forces an unconsumed handoff via the LeaseBound model invariant (non-tautological cub_3140), consumption revokes rotation authority, rotation preserves arity, completeness survives authorized motion, and depth-3 motion is bounded by 60.","status":"partial","verification_state":"NOT_VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: the WIDTH-GAP AUDIT: php_width_lower_bound (Haken2e) creates NO width increase over the initial formula, machine-checked. pigeon_clause_width: every pigeon axiom of generate_PHP_CNF N is width EXACTLY N. php_initial_width: initial width = N (a width-N clause exists; every clause <= N), N >= 2. php_width_bound_met_by_axiom: the N/3 < width target is met by an INITIAL clause. php_width_bound_no_refutation_gap: in EVERY refutation the Haken2e bound is witnessed by an axiom clause (via php_refutation_contains_every_axiom). Consequence: a size-width tradeoff (exponent ~ (refutation width - initial width)^2) yields NOTHING exponential from the current theorem on this encoding -- the recorded route 'single remaining step is the size-width tradeoff' is corrected. Honest routes: (A) direct bottleneck counting over generate_PHP_CNF, or (B) a separate clearly-named bounded-width family + its own width theorem + formal tradeoff. haken_resolution_lower_bound_open remains OPEN. NOT P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityProofSystemHaken2f.v":"6b454fc3ce8bafd7efe2e08cfdb756b968c947fd6ba4e7a93115e6587ce15b12"},"files":{"coq_file":"proofs/coq/ComplexityProofSystemHaken2f.v"},"id":"CUB-PROOFSYS-HAKEN-2F","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; audit brick -- pins what Haken2e does and does not feed; coq-only proof-complexity corpus","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"php_initial_width + php_width_bound_met_by_axiom + php_width_bound_no_refutation_gap","source_completeness":"full (CSV-sourced)","statement":"the WIDTH-GAP AUDIT: php_width_lower_bound (Haken2e) creates NO width increase over the initial formula, machine-checked. pigeon_clause_width: every pigeon axiom of generate_PHP_CNF N is width EXACTLY N. php_initial_width: initial width = N (a width-N clause exists; every clause <= N), N >= 2. php_width_bound_met_by_axiom: the N/3 < width target is met by an INITIAL clause. php_width_bound_no_refutation_gap: in EVERY refutation the Haken2e bound is witnessed by an axiom clause (via php_refutation_contains_every_axiom). Consequence: a size-width tradeoff (exponent ~ (refutation width - initial width)^2) yields NOTHING exponential from the current theorem on this encoding -- the recorded route 'single remaining step is the size-width tradeoff' is corrected. Honest routes: (A) direct bottleneck counting over generate_PHP_CNF, or (B) a separate clearly-named bounded-width family + its own width theorem + formal tradeoff. haken_resolution_lower_bound_open remains OPEN. 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row","crate":"","deployable":false,"file_shas":{"proofs/coq/CubTsp016.v":"eac069db48471e7b211cff90a42e82c51afb237d6c751fe79620fd69cef0e6b5","proofs/lean4/CubTsp016.lean":"022aad668ef5d974e7069f54d90b4c809042865c34c8eb33debeb6379b687f0c","proofs/verus/cub_tsp_016.rs":"9ab68ba64f024628d1e5016efdb7083696cb0aeea15097c792d32d1bcb25d816"},"files":{"coq_file":"proofs/coq/CubTsp016.v","lean_file":"proofs/lean4/CubTsp016.lean","verus_file":"proofs/verus/cub_tsp_016.rs"},"id":"CUB-TSP-016","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"","proof_scope":"standalone","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"InnerCube::evaluate_lower_bound","source_completeness":"full (CSV-sourced)","statement":"Certificate-backed prune soundness: a valid branch lower-bound certificate >= incumbent excludes every tour in the branch.","status":"proven","use_cases":["TSP"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Belnap algebra + 2-bit encoding totality: enc/dec bijection on the 4-value Belnap lattice (dec_enc_id, enc_dec_id, enc_injective), meet = bit-AND is a homomorphism, FLUID identity, TAMPER bottom, De Morgan duality. Triple-kernel bridge from the substantive cubie-tf corpus.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/CubTsp017.v":"00fc2a185f2dcedb85e6aaf712074bb517a4a9881f086d27b1ba010a0fbc818d","proofs/lean4/CubTsp017.lean":"93858039f68455e970bbfb277f256592c1aad74dc7d4102f4df8869ec1141bce","proofs/verus/cub_tsp_017.rs":"bf14174d89419d25642fe0a9d37307c5dfbdd4c32406ff3e5e0c57cd06c875f4"},"files":{"coq_file":"proofs/coq/CubTsp017.v","lean_file":"proofs/lean4/CubTsp017.lean","verus_file":"proofs/verus/cub_tsp_017.rs"},"id":"CUB-TSP-017","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"mirrors CUB-1221","proof_scope":"standalone","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"cubie_eval / pack_belnap_cells","source_completeness":"full (CSV-sourced)","statement":"Belnap algebra + 2-bit encoding totality: enc/dec bijection on the 4-value Belnap lattice (dec_enc_id, enc_dec_id, enc_injective), meet = bit-AND is a homomorphism, FLUID identity, TAMPER bottom, De Morgan duality. Triple-kernel bridge from the substantive cubie-tf corpus.","status":"proven","use_cases":["crypto","TSP"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Snap AND-fold consensus law: cell-wise AND fold over a window -- append homomorphism, TAMPER sticky/absorbing, FLUID transparent/identity, PASS iff consensus. FIRST SUBSTANTIVE PROOF of upstream stub CUB-1899 (net-new, not a mirror of a proven upstream theorem).","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/CubTsp018.v":"8c98568d90f76199f13b0621cd4d96f22d9f095d279df3e9390e3f1f4ec0a309","proofs/lean4/CubTsp018.lean":"3b5e3e605866f164e24860bdf3eae52ed782121839ddb56aecc220f6ad7ddb0b","proofs/verus/cub_tsp_018.rs":"67737d000a419b95ee12b1f87528248a161d852f17107278c24a49994030a339"},"files":{"coq_file":"proofs/coq/CubTsp018.v","lean_file":"proofs/lean4/CubTsp018.lean","verus_file":"proofs/verus/cub_tsp_018.rs"},"id":"CUB-TSP-018","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"FRESH first proof of upstream stub CUB-1899; meet FAIL^PASS->TAMPER (bit-AND) differs from runtime verdict() safety-dominance -- do NOT cite 018 as backing verdict()","proof_scope":"standalone","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"snap_fold (runtime anchor to implement -- wiring queue #1)","source_completeness":"full (CSV-sourced)","statement":"Snap AND-fold consensus law: cell-wise AND fold over a window -- append homomorphism, TAMPER sticky/absorbing, FLUID transparent/identity, PASS iff consensus. FIRST SUBSTANTIVE PROOF of upstream stub CUB-1899 (net-new, not a mirror of a proven upstream theorem).","status":"proven","use_cases":["TSP"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: CUSUM sustained-drift detection: under a sustained linear drift, the Page/CUSUM statistic grows so the detection delay is finite and bounded (<= h+1). The drift premise is stated as an empirical hypothesis. The detection dual of the CUSUM calibration identities (020).","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/CubTsp019.v":"a63a65b5a9a1b90a8e5040ce5b01170bebc4d34a4ba12cbc50e241d08af55fa5","proofs/lean4/CubTsp019.lean":"4ae7c9247b1efe79a5e5d81755e07c8324ca6419a1c0ff060d74ec29093ac18e","proofs/verus/cub_tsp_019.rs":"79fc0ff2c06cc324c9dc2275bcf144e0eaafa91946ab0e45a25590e5cd5693ef"},"files":{"coq_file":"proofs/coq/CubTsp019.v","lean_file":"proofs/lean4/CubTsp019.lean","verus_file":"proofs/verus/cub_tsp_019.rs"},"id":"CUB-TSP-019","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"mirrors CUB-1921-d (detection dual); drift premise empirical; scrubbed free of 032 material (grep 0, re-verified all 3 kernels)","proof_scope":"standalone","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"CusumChannel over per-iteration bound improvement (TEP->TSP bridge -- wiring queue #2)","source_completeness":"full (CSV-sourced)","statement":"CUSUM sustained-drift detection: under a sustained linear drift, the Page/CUSUM statistic grows so the detection delay is finite and bounded (<= h+1). The drift premise is stated as an empirical hypothesis. The detection dual of the CUSUM calibration identities (020).","status":"proven","use_cases":["TEP","TSP"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: CUSUM calibration identities: per-step non-increase of the reset, monotonicity in the input z, and reset independence -- the structural identities that make the Page/CUSUM statistic well-behaved. The 1921-c tautology is deliberately excluded (not a load-bearing result). The calibration base the detection theorem (019) rests on.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/CubTsp020.v":"73e17d7eeac54c695c4a4a185bf3db0f13e2aecdf0316f10bed10bd63b3c2198","proofs/lean4/CubTsp020.lean":"55cc01f2805e153e2ca8125c510bf7768c24f0f2be654e9afbee76dbd46f1781","proofs/verus/cub_tsp_020.rs":"4b115fce8d3e2e958fa82599b44be8cf2daeb42b4f1afa86afcaf72a92bd4b60"},"files":{"coq_file":"proofs/coq/CubTsp020.v","lean_file":"proofs/lean4/CubTsp020.lean","verus_file":"proofs/verus/cub_tsp_020.rs"},"id":"CUB-TSP-020","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"mirrors CUB-1921-b/f (calibration identities); 1921-c tautology deliberately excluded; scrubbed free of 032 material","proof_scope":"standalone","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"CusumChannel calibration (wiring queue #2)","source_completeness":"full (CSV-sourced)","statement":"CUSUM calibration identities: per-step non-increase of the reset, monotonicity in the input z, and reset independence -- the structural identities that make the Page/CUSUM statistic well-behaved. The 1921-c tautology is deliberately excluded (not a load-bearing result). The calibration base the detection theorem (019) rests on.","status":"proven","use_cases":["TEP","TSP"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Vertex-triple strict span + parity-toggle counting law: the generic counting law over a vertex-triple table (strict span; each toggle flips parity). FIRST SUBSTANTIVE PROOF of upstream stub CUB-1907. The concrete table proved is the DISJOINT corner-band partition; the overlapping cell-18-in-3-triples instance was deliberately NOT fabricated -- the generic law covers it, and the runtime VERTEX_TRIPLES IS that overlapping table.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/CubTsp021.v":"f0c1be3a6602c0a999c2682551ed6225dcfc7c169b4d93897308aab12c945e12","proofs/lean4/CubTsp021.lean":"33c28ef26755494b46796b1fd6f127bd1663b223f14b79f6737e594afa84824b","proofs/verus/cub_tsp_021.rs":"9ef1df1dfc373d57ba519d1194824357378f4e7e4b4e3a6228ef634a627cf1b1"},"files":{"coq_file":"proofs/coq/CubTsp021.v","lean_file":"proofs/lean4/CubTsp021.lean","verus_file":"proofs/verus/cub_tsp_021.rs"},"id":"CUB-TSP-021","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"FRESH first proof of upstream stub CUB-1907; concrete table = disjoint corner-band partition (overlapping cell-18 instance NOT fabricated; runtime VERTEX_TRIPLES is the overlapping table, generic law covers it; a future rev may add that instance)","proof_scope":"standalone","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"VERTEX_TRIPLES syndrome loop (cubie_evidence.rs:86-95)","source_completeness":"full (CSV-sourced)","statement":"Vertex-triple strict span + parity-toggle counting law: the generic counting law over a vertex-triple table (strict span; each toggle flips parity). FIRST SUBSTANTIVE PROOF of upstream stub CUB-1907. The concrete table proved is the DISJOINT corner-band partition; the overlapping cell-18-in-3-triples instance was deliberately NOT fabricated -- the generic law covers it, and the runtime VERTEX_TRIPLES IS that overlapping table.","status":"proven","use_cases":["QEC","TSP","topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Seam validity closure under append + reversal: a valid seam stays valid under append and under segment reversal (seam X-parity preserved). The formal twin of the reversal metamorphic fleet test.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/CubTsp022.v":"e8cf9bf306e41054cd3a698f7f67b17354b5606f162b7437621fde13c2df9ac3","proofs/lean4/CubTsp022.lean":"406ca4db50407c505b2415138c26957bb478c2cfb39f9f40297e370a917b0434","proofs/verus/cub_tsp_022.rs":"0f64032188235c455d0a4fc155112ca9139149017819b4bb28107ee40cee9382"},"files":{"coq_file":"proofs/coq/CubTsp022.v","lean_file":"proofs/lean4/CubTsp022.lean","verus_file":"proofs/verus/cub_tsp_022.rs"},"id":"CUB-TSP-022","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"mirrors CUB-1939/1940/1944; formal twin of the reversal metamorphic fleet test","proof_scope":"standalone","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"seam X-parity + measured reversal invariance","source_completeness":"full (CSV-sourced)","statement":"Seam validity closure under append + reversal: a valid seam stays valid under append and under segment reversal (seam X-parity preserved). The formal twin of the reversal metamorphic fleet test.","status":"proven","use_cases":["TDX","TSP","topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Egress mismatch detection + core-mask opacity: XOR-masking the egress boundary bits detects any boundary mismatch (zero iff boundary-equal) while the core mask stays opaque. Refines TSP-004 (the shadow-mismatch detection theorem).","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/CubTsp023.v":"ccd66326b494a2b57a6b5ab46f7799a5aaab10a00207b6ec19cdb1eb7f3e64b0","proofs/lean4/CubTsp023.lean":"824c43aadd1cff9946c316156669e1d4c812ba11ea6f0dce0b5ff9b7f1198aea","proofs/verus/cub_tsp_023.rs":"6b72f4153042783d0204a7ed8b01a38b9bb326090be511612f78214ad401af62"},"files":{"coq_file":"proofs/coq/CubTsp023.v","lean_file":"proofs/lean4/CubTsp023.lean","verus_file":"proofs/verus/cub_tsp_023.rs"},"id":"CUB-TSP-023","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"mirrors CUB-1437-1441; refines TSP-004; runtime egress_xor anchor queued (wiring #3)","proof_scope":"standalone","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"egress_xor over the 6 FACE_CENTERS on CubieTspEvidence54 (anchor to implement -- wiring queue #3)","source_completeness":"full (CSV-sourced)","statement":"Egress mismatch detection + core-mask opacity: XOR-masking the egress boundary bits detects any boundary mismatch (zero iff boundary-equal) while the core mask stays opaque. Refines TSP-004 (the shadow-mismatch detection theorem).","status":"proven","use_cases":["crypto","TSP","topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Shatter irreversibility via gcd(7,108)=1: because gcd(7,108)=1 the step-7 rotation is a generator of Z/108, so iterating it sweeps the full window with no fixed point short of a full cycle -- the shatter cannot be reversed. Verified by reflection over the full window.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/CubTsp024.v":"a663b83887eb0827b35929ae0ba8aec6b2dec77ab8c069d0d05a9dd3f9f0401e","proofs/lean4/CubTsp024.lean":"ac01bd91c1f71bc04e2821116b90be3151a5a3eac0cb327b297b60ef62be07e8","proofs/verus/cub_tsp_024.rs":"4805c1f5f98e30069daa2904b831f6a13486289608620652b124d516e840d58d"},"files":{"coq_file":"proofs/coq/CubTsp024.v","lean_file":"proofs/lean4/CubTsp024.lean","verus_file":"proofs/verus/cub_tsp_024.rs"},"id":"CUB-TSP-024","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"mirrors CUB-1819; verified reflection over the full Z/108 window","proof_scope":"standalone","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"InnerCube shatter events (semantic anchor; standalone by house style)","source_completeness":"full (CSV-sourced)","statement":"Shatter irreversibility via gcd(7,108)=1: because gcd(7,108)=1 the step-7 rotation is a generator of Z/108, so iterating it sweeps the full window with no fixed point short of a full cycle -- the shatter cannot be reversed. Verified by reflection over the full window.","status":"proven","use_cases":["TEP","crypto","TSP"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Move-trace cost reconciliation and monotonicity: final = initial + sum of deltas; an all-improving trace is non-increasing.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/CubTsp025.v":"932b8da29706c6e28be8bc2286af1907360082737fe340e51b2c50bb8f80ece0","proofs/lean4/CubTsp025.lean":"546dae893ee717cabf445b94975c526318b91220f9e717f62d88344c30861807","proofs/verus/cub_tsp_025.rs":"46b6ba7190d5026102ded5adcb5864e98765886c259d3f520d1efb2adc195d1f"},"files":{"coq_file":"proofs/coq/CubTsp025.v","lean_file":"proofs/lean4/CubTsp025.lean","verus_file":"proofs/verus/cub_tsp_025.rs"},"id":"CUB-TSP-025","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"","proof_scope":"standalone","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"ShadowCubieLog::to_jsonl; TourState::from_route","source_completeness":"full (CSV-sourced)","statement":"Move-trace cost reconciliation and monotonicity: final = initial + sum of deltas; an all-improving trace is non-increasing.","status":"proven","use_cases":["crypto","TSP"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Cube-shatter as a sound prove/disprove decider: bounded search snaps (Proven) on a witness and shatters-all (Disproven) otherwise; sound and complete.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/CubTsp026.v":"191ad94f0fc7b17210cd5ab637c91a0f2342ae04fb3f2fea4dcb71bc8794b1d0","proofs/lean4/CubTsp026.lean":"f65b680cc6fcafda0e2f3da3fed34060d93ba79eb11349f68d17514996366afc","proofs/verus/cub_tsp_026.rs":"fe7b4efbde50272c996ebd070be3ce43c0d8fca175e1abdcb3ec936de958ea1c"},"files":{"coq_file":"proofs/coq/CubTsp026.v","lean_file":"proofs/lean4/CubTsp026.lean","verus_file":"proofs/verus/cub_tsp_026.rs"},"id":"CUB-TSP-026","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"","proof_scope":"standalone","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"InnerCube snap/shatter (meta-decider)","source_completeness":"full (CSV-sourced)","statement":"Cube-shatter as a sound prove/disprove decider: bounded search snaps (Proven) on a witness and shatters-all (Disproven) otherwise; sound and complete.","status":"proven","use_cases":["crypto","TSP"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Optimality-certificate soundness: a feasible tour attaining a valid lower bound is optimal (backs the Held-Karp berlin52 result: LB 7542 == incumbent => optimal).","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/CubTsp027.v":"f857545fd7406ea635d5c3ff14db740174ce8e892e1a88ea02279b113ada7bb7","proofs/lean4/CubTsp027.lean":"c7593fb13141a9bae5a22ef35225794fdd61caf0238e3f76d736ad3be1c8035b","proofs/verus/cub_tsp_027.rs":"2a396a47bc973ab9f617c37a677de890b172f4305ec820b9268072d472da2a70"},"files":{"coq_file":"proofs/coq/CubTsp027.v","lean_file":"proofs/lean4/CubTsp027.lean","verus_file":"proofs/verus/cub_tsp_027.rs"},"id":"CUB-TSP-027","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"","proof_scope":"standalone","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"cubie_tsp_prove_optimal (Held-Karp 1-tree)","source_completeness":"full (CSV-sourced)","statement":"Optimality-certificate soundness: a feasible tour attaining a valid lower bound is optimal (backs the Held-Karp berlin52 result: LB 7542 == incumbent => optimal).","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: End-to-end optimality certificate: feasible tour + recomputed objective + valid lower bound + bound == objective => globally optimal (0 axioms in all 3 kernels).","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/CubTsp028.v":"b85d334df059adeb205bc9c903104be335a46f56aaf0976d34e8233878dd681f","proofs/lean4/CubTsp028.lean":"5afb7fa326fc5ecb27292b6f828012255208611321eccd3ae1999d2f140d4ef6","proofs/verus/cub_tsp_028.rs":"52d93863084237d682f1af59da0bfd1b896470e7f5b4b355f2f0c634b005ac92"},"files":{"coq_file":"proofs/coq/CubTsp028.v","lean_file":"proofs/lean4/CubTsp028.lean","verus_file":"proofs/verus/cub_tsp_028.rs"},"id":"CUB-TSP-028","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"","proof_scope":"standalone","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"cubie_tsp_prove_optimal / cubie_tsp_bnb","source_completeness":"full (CSV-sourced)","statement":"End-to-end optimality certificate: feasible tour + recomputed objective + valid lower bound + bound == objective => globally optimal (0 axioms in all 3 kernels).","status":"proven","use_cases":["TSP"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Branch-and-bound tree size is 2^(#edges) -- EXPONENTIAL not polynomial: size < 2^(k+1) and the full tree attains 2^(k+1)-1 (tight); the solver is NOT O(n^k) and bears nothing on P vs NP.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/CubTsp029.v":"f7c5ca6585800747e874724ee96e314613e8716a38ff46557f0d536e5aaae0b4","proofs/lean4/CubTsp029.lean":"b355f465a652a6f136606a9f9efcd846fcd2db2f9d81526031c17d98dbd77079","proofs/verus/cub_tsp_029.rs":"5f9552571302c41102542681d27d84f08f62e72b9228bfa4b4ce6d205541c94f"},"files":{"coq_file":"proofs/coq/CubTsp029.v","lean_file":"proofs/lean4/CubTsp029.lean","verus_file":"proofs/verus/cub_tsp_029.rs"},"id":"CUB-TSP-029","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"","proof_scope":"standalone","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"cubie_tsp_bnb (complexity witness)","source_completeness":"full (CSV-sourced)","statement":"Branch-and-bound tree size is 2^(#edges) -- EXPONENTIAL not polynomial: size < 2^(k+1) and the full tree attains 2^(k+1)-1 (tight); the solver is NOT O(n^k) and bears nothing on P vs NP.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Metric shortcutting: under the triangle inequality skipping an intermediate vertex never increases path cost (a pillar of the 2-approximation).","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"cubie-tsp-verifier","deployable":false,"file_shas":{"proofs/coq/CubTsp030.v":"e41475d72331c71c7eb7f7219b5b4f27bf1cbd0dff8de0f3537cee4099937dc1","proofs/lean4/CubTsp030.lean":"250717539941ab2cc86bc421cacd017325854cc707d7e567026316dd573f28da","proofs/verus/cub_tsp_030.rs":"463224ff7fb9e1670b98c96f8a0259e8dc54f72f9139f8865ecdfd788a675bb8"},"files":{"coq_file":"proofs/coq/CubTsp030.v","lean_file":"proofs/lean4/CubTsp030.lean","verus_file":"proofs/verus/cub_tsp_030.rs"},"id":"CUB-TSP-030","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"","proof_scope":"standalone","repo":"cubie-research","riscv":"no","riscv_status":"no","rust_anchor":"double_tree_tour (crates/cubie-tsp-verifier/src/double_tree.rs) -- executable discharge, wired as B&B incumbent candidate","source_completeness":"full (CSV-sourced)","statement":"Metric shortcutting: under the triangle inequality skipping an intermediate vertex never increases path cost (a pillar of the 2-approximation).","status":"proven","use_cases":["TSP","topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: MST lower bound: Cost(MST) <= Cost(optimal tour); composes with 030 to give the 2-approximation Cost(tour) <= 2*Cost(optimal).","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"cubie-tsp-verifier","deployable":false,"file_shas":{"proofs/coq/CubTsp031.v":"5c85bb750ebacab5a805515802c64f966b06582984601d09b220fa1cb4ae8c90","proofs/lean4/CubTsp031.lean":"0869930177b7d6a3a20620172e6986bd74e4d6c0ef94b8a92de1a50a3a260ba2","proofs/verus/cub_tsp_031.rs":"59601b37c6843a6e32921fd575d88e12769304cbcf1a49a5893cd06fd6cf63e4"},"files":{"coq_file":"proofs/coq/CubTsp031.v","lean_file":"proofs/lean4/CubTsp031.lean","verus_file":"proofs/verus/cub_tsp_031.rs"},"id":"CUB-TSP-031","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"","proof_scope":"standalone","repo":"cubie-research","riscv":"no","riscv_status":"no","rust_anchor":"prim_mst (crates/cubie-tsp-verifier/src/double_tree.rs) -- executable discharge; tests assert MST <= published optimum fleet-wide","source_completeness":"full (CSV-sourced)","statement":"MST lower bound: Cost(MST) <= Cost(optimal tour); composes with 030 to give the 2-approximation Cost(tour) <= 2*Cost(optimal).","status":"proven","use_cases":["TSP"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: Optimality-certificate checker (concrete schema): tour validity = permutation of 0..n-1, tour_cost = consecutive edges + closing edge over a nat->nat->nat matrix; a lower-bound witness (forall valid t, LB <= tour_cost t) attained by a valid tour certifies optimality, and any two certified tours have equal cost (LB values coincide). Discharges CUB-TSP-027's abstract tour type; backs berlin52 CERTIFIED OPTIMAL (HK LB 7542 = incumbent).","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"cubie-tsp-verifier","deployable":false,"file_shas":{"proofs/coq/CubTsp033.v":"7570fba0c8ec572b58541dbdb273507d356c35e4841b98fd0985505d25f2c224","proofs/lean4/CubTsp033.lean":"6aa3b8a790e527f7098188fb4d0e00fe3ecf56130a4fc3ec933cc36f5f30dfb9","proofs/verus/cub_tsp_033.rs":"6129ec9e1ac03a5abe457e6de945224f639b58ffcdc2af4d6757f0c0fbc8b387"},"files":{"coq_file":"proofs/coq/CubTsp033.v","lean_file":"proofs/lean4/CubTsp033.lean","verus_file":"proofs/verus/cub_tsp_033.rs"},"id":"CUB-TSP-033","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; symmetry of the matrix not needed (schema covers asymmetric TSP); CUB-TSP-032 is IP-guarded/git-excluded so 033 is the next ledgered ID","proof_scope":"standalone","repo":"cubie-research","riscv":"no","riscv_status":"no","rust_anchor":"held_karp_exact (crates/cubie-tsp-verifier/src/lib.rs) + certify step ex_ceil >= incumbent in cubie_tsp_prove_optimal (crates/cubie-tsp-verifier/src/prove_optimal.rs)","source_completeness":"full (CSV-sourced)","statement":"Optimality-certificate checker (concrete schema): tour validity = permutation of 0..n-1, tour_cost = consecutive edges + closing edge over a nat->nat->nat matrix; a lower-bound witness (forall valid t, LB <= tour_cost t) attained by a valid tour certifies optimality, and any two certified tours have equal cost (LB values coincide). Discharges CUB-TSP-027's abstract tour type; backs berlin52 CERTIFIED OPTIMAL (HK LB 7542 = incumbent).","status":"proven","use_cases":["TEP","TSP","complexity","consent"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: FLUID PLACEMENT: context-to-cell wiring on the 54-cell cube, triple-kernel. Positional semantics: cell = 9*face + position; position 4 = CENTER (arity-1 anchor), {1,3,5,7} = EDGE (arity-2, realized on one of the 12 seams), {0,2,6,8} = CORNER (arity-3, realized on one of the 8 vertex triples); standard-cube seam/vertex tables kernel-checked (perfect edge matching, corner partition). THEOREMS: grade <= total; grade = total IFF every declared anchor/pairwise/three-way interrelationship is realized (the guess->grade loop acceptance criterion); argmax search over any finite candidate set finds a complete placement whenever one exists (loop soundness). INSTANCES (Coq vm_compute + Lean decide): TSP evidence context (CUB-TSP-027/002/004/006 wiring, grade 10/10) and TEP context (CUB-1921 recursion pair, CUB-1952 h=1.5x-peak pair, CUB-1953 OR-gate pair + output triple, CUB-1954 layout pair; grade 11/11); one misplaced variable caught (grade 10/11); search recovers from a bad seed. Verus carries the full theorem family (20 verified, 0 errors); instances are Coq+Lean. Certifies the placement CALCULUS, not any solver result; capacity honest (12+8 per level, overflow stays FLUID or recurses).","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"cubie-tsp-rust-optimal","deployable":false,"file_shas":{"proofs/coq/CubTsp034.v":"5954d579d796f652ee50fd4ac1e0807cc9d9d575698af63e325680ffba038d82","proofs/lean4/CubTsp034.lean":"8e7cd744c410c9163d844f5358d1f8ef8802a78c9df62fd41a4485f5cfd00cf8","proofs/verus/cub_tsp_034.rs":"6c6b73802d372260fa30e744706107090b912e4a291c840291ffef7450a2d447"},"files":{"coq_file":"proofs/coq/CubTsp034.v","lean_file":"proofs/lean4/CubTsp034.lean","verus_file":"proofs/verus/cub_tsp_034.rs"},"id":"CUB-TSP-034","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; Print Assumptions x4 closed; Lean core decide-only (no native_decide); Verus 20 verified 0 errors; design record docs/FLUID_PLACEMENT_DESIGN_2026-07-14.md; derived Evidence54 mapping pinned in proofs/coq/CubTsp034Derived.v (10/10 from tools/derive_evidence54_mapping.py, 82 overflow edges FLUID per capacity law); runtime mirror crates/cubie-tsp-rust-optimal/src/placement.rs; arity-3 triples-first re-derivation pinned in proofs/coq/CubTsp034DerivedTriples.v (5 triples + 4 pairs, 9/9; incl. self-referential pairs 020-036 and 034-035 from the same-day wiring)","proof_scope":"standalone","repo":"cubie-research","riscv":"no","riscv_status":"no","rust_anchor":"evaluate_bindings + CubieTspEvidence54 (crates/cubie-tsp-rust-optimal/src/lib.rs)","source_completeness":"full (CSV-sourced)","statement":"FLUID PLACEMENT: context-to-cell wiring on the 54-cell cube, triple-kernel. Positional semantics: cell = 9*face + position; position 4 = CENTER (arity-1 anchor), {1,3,5,7} = EDGE (arity-2, realized on one of the 12 seams), {0,2,6,8} = CORNER (arity-3, realized on one of the 8 vertex triples); standard-cube seam/vertex tables kernel-checked (perfect edge matching, corner partition). THEOREMS: grade <= total; grade = total IFF every declared anchor/pairwise/three-way interrelationship is realized (the guess->grade loop acceptance criterion); argmax search over any finite candidate set finds a complete placement whenever one exists (loop soundness). INSTANCES (Coq vm_compute + Lean decide): TSP evidence context (CUB-TSP-027/002/004/006 wiring, grade 10/10) and TEP context (CUB-1921 recursion pair, CUB-1952 h=1.5x-peak pair, CUB-1953 OR-gate pair + output triple, CUB-1954 layout pair; grade 11/11); one misplaced variable caught (grade 10/11); search recovers from a bad seed. Verus carries the full theorem family (20 verified, 0 errors); instances are Coq+Lean. Certifies the placement CALCULUS, not any solver result; capacity honest (12+8 per level, overflow stays FLUID or recurses).","status":"proven","use_cases":["TDX","TEP","TSP","topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: CONVERGENCE of the iterated guess->grade->restart search, triple-kernel. Abstract core: for any grade g bounded by B and any step satisfying the guess->grade dichotomy (stand still or strictly improve), iteration reaches a FIXPOINT within B - g(p) rounds, hence within B rounds from any start; monotone steps never lose grade. Concrete corollary (Coq, imports CubTsp034): the placement argmax `best` satisfies the dichotomy (best_progress), completeness once reached is stable (complete_stable), iterating converges within total(ctx) rounds, and with a complete placement in the pool EVERY iterate from round 1 is complete; kernel-checked TEP instance (misplaced seed -> complete in 1 round, stable at 2). Kernel scope: Coq = core + corollary; Lean/Verus = core + self-contained non-vacuity instance.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"cubie-tsp-rust-optimal","deployable":false,"file_shas":{"proofs/coq/CubTsp035.v":"1942ae3ecb68974c0df24b0406adaed107b2c233ab19dd3a7ee8169ac9ee23b5","proofs/lean4/CubTsp035.lean":"7c5d91d240ab2014b37d84b554c05354d1129d93cc6962a9d61fbfc2dd6251ec","proofs/verus/cub_tsp_035.rs":"29489e986a442d40e4765783dacc6bca999e964f547137f7a43aeacc11f18bab"},"files":{"coq_file":"proofs/coq/CubTsp035.v","lean_file":"proofs/lean4/CubTsp035.lean","verus_file":"proofs/verus/cub_tsp_035.rs"},"id":"CUB-TSP-035","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; Print Assumptions x3 closed; Lean decide-only no sorry; Verus 6 verified 0 errors; fixpoint bound exercised in runtime test iterate_reaches_fixpoint_within_total","proof_scope":"standalone","repo":"cubie-research","riscv":"no","riscv_status":"no","rust_anchor":"placement::iterate + placement::best (crates/cubie-tsp-rust-optimal/src/placement.rs)","source_completeness":"full (CSV-sourced)","statement":"CONVERGENCE of the iterated guess->grade->restart search, triple-kernel. Abstract core: for any grade g bounded by B and any step satisfying the guess->grade dichotomy (stand still or strictly improve), iteration reaches a FIXPOINT within B - g(p) rounds, hence within B rounds from any start; monotone steps never lose grade. Concrete corollary (Coq, imports CubTsp034): the placement argmax `best` satisfies the dichotomy (best_progress), completeness once reached is stable (complete_stable), iterating converges within total(ctx) rounds, and with a complete placement in the pool EVERY iterate from round 1 is complete; kernel-checked TEP instance (misplaced seed -> complete in 1 round, stable at 2). Kernel scope: Coq = core + corollary; Lean/Verus = core + self-contained non-vacuity instance.","status":"proven","use_cases":["TEP","TSP"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: THE GAP-ANCHORED-SLACK SEAM THEOREM, triple-kernel. Over the Page recursion (nat clamp; the CUB-TSP-019/020 channel): cusum_ge says the channel dominates aggregate shortfall; silence through budget T implies collected improvement >= k*T-h. If the EXPLICIT stream premise sum<=g holds and g+h0; allowance-meeting streams remain silent. Boundary: a fire alone does not prove global/future stagnation or justify lossless early exit. Kernel numeric control g=1284,h=4,T=100 gives k=13. Live receipts instead anchor g to the exact zero-potential Held-Karp 1-tree origin, convert all quantities to Q16.16, and expose origin<=incumbent, nonzero-budget, and sum(improvements)<=g before citing the theorem.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"cubie-tsp-verifier","deployable":false,"file_shas":{"proofs/coq/CubTsp036.v":"74c0c3e7b79a6981c3762ca6cd35b9fb68714358659be6435e3051316b3ce0a0","proofs/lean4/CubTsp036.lean":"033831837f7434597652551316433a8dbead96e4e52f526999ba272aa4cb48be","proofs/verus/cub_tsp_036.rs":"6291c28bfbf0b65bb411ad0e3236b89b8d7676a97d6f1943600da21df5928276"},"files":{"coq_file":"proofs/coq/CubTsp036.v","lean_file":"proofs/lean4/CubTsp036.lean","verus_file":"proofs/verus/cub_tsp_036.rs"},"id":"CUB-TSP-036","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; Print Assumptions x4 closed; Lean decide-only no sorry; Verus 13 verified 0 errors; runtime berlin52 control g=1370 cost units = 89784320 Q16 and stream sum matches; over-bound exact certificate mutation is TAMPER","proof_scope":"standalone","repo":"cubie-research","riscv":"no","riscv_status":"no","rust_anchor":"gap_anchored_k + detect_gap_anchored_stagnation + held_karp_initial_exact_q (crates/cubie-tsp-verifier/src/lib.rs)","source_completeness":"full (CSV-sourced)","statement":"THE GAP-ANCHORED-SLACK SEAM THEOREM, triple-kernel. Over the Page recursion (nat clamp; the CUB-TSP-019/020 channel): cusum_ge says the channel dominates aggregate shortfall; silence through budget T implies collected improvement >= k*T-h. If the EXPLICIT stream premise sum<=g holds and g+h0; allowance-meeting streams remain silent. Boundary: a fire alone does not prove global/future stagnation or justify lossless early exit. Kernel numeric control g=1284,h=4,T=100 gives k=13. Live receipts instead anchor g to the exact zero-potential Held-Karp 1-tree origin, convert all quantities to Q16.16, and expose origin<=incumbent, nonzero-budget, and sum(improvements)<=g before citing the theorem.","status":"proven","use_cases":["TDX","TEP","admission","TSP","complexity","topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: EMBEDDING EXISTENCE: every context within capacity admits a complete placement, CONSTRUCTIVELY. If length anchors <= 6, length rels2 <= 12, length rels3 <= 8, and all declared metrics are distinct (NoDup), then `build ctx` -- i-th anchor to i-th center, i-th pair to i-th seam, i-th triple to i-th vertex -- satisfies complete (build ctx) ctx = true (cub_tsp_037_embedding_exists; existential corollary cub_tsp_037_placement_exists). So the fluid loop ALWAYS has a target when the context fits capacity, and CUB-TSP-035 says the search reaches it. Falsifiers: builder reproduces the kernel TEP context (11/11); an over-capacity 13-pair context genuinely fails at the 13th pair (12/13) -- the capacity wall is real. Kernel scope (honest, 035 pattern): Coq = full general theorem (anchors+pairs+triples blocks); Lean = anchors block general + decide-checked instances incl. the over-capacity falsifier; Verus = builder + anchors block general (5 verified 0 errors).","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"cubie-tsp-rust-optimal","deployable":false,"file_shas":{"proofs/coq/CubTsp037.v":"9a491f6013581657eccd829bc506223dcd2d7d54ca2655aa219034f8769ac3ae","proofs/lean4/CubTsp037.lean":"01c4fb7bc48407e4de5e1301c73a6992c610616177c030dcf92b35df6e9e1ec8","proofs/verus/cub_tsp_037.rs":"cb2fa6033be6937d088686c1d2549d1a7465eacf4f332acb7e89f68d57da107e"},"files":{"coq_file":"proofs/coq/CubTsp037.v","lean_file":"proofs/lean4/CubTsp037.lean","verus_file":"proofs/verus/cub_tsp_037.rs"},"id":"CUB-TSP-037","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; Print Assumptions x3 closed; Lean decide-only no sorry; Verus 5 verified 0 errors; capacity boundary stated (overflow stays FLUID or recurses -- Fabric layer open)","proof_scope":"standalone","repo":"cubie-research","riscv":"no","riscv_status":"no","rust_anchor":"placement::grade + placement::best consumers (crates/cubie-tsp-rust-optimal/src/placement.rs)","source_completeness":"full (CSV-sourced)","statement":"EMBEDDING EXISTENCE: every context within capacity admits a complete placement, CONSTRUCTIVELY. If length anchors <= 6, length rels2 <= 12, length rels3 <= 8, and all declared metrics are distinct (NoDup), then `build ctx` -- i-th anchor to i-th center, i-th pair to i-th seam, i-th triple to i-th vertex -- satisfies complete (build ctx) ctx = true (cub_tsp_037_embedding_exists; existential corollary cub_tsp_037_placement_exists). So the fluid loop ALWAYS has a target when the context fits capacity, and CUB-TSP-035 says the search reaches it. Falsifiers: builder reproduces the kernel TEP context (11/11); an over-capacity 13-pair context genuinely fails at the 13th pair (12/13) -- the capacity wall is real. Kernel scope (honest, 035 pattern): Coq = full general theorem (anchors+pairs+triples blocks); Lean = anchors block general + decide-checked instances incl. the over-capacity falsifier; Verus = builder + anchors block general (5 verified 0 errors).","status":"proven","use_cases":["TDX","TEP","admission","TSP","topology"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""} {"axiom_free_status":"not measured for this row","context_purpose":"DERIVED: -- registry statement: SHARDED OVERFLOW EMBEDDING (Fabric brick 1), triple-kernel. Globally occurrence-distinct pair/triple metric families of arbitrary finite cardinality embed across SHARDS. Pairs are chunked in blocks of 12 and triples in blocks of 8; cover_chunks supplies one empty coordinate for a one-sided or empty relation family, so the Cartesian shard list is never vacuous. Every shard is in-capacity and embeds via the 037 builder (cub_tsp_038_shard_embeds); every declared pair/triple has existential witnesses for an ACTUAL complete shard and is realized there (cub_tsp_038_pair/triple_realized_somewhere). The global NoDup(flattened metric soup) premise is load-bearing: shared occurrences such as (1,2),(1,3) are outside this theorem, and anchors are not modeled. The 13-pair context spans 2 shards. Kernel scope: Coq = full shard construction and realized-somewhere result; Lean/Verus = general chunk capacity + lossless reassembly; the over13 executable instance is Coq+Lean only. Honest boundary: relations do not span shards; inter-shard structure is an index, not geometry; portal cells, recursive inner cubes, runtime sharding, physical sticker legality, and global placement optimality remain open.","coq_statement_full":"","coq_verified":"not stated in registry status for this row","crate":"","deployable":false,"file_shas":{"proofs/coq/CubTsp038.v":"4e2d2f26270ccbb5000b8a0c90138d36d6680a90937069067eb61d3f52984e0c","proofs/lean4/CubTsp038.lean":"810daafa6c3e20f24d145349d9358b872bcee57f7c019610d8a06e5af280b403","proofs/verus/cub_tsp_038.rs":"03fae35ac1d9243e3f6ecce6973c315683b4ec3f6ba76ca89e25c65cf8431fce"},"files":{"coq_file":"proofs/coq/CubTsp038.v","lean_file":"proofs/lean4/CubTsp038.lean","verus_file":"proofs/verus/cub_tsp_038.rs"},"id":"CUB-TSP-038","lean_statement_full":"","lean_verified":"not stated in registry status for this row","note":"coqchk Axioms:; Print Assumptions x3 closed; Lean decide-only no sorry; Verus 6 verified 0 errors; pair-only/triple-only/empty-axis controls; shared-metric negative boundary","proof_scope":"standalone","repo":"cubie-research","riscv":"","riscv_status":"(empty -- not bound to any bare-metal exec fn/crate)","rust_anchor":"model-only; no runtime shard implementation","source_completeness":"full (CSV-sourced)","statement":"SHARDED OVERFLOW EMBEDDING (Fabric brick 1), triple-kernel. Globally occurrence-distinct pair/triple metric families of arbitrary finite cardinality embed across SHARDS. Pairs are chunked in blocks of 12 and triples in blocks of 8; cover_chunks supplies one empty coordinate for a one-sided or empty relation family, so the Cartesian shard list is never vacuous. Every shard is in-capacity and embeds via the 037 builder (cub_tsp_038_shard_embeds); every declared pair/triple has existential witnesses for an ACTUAL complete shard and is realized there (cub_tsp_038_pair/triple_realized_somewhere). The global NoDup(flattened metric soup) premise is load-bearing: shared occurrences such as (1,2),(1,3) are outside this theorem, and anchors are not modeled. The 13-pair context spans 2 shards. Kernel scope: Coq = full shard construction and realized-somewhere result; Lean/Verus = general chunk capacity + lossless reassembly; the over13 executable instance is Coq+Lean only. Honest boundary: relations do not span shards; inter-shard structure is an index, not geometry; portal cells, recursive inner cubes, runtime sharding, physical sticker legality, and global placement optimality remain open.","status":"proven","use_cases":["crypto","TSP"],"verification_state":"VERIFIED","verus_statement_full":"","verus_verified":"not stated in registry status for this row","verus_via_covers_rescue":""}