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{"axiom_profile":"","crate":"","deployable":false,"file_shas":{"coq/v1_3_DriveMathFormalization_0521.v":"31f1a158dcca755dc450c6bcf998c166f2d92e9fa6c8670025817a2e9114c6a7","lean/CubieDriveMathV1_3.lean":"fad819e16b170485ae21c6908f2ee7734aa552dda974e01c1ba64761d1ab790b"},"files":{"coq_file":"coq/v1_3_DriveMathFormalization_0521.v","lean_file":"lean/CubieDriveMathV1_3.lean"},"formal_systems":"Coq+Lean+Verus","id":"CUB-1671","invocation":"unwired","kernels":"none","kind":"Lemma","module":"CubieDriveMathV1_3","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","shas":{"coq_sha256":"31f1a158dcca755d...","lean_sha256":"fad819e16b170485..."},"statement":"Drive Math","status":"DRAFT","theorem_name":"two_pow_pos","verification_state":"NOT_VERIFIED","wiring":"ALIASED"}
{"axiom_profile":"","crate":"","deployable":false,"file_shas":{"coq/v1_3_DriveMathFormalization_0521.v":"31f1a158dcca755dc450c6bcf998c166f2d92e9fa6c8670025817a2e9114c6a7","lean/CubieDriveMathV1_3.lean":"fad819e16b170485ae21c6908f2ee7734aa552dda974e01c1ba64761d1ab790b"},"files":{"coq_file":"coq/v1_3_DriveMathFormalization_0521.v","lean_file":"lean/CubieDriveMathV1_3.lean"},"formal_systems":"Coq+Lean+Verus","id":"CUB-1672","invocation":"unwired","kernels":"none","kind":"Lemma","module":"CubieDriveMathV1_3","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","shas":{"coq_sha256":"31f1a158dcca755d...","lean_sha256":"fad819e16b170485..."},"statement":"Drive Math","status":"DRAFT","theorem_name":"n_lt_two_pow","verification_state":"NOT_VERIFIED","wiring":"ALIASED"}
{"axiom_profile":"","crate":"","deployable":false,"file_shas":{"coq/v1_3_DriveMathFormalization_0521.v":"31f1a158dcca755dc450c6bcf998c166f2d92e9fa6c8670025817a2e9114c6a7","lean/CubieDriveMathV1_3.lean":"fad819e16b170485ae21c6908f2ee7734aa552dda974e01c1ba64761d1ab790b","verus/CUB_1673_reserved_stub_spec.rs":"85bb67cbbcae90cd7a1a1abcb98d0551cfb4c2b127a55a0de281104ae7249b0d"},"files":{"coq_file":"coq/v1_3_DriveMathFormalization_0521.v","lean_file":"lean/CubieDriveMathV1_3.lean","verus_file":"verus/CUB_1673_reserved_stub_spec.rs"},"formal_systems":"Coq+Lean+Verus","id":"CUB-1673","invocation":"unwired","kernels":"VCL","kind":"Lemma","module":"CubieDriveMathV1_3","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","shas":{"coq_sha256":"31f1a158dcca755d...","lean_sha256":"fad819e16b170485..."},"statement":"Drive Math","status":"DRAFT","theorem_name":"pow_le_pow_base","verification_state":"NOT_VERIFIED","wiring":"SPEC-ONLY"}
{"crate":"cubie-wwt-gateway","deployable":false,"exec_file":"agentic-cybersecurity/cubie-wwt-gateway/src/engine.rs","file_shas":{"verus/cubie_avx2_equiv_spec.rs":"dbd85d4d8131f3ea0968f8912355084dae050359370b4039ae802b770143cad6"},"files":{"verus_file":"verus/cubie_avx2_equiv_spec.rs"},"id":"CUB-1674","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"no","use_cases":["gateway"],"wiring":"DOC-REFERENCE"}
{"crate":"cubie-platform","deployable":false,"exec_file":"cubie-platform/src/admit.rs","file_shas":{"verus/CUB_1676_admit_batch4_lane_independence_spec.rs":"52eacf3da6a34a64538a684e14c24f920ccc6ce200298dc6408b29ed66803a29"},"files":{"verus_file":"verus/CUB_1676_admit_batch4_lane_independence_spec.rs"},"id":"CUB-1676","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"yes","use_cases":["admission"],"wiring":"DOC-REFERENCE"}
{"crate":"","deployable":false,"file_shas":{"verus/cubie_topology_counting_v8_0_spec.rs":"f9479ad0ee7d6538934a4dcf51b64a598d67e1891f6273d00ac7aeac7c9ac5be"},"files":{"verus_file":"verus/cubie_topology_counting_v8_0_spec.rs"},"id":"CUB-1677","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","wiring":"SPEC-ONLY"}
{"crate":"bare-metal","deployable":false,"exec_file":"bare-metal/src/lib.rs","file_shas":{"verus/CUB_1676_admit_batch4_lane_independence_spec.rs":"52eacf3da6a34a64538a684e14c24f920ccc6ce200298dc6408b29ed66803a29"},"files":{"verus_file":"verus/CUB_1676_admit_batch4_lane_independence_spec.rs"},"id":"CUB-1678","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"no","wiring":"DOC-REFERENCE"}
{"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","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-1679","invocation":"unwired","kernels":"VCL","kind":"Theorem","module":"CubieBexarMetalV1_4Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","shas":{"coq_sha256":"b97d336c8a5e340c...","lean_sha256":"c174ee9798757916..."},"statement":"Bexar Metal","status":"Coq PENDING-COQ-KERNEL; Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"interface_count","use_cases":["topology"],"verification_state":"NOT_VERIFIED","wiring":"SPEC-ONLY"}
{"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","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","module":"CubieBexarMetalV1_4Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","shas":{"coq_sha256":"b97d336c8a5e340c...","lean_sha256":"c174ee9798757916..."},"statement":"Bexar Metal","status":"Coq PENDING-COQ-KERNEL; Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"interface_dominates","use_cases":["topology"],"verification_state":"NOT_VERIFIED","wiring":"SPEC-ONLY"}
{"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_1681_bexar_pow_le_pow_base: depends on axioms: propext; no sorryAx","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-1681","invocation":"unwired","kernels":"VCL","kind":"Theorem","module":"CubieBexarMetalV1_4Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","shas":{"coq_sha256":"b97d336c8a5e340c...","lean_sha256":"c174ee9798757916..."},"statement":"Bexar Metal","status":"Coq PENDING-COQ-KERNEL; Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"bexar_pow_le_pow_base","verification_state":"NOT_VERIFIED","wiring":"SPEC-ONLY"}
{"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","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","module":"CubieBexarMetalV1_4Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","shas":{"coq_sha256":"b97d336c8a5e340c...","lean_sha256":"c174ee9798757916..."},"statement":"Bexar Metal","status":"Coq PENDING-COQ-KERNEL; Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"witness_64_byte_atomic","verification_state":"NOT_VERIFIED","wiring":"SPEC-ONLY"}
{"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","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","module":"CubieBexarMetalV1_4Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","shas":{"coq_sha256":"b97d336c8a5e340c...","lean_sha256":"c174ee9798757916..."},"statement":"Bexar Metal","status":"Coq PENDING-COQ-KERNEL; Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"belnap_idem","verification_state":"NOT_VERIFIED","wiring":"SPEC-ONLY"}
{"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","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","module":"CubieBexarMetalV1_4Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","shas":{"coq_sha256":"b97d336c8a5e340c...","lean_sha256":"c174ee9798757916..."},"statement":"Bexar Metal","status":"Coq PENDING-COQ-KERNEL; Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"belnap_top_unit","verification_state":"NOT_VERIFIED","wiring":"SPEC-ONLY"}
{"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","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","module":"CubieBexarMetalV1_4Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","shas":{"coq_sha256":"b97d336c8a5e340c...","lean_sha256":"c174ee9798757916..."},"statement":"Bexar Metal","status":"Coq PENDING-COQ-KERNEL; Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"belnap_assoc","verification_state":"NOT_VERIFIED","wiring":"SPEC-ONLY"}
{"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","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","module":"CubieBexarMetalV1_4Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","shas":{"coq_sha256":"b97d336c8a5e340c...","lean_sha256":"c174ee9798757916..."},"statement":"Bexar Metal","status":"Coq PENDING-COQ-KERNEL; Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"vn_symmetry","verification_state":"NOT_VERIFIED","wiring":"SPEC-ONLY"}
{"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","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","module":"CubieBexarMetalV1_4Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","shas":{"coq_sha256":"b97d336c8a5e340c...","lean_sha256":"c174ee9798757916..."},"statement":"Bexar Metal","status":"Coq PENDING-COQ-KERNEL; Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"surface_spoofing_kill","use_cases":["QEC","topology"],"verification_state":"NOT_VERIFIED","wiring":"SPEC-ONLY"}
{"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","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","module":"CubieBexarMetalV1_4Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","shas":{"coq_sha256":"b97d336c8a5e340c...","lean_sha256":"c174ee9798757916..."},"statement":"Bexar Metal","status":"Coq PENDING-COQ-KERNEL; Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"seam_requires_lineage","use_cases":["TDX","topology"],"verification_state":"NOT_VERIFIED","wiring":"SPEC-ONLY"}
{"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","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","module":"CubieBexarMetalV1_4Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","shas":{"coq_sha256":"b97d336c8a5e340c...","lean_sha256":"c174ee9798757916..."},"statement":"Bexar Metal","status":"Coq PENDING-COQ-KERNEL; Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"goodput_no_overcommit","verification_state":"NOT_VERIFIED","wiring":"SPEC-ONLY"}
{"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","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","module":"CubieBexarMetalV1_4Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","shas":{"coq_sha256":"b97d336c8a5e340c...","lean_sha256":"c174ee9798757916..."},"statement":"Bexar Metal","status":"Coq PENDING-COQ-KERNEL; Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"ha_fail_closed","verification_state":"NOT_VERIFIED","wiring":"SPEC-ONLY"}
{"crate":"","deployable":false,"file_shas":{"verus/cubie_omega_master_v1_0_spec.rs":"bd9ae0eca785b63cd7f79f4513821f6609083ced3c7d66846c2293f49a707add"},"files":{"verus_file":"verus/cubie_omega_master_v1_0_spec.rs"},"id":"CUB-1691","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","wiring":"SPEC-ONLY"}
{"crate":"","deployable":false,"file_shas":{"verus/cubie_omega_master_v1_0_spec.rs":"bd9ae0eca785b63cd7f79f4513821f6609083ced3c7d66846c2293f49a707add"},"files":{"verus_file":"verus/cubie_omega_master_v1_0_spec.rs"},"id":"CUB-1692","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","wiring":"SPEC-ONLY"}
{"crate":"","deployable":false,"file_shas":{"verus/cubie_omega_master_v1_0_spec.rs":"bd9ae0eca785b63cd7f79f4513821f6609083ced3c7d66846c2293f49a707add"},"files":{"verus_file":"verus/cubie_omega_master_v1_0_spec.rs"},"id":"CUB-1693","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","wiring":"SPEC-ONLY"}
{"crate":"","deployable":false,"file_shas":{"verus/cubie_omega_master_v1_0_spec.rs":"bd9ae0eca785b63cd7f79f4513821f6609083ced3c7d66846c2293f49a707add"},"files":{"verus_file":"verus/cubie_omega_master_v1_0_spec.rs"},"id":"CUB-1694","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","wiring":"SPEC-ONLY"}
{"crate":"cubie-core","deployable":false,"exec_file":"cubie-core/src/derived_candidates.rs","file_shas":{"verus/cubie_seam_compiler_v1_1_spec.rs":"d9955a85faa060fd41211eb96baaafaab498f9f27be2cd77b855bc03b58dc3b8"},"files":{"verus_file":"verus/cubie_seam_compiler_v1_1_spec.rs"},"id":"CUB-1695","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"yes","wiring":"DOC-REFERENCE"}
{"crate":"","deployable":false,"file_shas":{"verus/cubie_seam_compiler_v1_1_spec.rs":"d9955a85faa060fd41211eb96baaafaab498f9f27be2cd77b855bc03b58dc3b8"},"files":{"verus_file":"verus/cubie_seam_compiler_v1_1_spec.rs"},"id":"CUB-1696","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","wiring":"SPEC-ONLY"}
{"crate":"","deployable":false,"file_shas":{"verus/cubie_seam_compiler_v1_1_spec.rs":"d9955a85faa060fd41211eb96baaafaab498f9f27be2cd77b855bc03b58dc3b8"},"files":{"verus_file":"verus/cubie_seam_compiler_v1_1_spec.rs"},"id":"CUB-1697","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","wiring":"SPEC-ONLY"}
{"crate":"","deployable":false,"file_shas":{"verus/cubie_seam_compiler_v1_1_spec.rs":"d9955a85faa060fd41211eb96baaafaab498f9f27be2cd77b855bc03b58dc3b8"},"files":{"verus_file":"verus/cubie_seam_compiler_v1_1_spec.rs"},"id":"CUB-1698","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","wiring":"SPEC-ONLY"}
{"crate":"","deployable":false,"file_shas":{"verus/cubie_seam_compiler_v1_1_spec.rs":"d9955a85faa060fd41211eb96baaafaab498f9f27be2cd77b855bc03b58dc3b8"},"files":{"verus_file":"verus/cubie_seam_compiler_v1_1_spec.rs"},"id":"CUB-1699","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","wiring":"SPEC-ONLY"}
{"crate":"","deployable":false,"file_shas":{"verus/cubie_seam_compiler_v1_1_spec.rs":"d9955a85faa060fd41211eb96baaafaab498f9f27be2cd77b855bc03b58dc3b8"},"files":{"verus_file":"verus/cubie_seam_compiler_v1_1_spec.rs"},"id":"CUB-1700","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","wiring":"SPEC-ONLY"}
{"crate":"","deployable":false,"file_shas":{"verus/cubie_seam_compiler_v1_1_spec.rs":"d9955a85faa060fd41211eb96baaafaab498f9f27be2cd77b855bc03b58dc3b8"},"files":{"verus_file":"verus/cubie_seam_compiler_v1_1_spec.rs"},"id":"CUB-1701","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","wiring":"SPEC-ONLY"}
{"crate":"","deployable":false,"file_shas":{"verus/cubie_seam_compiler_v1_1_spec.rs":"d9955a85faa060fd41211eb96baaafaab498f9f27be2cd77b855bc03b58dc3b8"},"files":{"verus_file":"verus/cubie_seam_compiler_v1_1_spec.rs"},"id":"CUB-1702","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","wiring":"SPEC-ONLY"}
{"crate":"","deployable":false,"file_shas":{"verus/cubie_row_closure_v1_2_spec.rs":"03bed2f7e625a426750ceacac54949cd407c1e4831e75ff12b0ae15d8b00e769"},"files":{"verus_file":"verus/cubie_row_closure_v1_2_spec.rs"},"id":"CUB-1703","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","wiring":"SPEC-ONLY"}
{"crate":"","deployable":false,"file_shas":{"verus/cubie_row_closure_v1_2_spec.rs":"03bed2f7e625a426750ceacac54949cd407c1e4831e75ff12b0ae15d8b00e769"},"files":{"verus_file":"verus/cubie_row_closure_v1_2_spec.rs"},"id":"CUB-1704","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","wiring":"SPEC-ONLY"}
{"crate":"","deployable":false,"file_shas":{"verus/cubie_row_closure_v1_2_spec.rs":"03bed2f7e625a426750ceacac54949cd407c1e4831e75ff12b0ae15d8b00e769"},"files":{"verus_file":"verus/cubie_row_closure_v1_2_spec.rs"},"id":"CUB-1705","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","wiring":"SPEC-ONLY"}
{"crate":"","deployable":false,"file_shas":{"verus/cubie_row_closure_v1_2_spec.rs":"03bed2f7e625a426750ceacac54949cd407c1e4831e75ff12b0ae15d8b00e769"},"files":{"verus_file":"verus/cubie_row_closure_v1_2_spec.rs"},"id":"CUB-1706","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","wiring":"SPEC-ONLY"}
{"crate":"","deployable":false,"file_shas":{"verus/cubie_row_closure_v1_2_spec.rs":"03bed2f7e625a426750ceacac54949cd407c1e4831e75ff12b0ae15d8b00e769"},"files":{"verus_file":"verus/cubie_row_closure_v1_2_spec.rs"},"id":"CUB-1707","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","wiring":"SPEC-ONLY"}
{"crate":"","deployable":false,"file_shas":{"verus/cubie_row_closure_v1_2_spec.rs":"03bed2f7e625a426750ceacac54949cd407c1e4831e75ff12b0ae15d8b00e769"},"files":{"verus_file":"verus/cubie_row_closure_v1_2_spec.rs"},"id":"CUB-1708","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","wiring":"SPEC-ONLY"}
{"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_1709_two_pow_pos: depends on axioms: propext; no sorryAx","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-1709","invocation":"unwired","kernels":"VCL","kind":"Theorem","module":"CubieDriveMathV1_3Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","shas":{"coq_sha256":"abc96f0177a114d7...","lean_sha256":"b3be7adc7f090b52..."},"statement":"Drive Math","status":"Coq PENDING-COQ-KERNEL; Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"two_pow_pos","verification_state":"NOT_VERIFIED","wiring":"SPEC-ONLY"}
{"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","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","module":"CubieDriveMathV1_3Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","shas":{"coq_sha256":"abc96f0177a114d7...","lean_sha256":"b3be7adc7f090b52..."},"statement":"Drive Math","status":"Coq PENDING-COQ-KERNEL; Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"n_lt_two_pow","verification_state":"NOT_VERIFIED","wiring":"SPEC-ONLY"}
{"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","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","module":"CubieDriveMathV1_3Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","shas":{"coq_sha256":"abc96f0177a114d7...","lean_sha256":"b3be7adc7f090b52..."},"statement":"Drive Math","status":"Coq PENDING-COQ-KERNEL; Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"drive_pow_le_pow_base","verification_state":"NOT_VERIFIED","wiring":"SPEC-ONLY"}
{"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","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","module":"CubieDriveMathV1_3Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","shas":{"coq_sha256":"abc96f0177a114d7...","lean_sha256":"b3be7adc7f090b52..."},"statement":"Drive Math","status":"Coq PENDING-COQ-KERNEL; Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"geometric_complexity_futility","use_cases":["complexity"],"verification_state":"NOT_VERIFIED","wiring":"SPEC-ONLY"}
{"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","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","module":"CubieDriveMathV1_3Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","shas":{"coq_sha256":"abc96f0177a114d7...","lean_sha256":"b3be7adc7f090b52..."},"statement":"Drive Math","status":"Coq PENDING-COQ-KERNEL; Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"hypercontraction_decay","verification_state":"NOT_VERIFIED","wiring":"SPEC-ONLY"}
{"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","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","module":"CubieDriveMathV1_3Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","shas":{"coq_sha256":"abc96f0177a114d7...","lean_sha256":"b3be7adc7f090b52..."},"statement":"Drive Math","status":"Coq PENDING-COQ-KERNEL; Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"fano_error_lower_bound","verification_state":"NOT_VERIFIED","wiring":"SPEC-ONLY"}
{"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","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","module":"CubieDriveMathV1_3Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","shas":{"coq_sha256":"abc96f0177a114d7...","lean_sha256":"b3be7adc7f090b52..."},"statement":"Drive Math","status":"Coq PENDING-COQ-KERNEL; Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"kl_zero_leak_no_advantage","verification_state":"NOT_VERIFIED","wiring":"SPEC-ONLY"}
{"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 axioms; no sorryAx","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-1716","invocation":"unwired","kernels":"VCL","kind":"Theorem","module":"CubieDriveMathV1_3Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","shas":{"coq_sha256":"abc96f0177a114d7...","lean_sha256":"b3be7adc7f090b52..."},"statement":"Drive Math","status":"Coq PENDING-COQ-KERNEL; Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"topological_entropy_exponential","verification_state":"NOT_VERIFIED","wiring":"SPEC-ONLY"}
{"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_1717_power_law_monotone: does not depend on any axioms; no sorryAx","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-1717","invocation":"unwired","kernels":"VCL","kind":"Theorem","module":"CubieDriveMathV1_3Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","shas":{"coq_sha256":"abc96f0177a114d7...","lean_sha256":"b3be7adc7f090b52..."},"statement":"Drive Math","status":"Coq PENDING-COQ-KERNEL; Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"power_law_monotone","verification_state":"NOT_VERIFIED","wiring":"SPEC-ONLY"}
{"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_1718_holevo_accessible_bounded: does not depend on any axioms; no sorryAx","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-1718","invocation":"unwired","kernels":"VCL","kind":"Theorem","module":"CubieDriveMathV1_3Omega","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","shas":{"coq_sha256":"abc96f0177a114d7...","lean_sha256":"b3be7adc7f090b52..."},"statement":"Drive Math","status":"Coq PENDING-COQ-KERNEL; Verus PENDING-VERUS-KERNEL; Lean kernel-checked 4.30.0","theorem_name":"holevo_accessible_bounded","verification_state":"NOT_VERIFIED","wiring":"SPEC-ONLY"}
{"crate":"","deployable":false,"file_shas":{"verus/cubie_admission_v1_6_spec.rs":"4b6062ac28e5c914a1ca121eaa9f9bfe76d06cf0cbcf08dc759cd8887e306987"},"files":{"verus_file":"verus/cubie_admission_v1_6_spec.rs"},"id":"CUB-1719","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","wiring":"SPEC-ONLY"}
{"crate":"","deployable":false,"file_shas":{"verus/cubie_admission_v1_6_spec.rs":"4b6062ac28e5c914a1ca121eaa9f9bfe76d06cf0cbcf08dc759cd8887e306987"},"files":{"verus_file":"verus/cubie_admission_v1_6_spec.rs"},"id":"CUB-1720","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","wiring":"SPEC-ONLY"}
{"crate":"","deployable":false,"file_shas":{"verus/cubie_admission_v1_6_spec.rs":"4b6062ac28e5c914a1ca121eaa9f9bfe76d06cf0cbcf08dc759cd8887e306987"},"files":{"verus_file":"verus/cubie_admission_v1_6_spec.rs"},"id":"CUB-1721","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","wiring":"SPEC-ONLY"}
{"crate":"","deployable":false,"file_shas":{"verus/cubie_admission_v1_6_spec.rs":"4b6062ac28e5c914a1ca121eaa9f9bfe76d06cf0cbcf08dc759cd8887e306987"},"files":{"verus_file":"verus/cubie_admission_v1_6_spec.rs"},"id":"CUB-1722","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","wiring":"SPEC-ONLY"}
{"crate":"","deployable":false,"file_shas":{"verus/cubie_admission_v1_6_spec.rs":"4b6062ac28e5c914a1ca121eaa9f9bfe76d06cf0cbcf08dc759cd8887e306987"},"files":{"verus_file":"verus/cubie_admission_v1_6_spec.rs"},"id":"CUB-1723","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","wiring":"SPEC-ONLY"}
{"crate":"","deployable":false,"file_shas":{"verus/cubie_admission_v1_6_spec.rs":"4b6062ac28e5c914a1ca121eaa9f9bfe76d06cf0cbcf08dc759cd8887e306987"},"files":{"verus_file":"verus/cubie_admission_v1_6_spec.rs"},"id":"CUB-1724","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","wiring":"SPEC-ONLY"}
{"crate":"","deployable":false,"file_shas":{"verus/cubie_admission_v1_6_spec.rs":"4b6062ac28e5c914a1ca121eaa9f9bfe76d06cf0cbcf08dc759cd8887e306987"},"files":{"verus_file":"verus/cubie_admission_v1_6_spec.rs"},"id":"CUB-1725","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","wiring":"SPEC-ONLY"}
{"crate":"","deployable":false,"file_shas":{"verus/cubie_admission_v1_6_spec.rs":"4b6062ac28e5c914a1ca121eaa9f9bfe76d06cf0cbcf08dc759cd8887e306987"},"files":{"verus_file":"verus/cubie_admission_v1_6_spec.rs"},"id":"CUB-1726","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","wiring":"SPEC-ONLY"}
{"crate":"","deployable":false,"file_shas":{"verus/CUB_1727_belnap_avx2_lowering_real_spec.rs":"1f64e5c0b3f5d36da84b3367ad09769b2503e7479c603ed5ff4ea8ac54e42378"},"files":{"verus_file":"verus/CUB_1727_belnap_avx2_lowering_real_spec.rs"},"id":"CUB-1727","invocation":"unwired","kernels":"VCL","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","proof_scope":"standalone","repo":"cubie-tf","riscv":"","wiring":"SPEC-ONLY"}
{"crate":"cubie-core","deployable":true,"exec_file":"cubie-core/src/parity_wiring.rs","exec_fn":"cub_1728_parity_popcnt_witness","exec_fns":["cub_1728_parity_popcnt_witness"],"file_shas":{"verus/CUB_1728_parity_pmovmskb_popcnt_real_spec.rs":"7a4c768db7ccbc6b12074e3d712c5a175c4ddd45644cb2271781c9ebba50d701"},"files":{"verus_file":"verus/CUB_1728_parity_pmovmskb_popcnt_real_spec.rs"},"id":"CUB-1728","invocation":"runtime","kernels":"VCL","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","proof_scope":"standalone","repo":"cubie-tf","riscv":"yes","wiring":"FUNCTION-IMPL"}
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{"axiom_profile":"none","crate":"cubie-wwt-gateway","deployable":false,"exec_file":"agentic-cybersecurity/cubie-wwt-gateway/src/theorem_runtime.rs","exec_fn":"independently_verify_settlement","exec_fns":["independently_verify_settlement"],"files":{},"formal_systems":"RuntimeProperty","id":"CUB-3258","invocation":"runtime","kernels":"none","kind":"Theorem","module":"ExecutionSettlementV2IndependentVerify","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","repo":"cubie-tf","riscv":"no","shas":{"coq_sha256":"pending","lean_sha256":"pending"},"statement":"Independent V2 verification recomputes the receipt link and rejects legacy schema/domain bytes plus tamper/replay/stale independent receipt or settlement epochs","status":"IN_PROGRESS","theorem_name":"independently_verify_settlement","use_cases":["gateway"],"verification_state":"NOT_VERIFIED","wiring":"DOC-REFERENCE"}
{"axiom_profile":"none","crate":"cubie-wwt-gateway","deployable":false,"exec_file":"agentic-cybersecurity/cubie-wwt-gateway/src/native_control_plane/logical_work_container_v2.rs","exec_fn":"from_v1_projection","exec_fns":["from_v1_projection"],"files":{},"formal_systems":"RuntimeProperty","id":"CUB-3259","invocation":"runtime","kernels":"none","kind":"Theorem","module":"LogicalWorkContainerV2Immutable","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","repo":"cubie-tf","riscv":"no","shas":{"coq_sha256":"pending","lean_sha256":"pending"},"statement":"LogicalWorkContainerV2 is immutable and excludes route/capacity grant refs","status":"IN_PROGRESS","theorem_name":"logical_work_container_v2","use_cases":["gateway"],"verification_state":"NOT_VERIFIED","wiring":"DOC-REFERENCE"}
{"axiom_profile":"none","crate":"cubie-wwt-gateway","deployable":false,"exec_file":"agentic-cybersecurity/cubie-wwt-gateway/src/native_control_plane/capacity_observations.rs","exec_fn":"unavailable","exec_fns":["unavailable"],"files":{},"formal_systems":"RuntimeProperty","id":"CUB-3260","invocation":"runtime","kernels":"none","kind":"Theorem","module":"AuthenticatedCapacityObservationV1","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","repo":"cubie-tf","riscv":"no","shas":{"coq_sha256":"pending","lean_sha256":"pending"},"statement":"Normalized capacity observations never invent absent measurements","status":"IN_PROGRESS","theorem_name":"capacity_observations","use_cases":["gateway"],"verification_state":"NOT_VERIFIED","wiring":"DOC-REFERENCE"}
{"axiom_profile":"none","crate":"cubie-wwt-gateway","deployable":false,"exec_file":"agentic-cybersecurity/cubie-wwt-gateway/src/native_control_plane/capacity_grant_v1.rs","exec_fn":"forecast_unavailable","exec_fns":["forecast_unavailable"],"files":{},"formal_systems":"RuntimeProperty","id":"CUB-3261","invocation":"runtime","kernels":"none","kind":"Theorem","module":"CapacityGrantV1ReceiverLease","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","repo":"cubie-tf","riscv":"no","shas":{"coq_sha256":"pending","lean_sha256":"pending"},"statement":"Forecast vs Granted vs Unavailable; HMAC shared-key; Forecast is not a receiver grant; capacity signals never security deny","status":"IN_PROGRESS","theorem_name":"capacity_grant_v1","use_cases":["crypto","gateway"],"verification_state":"NOT_VERIFIED","wiring":"DOC-REFERENCE"}
{"axiom_profile":"none","crate":"cubie-wwt-gateway","deployable":false,"exec_file":"agentic-cybersecurity/cubie-wwt-gateway/src/native_control_plane/virtual_queue.rs","exec_fn":"track_inflight","exec_fns":["observe","snapshot","track_inflight"],"files":{},"formal_systems":"RuntimeProperty","id":"CUB-3262","invocation":"runtime","kernels":"none","kind":"Theorem","module":"BoundedPhaseVirtualQueues","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","repo":"cubie-tf","riscv":"no","shas":{"coq_sha256":"pending","lean_sha256":"pending"},"statement":"Sharded prefill/decode/colocated queues with idle reclaim; schedule recommendation actuator off in Shadow","status":"IN_PROGRESS","theorem_name":"virtual_queue_phase","use_cases":["crypto","gateway"],"verification_state":"NOT_VERIFIED","wiring":"DOC-REFERENCE"}
{"axiom_profile":"none","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","module":"RoutePlanV1WouldRoute","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","repo":"cubie-tf","riscv":"no","shas":{"coq_sha256":"pending","lean_sha256":"pending"},"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","wiring":"DOC-REFERENCE"}
{"axiom_profile":"none","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","module":"ClosedLoopBackpressureNotices","no_holes":true,"production_consumption":"EXECUTABLE-RUNTIME","repo":"cubie-tf","riscv":"no","shas":{"coq_sha256":"pending","lean_sha256":"pending"},"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","wiring":"DOC-REFERENCE"}
{"axiom_profile":"0 axioms","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","module":"CubieArityMeet","no_holes":true,"production_consumption":"NOT-RUNTIME-CONSUMED","repo":"cubie-tf","riscv":"","shas":{"coq_sha256":"5deb8ed249f81a3f...","lean_sha256":"3c5be4f8f07ef14f..."},"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","wiring":"CSV-LEGACY"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityCore.v":"00c41e1b499c97ac38931797c7c63bb3cae3e24e09c4b7fc3409884b4f6ae1a9"},"files":{"coq_file":"proofs/coq/ComplexityCore.v"},"id":"CUB-COMPLEXITY-001","note":"","repo":"cubie-research","riscv":"","rust_anchor":"","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityTspLanguage.v":"e73ede21ff4f78be3db4c072381b2d91f86a95be47c78c7bbefc746443d9ec73"},"files":{"coq_file":"proofs/coq/ComplexityTspLanguage.v"},"id":"CUB-COMPLEXITY-002","note":"","repo":"cubie-research","riscv":"","rust_anchor":"","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"}
{"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","note":"verified-checker","proof_scope":"standalone","repo":"cubie-research","riscv":"","rust_anchor":"verify_satisficing_witness","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityReductions.v":"4a137b28fa9992d113c488a4d63dd9b135942fcbc7b0eb820175be6162bb6763"},"files":{"coq_file":"proofs/coq/ComplexityReductions.v"},"id":"CUB-COMPLEXITY-003","note":"canonical contract repair; canonical_poly_reduces_is_strict is reflexive; no semantic erasure bridge","repo":"cubie-research","riscv":"","rust_anchor":"","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/Complexity3SatLanguage.v":"3a8ae31ac86fb28fbb9c5c21387bf64acfcf889fa52b1e29cb2dcb172b73fb32"},"files":{"coq_file":"proofs/coq/Complexity3SatLanguage.v"},"id":"CUB-COMPLEXITY-004","note":"","repo":"cubie-research","riscv":"","rust_anchor":"","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityNpComplete.v":"c0c757b93c4ec7b78b0db61332ffbda5f154c89361e05eaa30fb152f523a9e7e"},"files":{"coq_file":"proofs/coq/ComplexityNpComplete.v"},"id":"CUB-COMPLEXITY-005","note":"open-obligation","repo":"cubie-research","riscv":"","rust_anchor":"","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityBoundary.v":"186e58d0b1e6978f6b4c0455589d5ade16a8b6ec06d974950c5dcb2088b8d56c"},"files":{"coq_file":"proofs/coq/ComplexityBoundary.v"},"id":"CUB-COMPLEXITY-BOUNDARY","note":"boundary-lemma","repo":"cubie-research","riscv":"","rust_anchor":"","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityDhcLanguage.v":"979a6259bdaca52712201eaf27a2e7d81f1414a6f65ee1d5422dc64242353598"},"files":{"coq_file":"proofs/coq/ComplexityDhcLanguage.v"},"id":"CUB-COMPLEXITY-DHC","note":"","repo":"cubie-research","riscv":"","rust_anchor":"","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityDhcToUhc.v":"927d5e9e9892099a70023bd26fae5816c9bedd95404518b5cda7e310e5973bb2"},"files":{"coq_file":"proofs/coq/ComplexityDhcToUhc.v"},"id":"CUB-COMPLEXITY-DHC-UHC","note":"","repo":"cubie-research","riscv":"","rust_anchor":"dhc_to_uhc_correct (forward+backward)","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityGenericReduction.v":"ba7432601bf84aa9bd2603ac9c963e6ac30a682006f20b3f993bf132c5562c7b"},"files":{"coq_file":"proofs/coq/ComplexityGenericReduction.v"},"id":"CUB-COMPLEXITY-GENERIC-REDUCTION","note":"many-one-level","repo":"cubie-research","riscv":"","rust_anchor":"many_one_trans + tsp_nphard_via_many_one","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: <none>.","status":"proven","use_cases":["admission","TSP","complexity"],"verification_state":"VERIFIED"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityKarpChain.v":"abe9aaa192f9d156faf285381141aa9980346e1a5f2387b55baa03942b5609c7"},"files":{"coq_file":"proofs/coq/ComplexityKarpChain.v"},"id":"CUB-COMPLEXITY-KARP-CHAIN","note":"instance chain closed in this module; canonical poly_reduces close is phase4_poly_reduces in proofs/coq/ComplexityStrictEncodeTsp.v","repo":"cubie-research","riscv":"","rust_anchor":"karp_chain_solvability_closed + threesat_to_dhc_reduction + word_reduce_correct","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityManyOneInstance.v":"d5d686fb30b3e7ecc1d9bc60e0d546ab01273b02be539ece6256d8e783605dc6"},"files":{"coq_file":"proofs/coq/ComplexityManyOneInstance.v"},"id":"CUB-COMPLEXITY-MANY-ONE-INSTANCE","note":"many-one-level","repo":"cubie-research","riscv":"","rust_anchor":"many_one_3sat_tsp + tsp_nphard_via_many_one_concrete","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: <none>.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityProofSystem.v":"4711afe41a7925574f9cbb1a06d29292e07dc1a200e7e66b4274cdd4fb05edac"},"files":{"coq_file":"proofs/coq/ComplexityProofSystem.v"},"id":"CUB-COMPLEXITY-PROOFSYS","note":"infrastructure","repo":"cubie-research","riscv":"","rust_anchor":"","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityProofSystemHaken1.v":"1dad280668fab6e2a526e1961d4dffb9fc07eed111ba8aff8d182ac4a575691d"},"files":{"coq_file":"proofs/coq/ComplexityProofSystemHaken1.v"},"id":"CUB-COMPLEXITY-PROOFSYS-HAKEN1","note":"coqchk Axioms:<none>; 34 Qed; coq-only proof-complexity corpus, no Lean/Verus mirror","repo":"cubie-research","riscv":"","rust_anchor":"php_unsatisfiable + php_refutation_contains_every_axiom + php_resolution_cubic_lower_bound + php1_refutation_min_size","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityProofSystemHaken2a.v":"5d4ec79367fc72b80f0d6aeef85ba9f031258f3061f1ef65b5bdf44631931003"},"files":{"coq_file":"proofs/coq/ComplexityProofSystemHaken2a.v"},"id":"CUB-COMPLEXITY-PROOFSYS-HAKEN2A","note":"coqchk Axioms:<none>; coq-only proof-complexity corpus","repo":"cubie-research","riscv":"","rust_anchor":"pmatching + pm_assign + entails_m + hole_axioms_entailed","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityProofSystemHaken2b.v":"fa6b06aa4aaec40b6aa9c48007f824e94824b948f1d1af6a3d2e123168203628"},"files":{"coq_file":"proofs/coq/ComplexityProofSystemHaken2b.v"},"id":"CUB-COMPLEXITY-PROOFSYS-HAKEN2B","note":"coqchk Axioms:<none>; coq-only proof-complexity corpus","repo":"cubie-research","riscv":"","rust_anchor":"covers + mu_at_most + mu_subadditive + mu_empty_clause_hard","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityProofSystemHaken2c.v":"44c3b24f7afd2d7ff3ba661644e358ecee3326f1cea2c00d8ad6564540c0dda1"},"files":{"coq_file":"proofs/coq/ComplexityProofSystemHaken2c.v"},"id":"CUB-COMPLEXITY-PROOFSYS-HAKEN2C","note":"coqchk Axioms:<none>; coq-only proof-complexity corpus","repo":"cubie-research","riscv":"","rust_anchor":"covers_b_iff + mu_at_most_b_iff + mu_at_most_dec","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityProofSystemHaken2d.v":"e2ca9c15efafaedd4355134f3586f58969a68e988aa2a4bd808709d7f5812f5d"},"files":{"coq_file":"proofs/coq/ComplexityProofSystemHaken2d.v"},"id":"CUB-COMPLEXITY-PROOFSYS-HAKEN2D","note":"coqchk Axioms:<none>; coq-only proof-complexity corpus","repo":"cubie-research","riscv":"","rust_anchor":"ivt_medium_mu + derivation_first_failure + mu_at_most_mono_k","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityProofSystemHaken2e.v":"db0a9a02aba0e5cb36d6b66f78f24938191befca010b7cadc60e555341e45aaf"},"files":{"coq_file":"proofs/coq/ComplexityProofSystemHaken2e.v"},"id":"CUB-COMPLEXITY-PROOFSYS-HAKEN2E","note":"coqchk Axioms:<none>; coq-only proof-complexity corpus; 351 lines","repo":"cubie-research","riscv":"","rust_anchor":"php_width_lower_bound + minimize_cover + swap_flip_literal","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictBudget.v":"95fbaf90dab398d455969c5d123d5507ff59b3611352fa8349239a554ecadfa3"},"files":{"coq_file":"proofs/coq/ComplexityStrictBudget.v"},"id":"CUB-COMPLEXITY-STRICT-BUDGET","note":"coqchk Axioms:<none>; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","rust_anchor":"s_phase4_from_stage_machines + stm_seq_clean_computes_poly + stm_seq_clean_preserves_poly + s_bounded_halt_has_first","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictCeilHalve.v":"bf9840cea33ab32205c69066b0db7ff085d21177f6c24561fbc4a812fd8dd16a"},"files":{"coq_file":"proofs/coq/ComplexityStrictCeilHalve.v"},"id":"CUB-COMPLEXITY-STRICT-CEIL-HALVE","note":"coqchk Axioms:<none>; wrong-halving and missing-successor Fail controls included","repo":"cubie-research","riscv":"","rust_anchor":"s_ceilhalve_run + ch_total_fuel_quadratic + s_ceilhalve_clean_pad","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictCell.v":"7d345ff6c267d7d0694f5458c1906e67435cc0c8e850e4371ef52cbdf1d8d69c"},"files":{"coq_file":"proofs/coq/ComplexityStrictCell.v"},"id":"CUB-COMPLEXITY-STRICT-CELL","note":"coqchk Axioms:<none>; 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":"","rust_anchor":"word_reduce_bit_form + s_encode_tsp_computes_bit_form + strict_cell_premise + strict_cell_residual_closed + strict_cell_residual_closed_canonical","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictClauseClean.v":"5f6c0568cc4994435dbd9215d61f1fb1ff173658d71150864ae833077ced202c"},"files":{"coq_file":"proofs/coq/ComplexityStrictClauseClean.v"},"id":"CUB-COMPLEXITY-STRICT-CLAUSE-CLEAN","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk Axioms:<none>; 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":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictClauseCount.v":"5176a3d74b81ba6818317816e161b64255b2b5de4c98f02b1df34e5579f857e6"},"files":{"coq_file":"proofs/coq/ComplexityStrictClauseCount.v"},"id":"CUB-COMPLEXITY-STRICT-CLAUSE-COUNT","note":"coqchk Axioms:<none>; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","rust_anchor":"clause_counter_counts_clauses + num_clauses_parse","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictClauseDefault.v":"a5d4a7eb4bcc14feb94fcbc8e0bbec2ea3f9be91371e6cc9529e028b0f77b495"},"files":{"coq_file":"proofs/coq/ComplexityStrictClauseDefault.v"},"id":"CUB-COMPLEXITY-STRICT-CLAUSE-DEFAULT","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":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictClauseFrame.v":"e3a5fb8257902ab86ca47c0d85907bda22ad7b5e5eeab761e8503fcfa446937f"},"files":{"coq_file":"proofs/coq/ComplexityStrictClauseFrame.v"},"id":"CUB-COMPLEXITY-STRICT-CLAUSE-FRAME","note":"coqchk Axioms:<none>; 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":"","rust_anchor":"s_clauseframe_raw_clean_pad + s_clauseframe_clean_pad + sat_parameter_frame_parse + sat_parameter_fields_exact","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictClauseNormalize.v":"8d3a02273eb83f80e4be2979fe9fae0df54da6c137f2346a0e915fc5165033b8"},"files":{"coq_file":"proofs/coq/ComplexityStrictClauseNormalize.v"},"id":"CUB-COMPLEXITY-STRICT-CLAUSE-NORMALIZE","note":"coqchk Axioms:<none>; Route B total normalizer; negative mutation control included","repo":"cubie-research","riscv":"","rust_anchor":"normalize_mod3_correct + s_clause_normalize_clean_pad","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictClauseQuery.v":"868f73287485dbc6d6792a809fd166182ecf7445f6be0315af8eb6b0283aa46b"},"files":{"coq_file":"proofs/coq/ComplexityStrictClauseQuery.v"},"id":"CUB-COMPLEXITY-STRICT-CLAUSE-QUERY","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":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictClauseQueryAll.v":"3d22b6e08ce4dc9ebdfff5204853d02904b52bed0b0422cc55b6d1b3d1630035"},"files":{"coq_file":"proofs/coq/ComplexityStrictClauseQueryAll.v"},"id":"CUB-COMPLEXITY-STRICT-CLAUSE-QUERY-ALL","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":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictClauseQueryNext.v":"369b40419625876ac3a7f9bd5b9bd353a2c87bda49a728cf8260367514f08485"},"files":{"coq_file":"proofs/coq/ComplexityStrictClauseQueryNext.v"},"id":"CUB-COMPLEXITY-STRICT-CLAUSE-QUERY-NEXT","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":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictClauseRange.v":"44dc70504faf6700b75d909297a40a1611f90888f7b5c70612be9ca04253d482"},"files":{"coq_file":"proofs/coq/ComplexityStrictClauseRange.v"},"id":"CUB-COMPLEXITY-STRICT-CLAUSE-RANGE","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":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictClauseReframe.v":"0713666924060c3ae7a2de9ad23c6169cdac0d9e359933863bb3bec0cc7032cf"},"files":{"coq_file":"proofs/coq/ComplexityStrictClauseReframe.v"},"id":"CUB-COMPLEXITY-STRICT-CLAUSE-REFRAME","note":"Print Assumptions Closed; pinned Coq compile; exact physical reframe and selector-ready handoff; in-range internal-layout brick","repo":"cubie-research","riscv":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictClauseRouter.v":"4151cd987c1402d58fdd39de880da9c1d5ecf543b6778ec52ed4d855364435ab"},"files":{"coq_file":"proofs/coq/ComplexityStrictClauseRouter.v"},"id":"CUB-COMPLEXITY-STRICT-CLAUSE-ROUTER","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk; exact 233-state physical router and 252-state total raw product; 69*span^2 least-halt bound; clean-pad interface remains open","repo":"cubie-research","riscv":"","rust_anchor":"s_clause_query_router_raw_state_bound + s_clause_query_router_raw_well_formed + sat_clause_query_router_true_rewind_exact + sat_clause_query_router_false_rewind_exact + sat_clause_query_router_true_first_halt_span + sat_clause_query_router_false_first_halt_span + sat_clause_query_router_literal_table_first_halt_span + s_sat_literal_table_raw_state_bound + s_sat_literal_table_raw_well_formed + sat_literal_table_raw_first_halt_span","statement":"Total parser-faithful raw serialized-literal-table machine. The 19-state range marker writes the physical Boolean j<num_clauses(parse_3sat w). The well-formed 233-state router reads only that tape marker, erases it to Blank, physically rewinds across the complete preserved sat_N_frame to its explicit Blank sentinel, and dispatches through disjoint finite slices: states [3,215) execute the existing 212-state in-range three-literal query and states [215,233) execute the existing 18-state parser-default cycle; malformed Blank marker starts halt closed. The well-formed 252-state s_sat_literal_table_raw composes marker and router for every w, unary i and j, polarity, incoming accumulator, and arbitrary base. Its first halt is bounded by 69*(clause_seek_span w i j)^2 and returns the exact selector-ready layout with accumulator acc OR serialized_literal_table(sat_N_frame w,i,j,pos), with no clause-range or delimiter premise. Executable and Fail Example controls cover both branches, empty/partial/complete formulas, greater out-of-range indices, sticky accumulation, polarity, arbitrary nonempty base, one-step-early nonhalting, malformed markers, wrong output, and wrong branch. This closes only the total RAW internal-layout stage; canonical clean padding, finite karp_edge, grid emission, encode_tsp, and the strict reduction capstone remain OPEN.","status":"proven","use_cases":["TEP","TSP","complexity","topology"],"verification_state":"VERIFIED"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictClauseSeekSat.v":"c4a76bea12d7e6aeae068d22dc5e570fb5d47de01c424d219403ed7e20891700"},"files":{"coq_file":"proofs/coq/ComplexityStrictClauseSeekSat.v"},"id":"CUB-COMPLEXITY-STRICT-CLAUSE-SEEK","note":"Print Assumptions Closed; targeted pinned Coq compile; default tally 1 parity control; selector is not a total literal-table transducer","repo":"cubie-research","riscv":"","rust_anchor":"s_clause_seek_raw_state_bound + s_clause_seek_raw_well_formed + ci_full_exact_run + ci_full_safe_run + sat_clause_seek_safe_first_halt_strict_cubic + ci_done_literal_init + sat_target_clause_or + sat_N_literal_table_out_of_range","statement":"IN-RANGE preservation-safe serialized clause selector and literal-query handoff. The 22-state s_clause_seek_raw is finite and well formed; ci_full_exact_run and ci_full_safe_run move across an explicit clause prefix, restore every skipped clause and query field, and halt with the target first tally under the head. SAT-frame glue proves a least halt within 424*|w|^3+424 when i and j are in range, identifies the selected three-tally OR with serialized_literal_table, and proves that resetting the halt state yields the existing 39-state slm_init_cfg with identical tapes. The parser's out-of-range value and positive-x0 default representation are pinned as pure semantics. The in-range three-tally product is closed separately; the total out-of-range branch, clean padding, karp_edge, grid, encode_tsp, and strict capstone remain OPEN.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictClauseSkip.v":"5348b334661091b145528e2a1f8ff178b82c6098b776c85b18ec9c4ceb9c3964"},"files":{"coq_file":"proofs/coq/ComplexityStrictClauseSkip.v"},"id":"CUB-COMPLEXITY-STRICT-CLAUSE-SKIP","note":"Print Assumptions Closed; targeted pinned Coq compile; exact delimiter crossings; in-range three-query product closed separately","repo":"cubie-research","riscv":"","rust_anchor":"s_tally_skip_raw_state_bound + s_tally_skip_raw_well_formed + tally_skip_exact_run + tally_skip_first_halt + s_tally_skip_two_raw_state_bound + s_tally_skip_two_raw_well_formed + tally_skip_two_exact_run + tally_skip_two_first_halt + sat_clause_seek_skip_to_second_query_reentry + sat_clause_seek_skip_to_third_query_reentry + sat_clause_skip_two_fuel_le_span","statement":"Preservation-safe clause-tally adapters. The well-formed 2-state s_tally_skip_raw scans one unary tally, crosses exactly one Bit-false delimiter, preserves every tape cell, and halts on the next tally in exactly k+1 steps. The well-formed 3-state s_tally_skip_two_raw directly crosses the first two delimiters after fresh reselection and lands on tally three in exactly (a+1)+(b+1) steps. Both have least-halt/no-early witnesses; resetting their halt states gives the exact existing literal-query starts. SAT specializations connect an in-range selector halt to either the second- or third-query start, and the two-skip fuel is bounded by clause_seek_span. Empty/nonempty controls and intentionally false over/under-skip results are checked. The complete in-range selector/query/reframe product is closed separately; the total out-of-range branch, clean padding, karp_edge, grid emission, encode_tsp, and strict capstone remain OPEN.","status":"proven","use_cases":["TEP","TSP","complexity"],"verification_state":"VERIFIED"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictCopy.v":"35bcc94ff0ab2f6efe7c50fe42a6761d0ba18ec105cc8c9c11f900ca9aa66fdf"},"files":{"coq_file":"proofs/coq/ComplexityStrictCopy.v"},"id":"CUB-COMPLEXITY-STRICT-COPY","note":"iter-emit-handoff","repo":"cubie-research","riscv":"","rust_anchor":"s_copy_run + s_copy_extract","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: <none>.","status":"proven","use_cases":["crypto","complexity"],"verification_state":"VERIFIED"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictDiv3.v":"73f3589dc8d3b5f0720270c3ce937c2609e458bd0a7c8c9262d308710f60fcea"},"files":{"coq_file":"proofs/coq/ComplexityStrictDiv3.v"},"id":"CUB-COMPLEXITY-STRICT-DIV3","note":"coqchk Axioms:<none>; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","rust_anchor":"s_div3_computes + clause_counter_computes","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeArithmetic.v":"f52dcaa9b075f106650ca0489191f572d29c40fd0d6b6aa449d1703c5e3ebde2"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeArithmetic.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-ARITHMETIC","note":"Print Assumptions Closed; division/modulo eliminated from the machine-facing evaluator; pure semantic bridge only","repo":"cubie-research","riscv":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeCompareCall.v":"63836e2efd02cd27907116a5c40f5ecf5c2d9ec91c0e4d49c3884365d7f9b333"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeCompareCall.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-COMPARE-CALL","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":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeCompareCleanup.v":"f2eaeabfd5d1defff18c2c7b02823ebad509973b6a6d59be4c6e26ba9d274acc"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeCompareCleanup.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-COMPARE-CLEANUP","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk; exact 12 states; physical marker dispatch and malformed refusal","repo":"cubie-research","riscv":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeCompareRecycle.v":"79a8fd8a845358c3669727478830dbca1840d7e83b80d1088ef24fa1e6d688a3"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeCompareRecycle.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-COMPARE-RECYCLE","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk; exact 10-state physical recycling; arbitrary base/header/meta preserved","repo":"cubie-research","riscv":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeEncoding.v":"c8d5f78f844f3652c4743c00afb2aa671bc094cd2a3a03690d8d7c53cca227d0"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeEncoding.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-ENCODING","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk; pure canonical encoding/decoder contract; no finite edge machine claimed","repo":"cubie-research","riscv":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeFieldPair.v":"be42937f7e130ed87e2392683998aa4c474219529d3fe72d179d59d07775fd5a"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeFieldPair.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-FIELD-PAIR","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk; reusable physical comparison and terminal cleanup products","repo":"cubie-research","riscv":"","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","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"}
{"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","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":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeFieldStage.v":"8957dc31e960dfd10f217bd4c1e4c1b5f13adbdac448c55cd21c846718ece52d"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeFieldStage.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-FIELD-STAGE","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":"","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","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"}
{"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","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk Axioms:<none>; exact six-state unpadded physical reentry for frame-derived scratch","repo":"cubie-research","riscv":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeHeaderRouter.v":"c7a870301847786af687e3dc5d1abe740743178d147930a8e71cbc757f4b44c6"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeHeaderRouter.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-HEADER-ROUTER","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":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeOperandAccumulate.v":"650e133334cea0008cbf13e7995a63c81f661e7eb37c7ef4b8c9b276659687bd"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeOperandAccumulate.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-OPERAND-ACCUMULATE","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":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeOperandPair.v":"3f092e5f1ca8b7d544bdbbc215b22b2f8dde708e62d9f99cdc9854e02527fdea"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeOperandPair.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-OPERAND-PAIR","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk; exact 3-state freeze and 4-state compare rearm","repo":"cubie-research","riscv":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeProgram.v":"609ffff98e14abceb6e06cb23460c64224667feab11a690f5bb8eeca2f50dd9c"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeProgram.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-PROGRAM","note":"Print Assumptions Closed; pure classifier/evaluator contract only; no machine claim","repo":"cubie-research","riscv":"","rust_anchor":"edge_dnode_id_eqb_decompose + edge_program_eval_correct","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeResultRewind.v":"bc75d49271b13d044eb6745c174b8b23f4722f11b7cdda3c29df8fb39a808a0b"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeResultRewind.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-RESULT-REWIND","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk; exact 5 states; physical result reset and descriptor rewind","repo":"cubie-research","riscv":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeSpec.v":"c2bf6184dfe456325bbadc4c7ce9ac33db26ba8199f690e3afc0f9530b29a019"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeSpec.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-SPEC","note":"Print Assumptions Closed; coqchk Axioms:<none>; pure specification only; executable query/edge/grid stages open","repo":"cubie-research","riscv":"","rust_anchor":"serialized_literal_table_parse + edge_dnode_adj_correct + edge_unode_adj_correct + edge_unode_descriptors_ids_closed + edge_descriptor_grid_correct","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeWorkStore.v":"d02b2e6bca9ec648b0ccafb3db02c5707e3d666bf560e43353499fd7db43b5e6"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeWorkStore.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-WORK-STORE","note":"Print Assumptions Closed; targeted pinned Coq compile and coqchk Axioms:<none>; exact 18-state physical work-bit fold; handler sequencing remains separate","repo":"cubie-research","riscv":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEdgeWorkspace.v":"65c02ba09263cdfbae00d2d01373d314adf2aeb84c5d258843c3a004b81d2d9e"},"files":{"coq_file":"proofs/coq/ComplexityStrictEdgeWorkspace.v"},"id":"CUB-COMPLEXITY-STRICT-EDGE-WORKSPACE","note":"Print Assumptions Closed; targeted pinned Coq compile; pure physical-layout contract only; no edge machine claimed","repo":"cubie-research","riscv":"","rust_anchor":"edge_workspace_seed_explicit + edge_workspace_query_payload + edge_workspace_marker_cfg_exact + edge_workspace_query_length","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEmit.v":"c19c567cc6de31684551762326120eb424a13e8841693e89fde26d929190c3be"},"files":{"coq_file":"proofs/coq/ComplexityStrictEmit.v"},"id":"CUB-COMPLEXITY-STRICT-EMIT","note":"travel-write-return","repo":"cubie-research","riscv":"","rust_anchor":"s_emit1_run + s_emit1_extract","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: <none>.","status":"proven","use_cases":["complexity"],"verification_state":"VERIFIED"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEmitGap.v":"3c6010114f0864372e8625fea331beb8ddc9ea3d662ecd06159e3adaae9da814"},"files":{"coq_file":"proofs/coq/ComplexityStrictEmitGap.v"},"id":"CUB-COMPLEXITY-STRICT-EMIT-GAP","note":"gap-travel-write-return","repo":"cubie-research","riscv":"","rust_anchor":"s_emit_run + s_emit_extract","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: <none>.","status":"proven","use_cases":["TEP","complexity"],"verification_state":"VERIFIED"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictEncodeTsp.v":"22bad3aaec4e75fad0f6bdd598f2db8b76dd94f48e7dbcd559e0198aa5c586bf"},"files":{"coq_file":"proofs/coq/ComplexityStrictEncodeTsp.v"},"id":"CUB-COMPLEXITY-STRICT-ENCODE-TSP","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:<none> required by the live proof gate","repo":"cubie-research","riscv":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun.v":"12ddb2cb94259f96b2d057a20afdf5ecfe3539633d48462bc446382791d5fded"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN","note":"coqchk Axioms:<none>; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","rust_anchor":"erode_mfalse + erode_dance + erode_rewind + erode_emit","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun10.v":"6d90a3b0e04c5877fe2dc9fc72e3efdf61d0f66ecd16c4f1e15af73365eb59ea"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun10.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN10","note":"coqchk Axioms:<none>; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","rust_anchor":"erode_scan + scan_fuel_gen + scan_state","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun11.v":"f21bf149f0759aef8350e7f5d503550583294a32cffafe30be3a6d7be6e81726"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun11.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN11","note":"coqchk Axioms:<none>; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","rust_anchor":"erode_pass_canon + pass_fuel_canon","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun12.v":"3507d07a45755dc5f2fd06e1115d27d93ab1d628e982e924c36437645fdad428"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun12.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN12","note":"coqchk Axioms:<none>; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","rust_anchor":"group_word_length + group_word_length_next_ts","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun13.v":"48f0e8eadd6172a4af57dd6b194e077a3046450ca3a4ae2e419ab3ad7db5748d"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun13.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN13","note":"coqchk Axioms:<none>; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","rust_anchor":"group_word_tallies_length + sum_tallies_bit_to_nat + trues_plus_falses","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun14.v":"6399f70e96c35a9217be560c032cf0d3244714b5be6e304aac77358a7a3776a9"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun14.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN14","note":"coqchk Axioms:<none>; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","rust_anchor":"group_word_tallies + split_clauses_nonempty + tallies_cons_ne","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun15.v":"aad0c07ec4b6d555d6ae7c5066a1e43759b6d50d9d667eaff1d30e48a3ef06a5"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun15.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN15","note":"coqchk Axioms:<none>; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","rust_anchor":"erode_scan_end + erode_scan_last + scan_bits_gen_app + has_pos_app","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun16.v":"e09b1712d942981ce46ef30859a946b351780df1f56e6fd6325447ef9d419acc"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun16.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN16","note":"coqchk Axioms:<none>; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","rust_anchor":"erode_pass1_canon","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun17.v":"2feedc5c30416f71b1619f504bc416f83576059436a91ac3caed8da8cabacc2c"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun17.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN17","note":"coqchk Axioms:<none>; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","rust_anchor":"erode_fold + erode_fold_fuel + erode_fold_flat + has_pos_false_tmax","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun18.v":"95a4c6ecb7ddac65aec958e6c26cb603be26b568add051bf45e394c4f56d578b"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun18.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN18","note":"coqchk Axioms:<none>; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","rust_anchor":"s_maxerode_computes + maxerode_fuel + final_extract + flat_extract","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun19.v":"78f918c2d4f004022a30d367f1931e20cc10ee2bf8d104d3a1d265f66b1960b6"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun19.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN19","note":"coqchk Axioms:<none>; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","rust_anchor":"maxerode_fuel_poly + maxerode_fuel_quad","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun2.v":"089167c637fb178dece8664a6f5c49415ae77f1822e9e2196745b6c552453abb"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun2.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN2","note":"coqchk Axioms:<none>; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","rust_anchor":"erode_group_interior","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun20.v":"78f199e52c2e9e37614146c29cb240029cf1f731c3b0b109e7dbb969c616daa4"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun20.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN20","note":"coqchk Axioms:<none>; exact scoped theorems proven; no total clean num_vars stage claimed; coq-only strict-TM corpus","repo":"cubie-research","riscv":"","rust_anchor":"s_maxerode_budget + s_maxerode_budget_first_halt + no_total_num_vars_postprocessor_from_run20_output","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun3.v":"7ceb71e84a9e3f705dab64098e3d1fd8a06dc11e162c8de8cd50717dd3da59e9"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun3.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN3","note":"coqchk Axioms:<none>; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","rust_anchor":"erode_group_final","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun4.v":"c6b8a96f9ab6322cb631f412e98da071bb79e93ed12da5e07f3843b486165b7f"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun4.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN4","note":"coqchk Axioms:<none>; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","rust_anchor":"tmax_next_ts + has_pos_next_ts + next_ts","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<t then [t-1;0] else [0]), NOT map pred -- eroding a group of tally t leaves (t-1) trues + TWO Bit false (eroded edge-true + the delimiter) = a group of tally (t-1) then a fresh empty group; Compute-certified vs the s_maxerode traces (next_ts [2;1]=[1;0;0;0], next_ts [1;0;2]=[0;0;0;1;0]). HEADLINE tmax_next_ts: tmax (next_ts ts) = pred (tmax ts) -- the bridge the multi-pass fold to EROSION_IS_MAX inducts on; has_pos_next_ts keeps the A0-on-Blank termination test sound and complete after a pass. s_maxerode_computes + the machine-side scan/rewind/emit composition 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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun5.v":"2c0ca47b4da16217e2b4c3df1e5846245a5167e4a7f77e17786fcecc63251588"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun5.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN5","note":"coqchk Axioms:<none>; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","rust_anchor":"erode_scan_pos + group_word_pos","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun6.v":"7c9bc96a90149f32a0007a4bdf48592f19e5ea1f1eef07432e1fa6ba6e632cd9"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun6.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN6","note":"coqchk Axioms:<none>; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","rust_anchor":"erode_rewind_to_gap + erode_rewind_to_gap_boundary","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun7.v":"8317a77f98a0d0c273c41024d2a38f58cbc83db3782bd211228333fed0efc794"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun7.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN7","note":"coqchk Axioms:<none>; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","rust_anchor":"scan_acc_map_bit + rev_scan_bits_group_word + group_word_app","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun8.v":"82ae78ef3e18f2105915935aaaec67df96820d8dc720723d0abcd48023befc5f"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun8.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN8","note":"coqchk Axioms:<none>; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","rust_anchor":"erode_pass1_pos","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictErodeRun9.v":"e344322b3236173369fc866da1a1b88d3aa7d8791136a23f6f971711660576de"},"files":{"coq_file":"proofs/coq/ComplexityStrictErodeRun9.v"},"id":"CUB-COMPLEXITY-STRICT-ERODE-RUN9","note":"coqchk Axioms:<none>; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","rust_anchor":"rev_scan_bits_gen_group_word + grp_bits_gen_rev_group_word","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictField.v":"10777b06ac2a9cbc115bdc6e7bfa84ddb7a1ab315a7651f1228ff246f76e29dd"},"files":{"coq_file":"proofs/coq/ComplexityStrictField.v"},"id":"CUB-COMPLEXITY-STRICT-FIELD","note":"field-emitter-clean-extract","repo":"cubie-research","riscv":"","rust_anchor":"s_field_extract","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: <none>.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictFrameNvStage.v":"ba59fa7bf4d6c44b0131635a35df40433d6455bf118c5d4d37a2821f93f26c9b"},"files":{"coq_file":"proofs/coq/ComplexityStrictFrameNvStage.v"},"id":"CUB-COMPLEXITY-STRICT-FRAME-NV-STAGE","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":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictFrameStage.v":"991cd23ea56ededbd0737417d2e46770efe79e899a7e55491fc77681a9969544"},"files":{"coq_file":"proofs/coq/ComplexityStrictFrameStage.v"},"id":"CUB-COMPLEXITY-STRICT-FRAME-STAGE","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":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictGridCostRecycle.v":"f27e87087a061b4dc938d39057811313ad92c68021c752dedf92b867050f2585"},"files":{"coq_file":"proofs/coq/ComplexityStrictGridCostRecycle.v"},"id":"CUB-COMPLEXITY-STRICT-GRID-COST-RECYCLE","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:<none> required by the live proof gate","repo":"cubie-research","riscv":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictGridCounterInit.v":"8ee4d6aa715a09aa40bed299b15d927253fd83ed8b2f2336d1e44c03b945bc60"},"files":{"coq_file":"proofs/coq/ComplexityStrictGridCounterInit.v"},"id":"CUB-COMPLEXITY-STRICT-GRID-COUNTER-INIT","note":"Coq-only strict-TM theorem; canonical sat_N_frame specialization is load-bearing; full proof gate 284/284 and coqchk Axioms:<none>","repo":"cubie-research","riscv":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictGridDescriptorMaterialize.v":"4d89a6ee8b4a549860a2fda82b9c11b2bd5aac5e98bb63ea8c4d200bb16f52fd"},"files":{"coq_file":"proofs/coq/ComplexityStrictGridDescriptorMaterialize.v"},"id":"CUB-COMPLEXITY-STRICT-GRID-DESCRIPTOR-MATERIALIZE","note":"Coq-only strict-TM corpus convention; canonical-header producer boundary and strict value<capacity precondition are explicit; Print Assumptions capstones present; coqchk Axioms:<none> required by the live proof gate","repo":"cubie-research","riscv":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictGridDescriptorOdometer.v":"896f19f288334f3a95aecf1f5321e2b54245abb6b67176b8dc8a1ec9ae83ce37"},"files":{"coq_file":"proofs/coq/ComplexityStrictGridDescriptorOdometer.v"},"id":"CUB-COMPLEXITY-STRICT-GRID-DESCRIPTOR-ODOMETER","note":"Coq-only strict-TM theorem; valid descriptor and canonical counter premises are explicit; full proof gate 284/284 and coqchk Axioms:<none>","repo":"cubie-research","riscv":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictGridFinalize.v":"9f75d1790ed55fae2e47d066bc120a91b510898b17bd48b41fa174d4260c89fb"},"files":{"coq_file":"proofs/coq/ComplexityStrictGridFinalize.v"},"id":"CUB-COMPLEXITY-STRICT-GRID-FINALIZE","note":"Coq-only strict-TM theorem; nil-base boundary on the extraction capstone is explicit; full proof gate 284/284 and coqchk Axioms:<none>","repo":"cubie-research","riscv":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictGridInit.v":"93f4124c53eb160d44f1d1b49ab6faf69d0d63d685dddf326a89601e81a700ff"},"files":{"coq_file":"proofs/coq/ComplexityStrictGridInit.v"},"id":"CUB-COMPLEXITY-STRICT-GRID-INIT","note":"Coq-only strict-TM theorem; exact reserve equality is explicit; full proof gate 284/284 and coqchk Axioms:<none>","repo":"cubie-research","riscv":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictGridPairSchedule.v":"d71204496794e68a30cf2cbdb2ec949709d55e3ee3be3caeed7069e0570bc446"},"files":{"coq_file":"proofs/coq/ComplexityStrictGridPairSchedule.v"},"id":"CUB-COMPLEXITY-STRICT-GRID-PAIR-SCHEDULE","note":"Coq-only pure schedule theorem; in-range index premise is load-bearing; full proof gate 284/284 and coqchk Axioms:<none>","repo":"cubie-research","riscv":"","rust_anchor":"gdo_pair_schedule_nth_error + gdo_pair_schedule_step_nonlast + gdo_pair_schedule_step_last + gdo_pair_schedule_reserve_step","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictGridPoly.v":"10aff8064491b35b06eda8ecf751a598dbaece064122a0d44d39b9e7b50458e0"},"files":{"coq_file":"proofs/coq/ComplexityStrictGridPoly.v"},"id":"CUB-COMPLEXITY-STRICT-GRID-POLY","note":"Coq-only quantitative theorem; prepared-layout scope and complete-encoder degree are explicit; full proof gate 284/284 and coqchk Axioms:<none>","repo":"cubie-research","riscv":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictGridPreparedLoop.v":"e258dea0f35ac1b1d4d1481c31509c4f0e5f39daf7ddf893827229d4359acb50"},"files":{"coq_file":"proofs/coq/ComplexityStrictGridPreparedLoop.v"},"id":"CUB-COMPLEXITY-STRICT-GRID-PREPARED-LOOP","note":"Coq-only strict-TM theorem; prepared-layout and reserve premises are load-bearing; full proof gate 284/284 and coqchk Axioms:<none>","repo":"cubie-research","riscv":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictGridSeed.v":"2aa7c8120827f9e2ce2f86eae196652cf6208fea30ae4955a7486a3cc8ff249b"},"files":{"coq_file":"proofs/coq/ComplexityStrictGridSeed.v"},"id":"CUB-COMPLEXITY-STRICT-GRID-SEED","note":"Coq-only strict-TM theorem; canonical frame and physical reserve semantics are explicit; full proof gate 284/284 and coqchk Axioms:<none>","repo":"cubie-research","riscv":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictGridWorkspaceMaterialize.v":"69127f2191b34ebd6006cd31aaa6ad0ef7093f2c341aab8ec108456158fb2388"},"files":{"coq_file":"proofs/coq/ComplexityStrictGridWorkspaceMaterialize.v"},"id":"CUB-COMPLEXITY-STRICT-GRID-WORKSPACE-MATERIALIZE","note":"Coq-only strict-TM theorem; producer-certified counter boundary is explicit; full proof gate 284/284 and coqchk Axioms:<none>","repo":"cubie-research","riscv":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictIter.v":"8b9b78149dd90c3ddcb2a83ccfbcb53bbf83597b8b3ced4090362cb98c4e766e"},"files":{"coq_file":"proofs/coq/ComplexityStrictIter.v"},"id":"CUB-COMPLEXITY-STRICT-ITER","note":"iterate-controller","repo":"cubie-research","riscv":"","rust_anchor":"s_iter_run + s_iter_extract","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: <none>.","status":"proven","use_cases":["TEP","complexity"],"verification_state":"VERIFIED"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictKarpEdge.v":"a0b6eb712ac92940f6d2db5e5a9c4843a5a41b1a32732f82c6de78aeb54a7df7"},"files":{"coq_file":"proofs/coq/ComplexityStrictKarpEdge.v"},"id":"CUB-COMPLEXITY-STRICT-KARP-EDGE","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":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictLiteralCall.v":"f8dcf50ad2d0dcc3480ef0ccc169e75d0b62f5c61f22b830cebc70f0a9b7b3e4"},"files":{"coq_file":"proofs/coq/ComplexityStrictLiteralCall.v"},"id":"CUB-COMPLEXITY-STRICT-LITERAL-CALL","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":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictLiteralQuery.v":"5e9bf79a14955a75f27c450b390f495bad0626e23cad0e9d04c088330a0da16e"},"files":{"coq_file":"proofs/coq/ComplexityStrictLiteralQuery.v"},"id":"CUB-COMPLEXITY-STRICT-LITERAL-QUERY","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":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictLoop.v":"52d960883de50e0349a50dc494d2a11e483933097ab04fd31723107a589e8ea1"},"files":{"coq_file":"proofs/coq/ComplexityStrictLoop.v"},"id":"CUB-COMPLEXITY-STRICT-LOOP","note":"loop-back-primitive","repo":"cubie-research","riscv":"","rust_anchor":"s_rewind_run + s_rewind_extract","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: <none>.","status":"proven","use_cases":["complexity"],"verification_state":"VERIFIED"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictMapPrepend.v":"113ddacf6426a59d423d3b0ff3a002679756ac5d54c91dde40da6218348dabc5"},"files":{"coq_file":"proofs/coq/ComplexityStrictMapPrepend.v"},"id":"CUB-COMPLEXITY-STRICT-MAP-PREPEND","note":"coqchk Axioms:<none>; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","rust_anchor":"s_map_prepend_clean_pad + mp_run + mp_no_early","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictMaxClean.v":"583cdfc4346984cfba48434f0ee725ee014ac609cade20a715dc24f2b23be8ad"},"files":{"coq_file":"proofs/coq/ComplexityStrictMaxClean.v"},"id":"CUB-COMPLEXITY-STRICT-MAX-CLEAN","note":"coqchk Axioms:<none>; finite state bound and exact runs","repo":"cubie-research","riscv":"","rust_anchor":"s_maxclean_layout + s_maxerode_halt_layout","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictMaxErode.v":"3ef185baabd2ccc9aefea930627636378340a0dfa18a6da4f99e3417ba32dc1f"},"files":{"coq_file":"proofs/coq/ComplexityStrictMaxErode.v"},"id":"CUB-COMPLEXITY-STRICT-MAX-ERODE","note":"coqchk Axioms:<none>; 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":"","rust_anchor":"s_maxerode_well_formed + me_check1-5 (Compute)","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictMaxPipeline.v":"8b7b7d0a84d335127b0a608f91968b22063155d461393cbff5edd1bccde771f9"},"files":{"coq_file":"proofs/coq/ComplexityStrictMaxPipeline.v"},"id":"CUB-COMPLEXITY-STRICT-MAX-PIPELINE","note":"coqchk Axioms:<none>; honest range-restricted middle stage","repo":"cubie-research","riscv":"","rust_anchor":"s_maxpipeline_clean_pad_on_terminated + maxpipeline_budget_bound","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictMaxSpec.v":"e610df1a64f84acb65e676b26399a4a657f4cad30d552986d880ae6bee6b1cdd"},"files":{"coq_file":"proofs/coq/ComplexityStrictMaxSpec.v"},"id":"CUB-COMPLEXITY-STRICT-MAX-SPEC","note":"coqchk Axioms:<none>; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","rust_anchor":"EROSION_IS_MAX + max_pos_iff + max_tally_le_length","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictMult.v":"249d9f5255c48e0f18566438e19a03583d8a75c94525f2605084b182666cfdad"},"files":{"coq_file":"proofs/coq/ComplexityStrictMult.v"},"id":"CUB-COMPLEXITY-STRICT-MULT","note":"unary-multiply-config-level","repo":"cubie-research","riscv":"","rust_anchor":"s_mult_run + s_mult_halted","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: <none>.","status":"proven","use_cases":["TEP","complexity"],"verification_state":"VERIFIED"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictNFrame.v":"feb7aa28a170d892c67ba012f051fcf2bf326f5bf3cd91d0cc6d6ac57f69c518"},"files":{"coq_file":"proofs/coq/ComplexityStrictNFrame.v"},"id":"CUB-COMPLEXITY-STRICT-N-FRAME","note":"Print Assumptions Closed; coqchk Axioms:<none>; total clean polynomial N stage closed; frame-to-grid pure spec closed; executable edge/grid/encode/final reduction open","repo":"cubie-research","riscv":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictNumClauses.v":"631baaf702a1447c720837f85523e3047bf742271b23015355c222fb3200bffd"},"files":{"coq_file":"proofs/coq/ComplexityStrictNumClauses.v"},"id":"CUB-COMPLEXITY-STRICT-NUM-CLAUSES","note":"coqchk Axioms:<none>; total clean polynomial num_clauses stage closed; joint nv/nc/formula frame and N/grid/final reduction open","repo":"cubie-research","riscv":"","rust_anchor":"s_clausecount_clean_pad + s_numclauses_clean_pad + s_numclauses_computes_strict + s_numclauses_stage_exists_with_state_bound","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictNumVars.v":"3ea1e814f2cec1f27c9e1fba9fd7f43d6ec1d00298808780d30efc83579f8e73"},"files":{"coq_file":"proofs/coq/ComplexityStrictNumVars.v"},"id":"CUB-COMPLEXITY-STRICT-NUM-VARS","note":"coqchk Axioms:<none>; total clean polynomial num_vars stage closed; N/grid/encode_tsp/final reduction open","repo":"cubie-research","riscv":"","rust_anchor":"s_numvars_clean_pad + s_numvars_computes_strict + s_numvars_stage_exists_with_state_bound","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictPad.v":"0ea7505cff2eabb67dd55c195c5fd1aafd8aebdf21554a84de92af14413a0f3c"},"files":{"coq_file":"proofs/coq/ComplexityStrictPad.v"},"id":"CUB-COMPLEXITY-STRICT-PAD","note":"coqchk Axioms:<none>; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","rust_anchor":"s_phase4_from_stage_machines_pad + no_clean_append_false + s_prepend_false_clean_pad","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictPadd.v":"3db3061ddc828d6615d95d1912761b9341a2376fdd61b2ec01e116dd991b3135"},"files":{"coq_file":"proofs/coq/ComplexityStrictPadd.v"},"id":"CUB-COMPLEXITY-STRICT-PADD","note":"source-preserving-add","repo":"cubie-research","riscv":"","rust_anchor":"s_padd_run + s_padd_extract","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: <none>.","status":"proven","use_cases":["complexity"],"verification_state":"VERIFIED"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictPipeline.v":"60d0f26712cbe87d15195e7f874cf8c551e25e6692fae73f189b1f7445155c3b"},"files":{"coq_file":"proofs/coq/ComplexityStrictPipeline.v"},"id":"CUB-COMPLEXITY-STRICT-PIPELINE","note":"coqchk Axioms:<none>; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","rust_anchor":"delim_counter_computes","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictRangeCompose.v":"f22be3d18a5852f3d3f063f46260ffb086be098ee115817979dc11ea2bd75c35"},"files":{"coq_file":"proofs/coq/ComplexityStrictRangeCompose.v"},"id":"CUB-COMPLEXITY-STRICT-RANGE-COMPOSE","note":"coqchk Axioms:<none>; reusable range/strict composition infrastructure","repo":"cubie-research","riscv":"","rust_anchor":"s_clean_transduces_pad_on + stm_seq_clean_pad_preserves_range_poly + s_clean_transduces_pad_computes_strict","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictStream.v":"2efe3bf9b8c229c4c2fb589eeef69a7a3b259e05dfdb57842b059fc996b9e218"},"files":{"coq_file":"proofs/coq/ComplexityStrictStream.v"},"id":"CUB-COMPLEXITY-STRICT-STREAM","note":"spec-pins-loop","repo":"cubie-research","riscv":"","rust_anchor":"word_reduce_stream_eq + s_phase4_from_stream","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: <none>.","status":"proven","use_cases":["TSP","complexity"],"verification_state":"VERIFIED"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictUnaryEq.v":"7b6379f43299246f1c7bf1735bf856db556f39e6802a05be0a6fa4a7f115f844"},"files":{"coq_file":"proofs/coq/ComplexityStrictUnaryEq.v"},"id":"CUB-COMPLEXITY-STRICT-UNARY-EQ","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":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictUnaryStage.v":"3d45b4123e9b12a09bc90410851f3a365771576089359c41f9dbffb47adbe8dc"},"files":{"coq_file":"proofs/coq/ComplexityStrictUnaryStage.v"},"id":"CUB-COMPLEXITY-STRICT-UNARY-STAGE","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":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictUnaryStageClean.v":"1e0a344d9838af70c0450570fd065a2c81196b3b64521406dc4e66dcc6b5b147"},"files":{"coq_file":"proofs/coq/ComplexityStrictUnaryStageClean.v"},"id":"CUB-COMPLEXITY-STRICT-UNARY-STAGE-CLEAN","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":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictVarFrame.v":"b73cbc00376900d09ac8a1d2aaafc52d807dac39e460182bdb3240a2aa522c0a"},"files":{"coq_file":"proofs/coq/ComplexityStrictVarFrame.v"},"id":"CUB-COMPLEXITY-STRICT-VAR-FRAME","note":"Print Assumptions Closed; coqchk Axioms:<none>; direct totalization plus semantic normalizer composition; coq-only strict-TM corpus","repo":"cubie-research","riscv":"","rust_anchor":"s_varframe_raw_clean_pad + s_varframe_clean_pad + s_parameter_frame_clean_pad + s_parameter_frame_stage_exists_with_state_bound","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictVarMax.v":"bbd175876f1bbb3a032964f6f0234a9cb2626b1d81004f5e97d773bb9e6d4e49"},"files":{"coq_file":"proofs/coq/ComplexityStrictVarMax.v"},"id":"CUB-COMPLEXITY-STRICT-VAR-MAX","note":"coqchk Axioms:<none>; total pure specification only, no finite normalization machine claimed; coq-only strict-TM corpus","repo":"cubie-research","riscv":"","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","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityStrictVarIdx.v":"fd238a218b34eef258a7627c529e2b53de2c18a8c3ed61d9745bc7d2e9a122da"},"files":{"coq_file":"proofs/coq/ComplexityStrictVarIdx.v"},"id":"CUB-COMPLEXITY-STRICT-VARIDX","note":"coqchk Axioms:<none>; coq-only strict-TM corpus (Complexity* convention), no Lean/Verus mirror","repo":"cubie-research","riscv":"","rust_anchor":"s_varidx_computes + kept0_is_varindex + vi_group","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityUhcLanguage.v":"225a15d028c1396d79796cfaac640b5aff37138936227dc578de693ced5b5ec9"},"files":{"coq_file":"proofs/coq/ComplexityUhcLanguage.v"},"id":"CUB-COMPLEXITY-UHC","note":"","repo":"cubie-research","riscv":"","rust_anchor":"","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityUhcToTsp.v":"420047619dbc7b8d797c6fa633dee05d3a51147146a9279c240837bb4d9e5991"},"files":{"coq_file":"proofs/coq/ComplexityUhcToTsp.v"},"id":"CUB-COMPLEXITY-UHC-TSP","note":"","repo":"cubie-research","riscv":"","rust_anchor":"uhc_to_tsp_instance","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"}
{"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","note":"coqchk Axioms:<none>; 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":"","rust_anchor":"cusum_maxsuffix_identity + subcritical_never_fires + supercritical_rate_fires + observed_27pct_never_fires","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"}
{"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","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":"","rust_anchor":"standalone spec, no product anchor yet (reroute witness calculus)","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"}
{"crate":"","deployable":false,"file_shas":{"recovered/CubieMotionV1.v":"ea68c9be7b773315e451a577133bd38ef9a21e0341867b56704f1e4afc32d8ba"},"files":{"coq_file":"recovered/CubieMotionV1.v"},"id":"CUB-MATH-CORE-3267","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":"","rust_anchor":"not wired (motion calculus over CUB-TSP-034 placement)","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"}
{"crate":"","deployable":false,"file_shas":{"recovered/CubieMotionV2_1.lean":"55f9022a7a50078d63a5f4826e7f35bbc2d4322c5242c1dc43c67fbfef23ddcf"},"files":{"lean_file":"recovered/CubieMotionV2_1.lean"},"id":"CUB-MATH-CORE-3268","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":"","rust_anchor":"not wired (bridges CubieAuth.rotateOk to LinearHandoff)","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"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/ComplexityProofSystemHaken2f.v":"6b454fc3ce8bafd7efe2e08cfdb756b968c947fd6ba4e7a93115e6587ce15b12"},"files":{"coq_file":"proofs/coq/ComplexityProofSystemHaken2f.v"},"id":"CUB-PROOFSYS-HAKEN-2F","note":"coqchk Axioms:<none>; audit brick -- pins what Haken2e does and does not feed; coq-only proof-complexity corpus","repo":"cubie-research","riscv":"","rust_anchor":"php_initial_width + php_width_bound_met_by_axiom + php_width_bound_no_refutation_gap","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.","status":"proven","use_cases":["TEP","complexity"],"verification_state":"VERIFIED"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/CubTsp001.v":"814d626ec0ceaf476bebc99934ebe9a090c9be026ac11d1ac8524d76f09359bb","proofs/lean4/CubTsp001.lean":"38996ab5146f00af9144220fcf9dde36efa7ba59841ade972b8c33742b4a415b","proofs/verus/cub_tsp_001.rs":"7768835786009bdbeaa716abbb72c3479c74b52ac1cd01ac6af9f84ae9dffe08"},"files":{"coq_file":"proofs/coq/CubTsp001.v","lean_file":"proofs/lean4/CubTsp001.lean","verus_file":"proofs/verus/cub_tsp_001.rs"},"id":"CUB-TSP-001","note":"","proof_scope":"standalone","repo":"cubie-research","riscv":"","rust_anchor":"TourState::from_route","statement":"A candidate route is well-formed iff it is a permutation of all supplied city IDs.","status":"proven","use_cases":["TSP"],"verification_state":"VERIFIED"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/CubTsp002.v":"a6a2a092608805a0996fa58174a156fe12956f0bdce2388e519dcf8ac1c23d80","proofs/lean4/CubTsp002.lean":"7b8e0a996d62704582751c69d3c678356c5df08215299e3fea554a7d59bd048f","proofs/verus/cub_tsp_002.rs":"4199faf68e44d318a404bc232c9d69dffbb867bb40a1ab92c0e2603f51a50a20"},"files":{"coq_file":"proofs/coq/CubTsp002.v","lean_file":"proofs/lean4/CubTsp002.lean","verus_file":"proofs/verus/cub_tsp_002.rs"},"id":"CUB-TSP-002","note":"","proof_scope":"standalone","repo":"cubie-research","riscv":"","rust_anchor":"TourState::from_route; ShadowMirror::from_tour","statement":"Successor/predecessor arrays generated from a route are inverse movement-string views.","status":"proven","use_cases":["crypto","TSP"],"verification_state":"VERIFIED"}
{"crate":"","deployable":false,"file_shas":{"proofs/coq/CubTsp003.v":"78f01988386abb9dfc0ec58d4f47ebed7bf32bbf9eb2811faeeab80f8d12fd60","proofs/lean4/CubTsp003.lean":"336ee9b85a663d24f941c4c4574fc4f22c8618a6c48498ecfbc9cca84f3f2fe9","proofs/verus/cub_tsp_003.rs":"091d7debcb9e0a32568219d79ba277601476eb2c95e91e44c43b9ef5edaac894"},"files":{"coq_file":"proofs/coq/CubTsp003.v","lean_file":"proofs/lean4/CubTsp003.lean","verus_file":"proofs/verus/cub_tsp_003.rs"},"id":"CUB-TSP-003","note":"","proof_scope":"standalone","repo":"cubie-research","riscv":"","rust_anchor":"TspCubeState::apply_segment_reverse","statement":"A synchronized segment reversal preserves route permutation well-formedness.","status":"proven","use_cases":["TSP"],"verification_state":"VERIFIED"}
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{"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","note":"","proof_scope":"standalone","repo":"cubie-research","riscv":"","rust_anchor":"cubie_tsp_bnb (complexity witness)","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"}
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{"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","note":"coqchk Axioms:<none>; 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","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)","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"}
{"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","note":"coqchk Axioms:<none>; 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","rust_anchor":"evaluate_bindings + CubieTspEvidence54 (crates/cubie-tsp-rust-optimal/src/lib.rs)","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"}
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{"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","note":"coqchk Axioms:<none>; 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","rust_anchor":"gap_anchored_k + detect_gap_anchored_stagnation + held_karp_initial_exact_q (crates/cubie-tsp-verifier/src/lib.rs)","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+h<k*T, the detector must fire within that recorded positive budget. The derived minimal allowance k0=(g+h)/T+1 establishes the inequality for T>0; 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"}
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{"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","note":"coqchk Axioms:<none>; 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":"","rust_anchor":"model-only; no runtime shard implementation","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"}