165	164,HA split-brain fail-closed theorem,"HA, split-brain, and degraded availability",abstract_passable_proof_obligation,VERIFIED_EXACT,V2.0,CubieTrustCompilerV2_0.ha_split_brain_fail_closed,CubieTrustCompilerV2_0.ha_split_brain_fail_closed,PASS,HA split-brain must fail closed on high-impact requests.,
166	165,Deterministic active-active decision theorem,"HA, split-brain, and degraded availability",abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
167	166,Degraded local epoch tick theorem,"HA, split-brain, and degraded availability",abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
168	167,"Degraded local epoch tick theorem, implementation version","HA, split-brain, and degraded availability",abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
169	168,Degraded epoch safety bound,"HA, split-brain, and degraded availability",abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
170	169,Nonce filter flush safety theorem,"HA, split-brain, and degraded availability",abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
171	170,Host Bloom saturation prevention theorem,"HA, split-brain, and degraded availability",abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
172	171,Append-only audit ledger integrity theorem,"Audit, privacy, and proof-ledger integrity",abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
173	172,Dual-ledger non-disclosure theorem,"Audit, privacy, and proof-ledger integrity",abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
174	173,Denial certificate privacy theorem,"Audit, privacy, and proof-ledger integrity",abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
175	174,Surface projection minimality theorem,"Audit, privacy, and proof-ledger integrity",abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
176	175,Cubie-to-Omega projection refinement theorem,Cubie/Omega substrate bridge and witness boundaries,abstract_passable_proof_obligation,ENGINEERING_INVARIANT,,,,PENDING,Runtime invariant with formal analogue — Verus bridges the gap.,Write Verus spec; escalate to Coq/Lean if formal proof needed.
177	176,Omega witness completeness theorem,Cubie/Omega substrate bridge and witness boundaries,abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
178	177,Per-witness denial theorem family,Cubie/Omega substrate bridge and witness boundaries,abstract_passable_proof_obligation,ENGINEERING_INVARIANT,,,,PENDING,Runtime invariant with formal analogue — Verus bridges the gap.,Write Verus spec; escalate to Coq/Lean if formal proof needed.
179	178,Hardware-key boundary condition theorem,Cubie/Omega substrate bridge and witness boundaries,abstract_passable_proof_obligation,ENGINEERING_INVARIANT,,,,PENDING,Runtime invariant with formal analogue — Verus bridges the gap.,Write Verus spec; escalate to Coq/Lean if formal proof needed.
180	179,Session-state freshness theorem,Cubie/Omega substrate bridge and witness boundaries,abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
181	180,CAISI RFI alignment theorem,"Regulatory, CAISI, and governance alignment",abstract_passable_proof_obligation,REWRITE_RULE,,,,PENDING,Has documentation guardrail component + formal obligation.,Rewrite doc claim; then formalize supporting theorem.
182	181,CAISI vector mapping table completeness theorem,"Regulatory, CAISI, and governance alignment",abstract_passable_proof_obligation,REWRITE_RULE,,,,PENDING,Has documentation guardrail component + formal obligation.,Rewrite doc claim; then formalize supporting theorem.
183	182,Traditional vulnerability coverage theorem,"Regulatory, CAISI, and governance alignment",abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
184	183,Prompt-injection seam denial theorem,"Regulatory, CAISI, and governance alignment",abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
185	184,Backdoor side-effect containment theorem,"Regulatory, CAISI, and governance alignment",abstract_passable_proof_obligation,REWRITE_RULE,,,,PENDING,Has documentation guardrail component + formal obligation.,Rewrite doc claim; then formalize supporting theorem.
186	185,Supply-chain backdoor provenance gate theorem,"Regulatory, CAISI, and governance alignment",abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
187	186,Misaligned objective pre-execution negation theorem,"Regulatory, CAISI, and governance alignment",abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
188	187,Rollback is late theorem,"Regulatory, CAISI, and governance alignment",abstract_passable_proof_obligation,REWRITE_RULE,,,,PENDING,Has documentation guardrail component + formal obligation.,Rewrite doc claim; then formalize supporting theorem.
189	188,Empirical replication requirement,"Regulatory, CAISI, and governance alignment",abstract_passable_proof_obligation,EMPIRICAL_CLAIM,,,,N/A,Empirical measurement + spec cleanup required.,Define benchmark target; clean up rewrite guardrail.
190	189,Gross-vs-net recovery separation rule,"Regulatory, CAISI, and governance alignment",abstract_passable_proof_obligation,REWRITE_RULE,,,,N/A,Terminology / spec guardrail — no formal proof required.,Audit documented claim; update whitepaper section.
191	190,Conditional QEC realization theorem,Conditional quantum and advanced research path,abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
192	191,Stabilizer validity theorem,Conditional quantum and advanced research path,abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
193	192,Holevo-bounded extraction theorem,Conditional quantum and advanced research path,abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
194	193,Measurement-collapse consent theorem,Conditional quantum and advanced research path,abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
195	194,Entanglement-induced correlation theorem,Conditional quantum and advanced research path,abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
196	195,Context-dependent measurement basis theorem,Conditional quantum and advanced research path,abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
197	196,Non-commutative consent algebra theorem,Conditional quantum and advanced research path,abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
198	197,Quantum consent channel theorem,Conditional quantum and advanced research path,abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
199	198,Contextual entanglement-wedge reconstruction theorem,Conditional quantum and advanced research path,abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
200	199,Information-percolation threshold theorem,Conditional quantum and advanced research path,abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
201	200,Consent capacity theorem,Conditional quantum and advanced research path,abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
202	201,Contextual consent kernel threshold theorem,Conditional quantum and advanced research path,abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
203	202,Dynamic consent mixing theorem,Conditional quantum and advanced research path,abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
204	203,Arbitrary-graph consent threshold complexity theorem,Conditional quantum and advanced research path,abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
205

164,HA split-brain fail-closed theorem,"HA, split-brain, and degraded availability",abstract_passable_proof_obligation,VERIFIED_EXACT,V2.0,CubieTrustCompilerV2_0.ha_split_brain_fail_closed,CubieTrustCompilerV2_0.ha_split_brain_fail_closed,PASS,HA split-brain must fail closed on high-impact requests.,
165,Deterministic active-active decision theorem,"HA, split-brain, and degraded availability",abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
166,Degraded local epoch tick theorem,"HA, split-brain, and degraded availability",abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
167,"Degraded local epoch tick theorem, implementation version","HA, split-brain, and degraded availability",abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
168,Degraded epoch safety bound,"HA, split-brain, and degraded availability",abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
169,Nonce filter flush safety theorem,"HA, split-brain, and degraded availability",abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
170,Host Bloom saturation prevention theorem,"HA, split-brain, and degraded availability",abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
171,Append-only audit ledger integrity theorem,"Audit, privacy, and proof-ledger integrity",abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
172,Dual-ledger non-disclosure theorem,"Audit, privacy, and proof-ledger integrity",abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
173,Denial certificate privacy theorem,"Audit, privacy, and proof-ledger integrity",abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
174,Surface projection minimality theorem,"Audit, privacy, and proof-ledger integrity",abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
175,Cubie-to-Omega projection refinement theorem,Cubie/Omega substrate bridge and witness boundaries,abstract_passable_proof_obligation,ENGINEERING_INVARIANT,,,,PENDING,Runtime invariant with formal analogue — Verus bridges the gap.,Write Verus spec; escalate to Coq/Lean if formal proof needed.
176,Omega witness completeness theorem,Cubie/Omega substrate bridge and witness boundaries,abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
177,Per-witness denial theorem family,Cubie/Omega substrate bridge and witness boundaries,abstract_passable_proof_obligation,ENGINEERING_INVARIANT,,,,PENDING,Runtime invariant with formal analogue — Verus bridges the gap.,Write Verus spec; escalate to Coq/Lean if formal proof needed.
178,Hardware-key boundary condition theorem,Cubie/Omega substrate bridge and witness boundaries,abstract_passable_proof_obligation,ENGINEERING_INVARIANT,,,,PENDING,Runtime invariant with formal analogue — Verus bridges the gap.,Write Verus spec; escalate to Coq/Lean if formal proof needed.
179,Session-state freshness theorem,Cubie/Omega substrate bridge and witness boundaries,abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
180,CAISI RFI alignment theorem,"Regulatory, CAISI, and governance alignment",abstract_passable_proof_obligation,REWRITE_RULE,,,,PENDING,Has documentation guardrail component + formal obligation.,Rewrite doc claim; then formalize supporting theorem.
181,CAISI vector mapping table completeness theorem,"Regulatory, CAISI, and governance alignment",abstract_passable_proof_obligation,REWRITE_RULE,,,,PENDING,Has documentation guardrail component + formal obligation.,Rewrite doc claim; then formalize supporting theorem.
182,Traditional vulnerability coverage theorem,"Regulatory, CAISI, and governance alignment",abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
183,Prompt-injection seam denial theorem,"Regulatory, CAISI, and governance alignment",abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
184,Backdoor side-effect containment theorem,"Regulatory, CAISI, and governance alignment",abstract_passable_proof_obligation,REWRITE_RULE,,,,PENDING,Has documentation guardrail component + formal obligation.,Rewrite doc claim; then formalize supporting theorem.
185,Supply-chain backdoor provenance gate theorem,"Regulatory, CAISI, and governance alignment",abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
186,Misaligned objective pre-execution negation theorem,"Regulatory, CAISI, and governance alignment",abstract_passable_proof_obligation,DERIVED_CANDIDATE,,,,PENDING,Likely derivable from verified stack — needs formal proof.,Identify parent theorems in source stack; write formal derivation.
187,Rollback is late theorem,"Regulatory, CAISI, and governance alignment",abstract_passable_proof_obligation,REWRITE_RULE,,,,PENDING,Has documentation guardrail component + formal obligation.,Rewrite doc claim; then formalize supporting theorem.
188,Empirical replication requirement,"Regulatory, CAISI, and governance alignment",abstract_passable_proof_obligation,EMPIRICAL_CLAIM,,,,N/A,Empirical measurement + spec cleanup required.,Define benchmark target; clean up rewrite guardrail.
189,Gross-vs-net recovery separation rule,"Regulatory, CAISI, and governance alignment",abstract_passable_proof_obligation,REWRITE_RULE,,,,N/A,Terminology / spec guardrail — no formal proof required.,Audit documented claim; update whitepaper section.
190,Conditional QEC realization theorem,Conditional quantum and advanced research path,abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
191,Stabilizer validity theorem,Conditional quantum and advanced research path,abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
192,Holevo-bounded extraction theorem,Conditional quantum and advanced research path,abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
193,Measurement-collapse consent theorem,Conditional quantum and advanced research path,abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
194,Entanglement-induced correlation theorem,Conditional quantum and advanced research path,abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
195,Context-dependent measurement basis theorem,Conditional quantum and advanced research path,abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
196,Non-commutative consent algebra theorem,Conditional quantum and advanced research path,abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
197,Quantum consent channel theorem,Conditional quantum and advanced research path,abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
198,Contextual entanglement-wedge reconstruction theorem,Conditional quantum and advanced research path,abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
199,Information-percolation threshold theorem,Conditional quantum and advanced research path,abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
200,Consent capacity theorem,Conditional quantum and advanced research path,abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
201,Contextual consent kernel threshold theorem,Conditional quantum and advanced research path,abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
202,Dynamic consent mixing theorem,Conditional quantum and advanced research path,abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.
203,Arbitrary-graph consent threshold complexity theorem,Conditional quantum and advanced research path,abstract_passable_proof_obligation,FUTURE_OBLIGATION,,,,PENDING,Requires new formal definitions — no proof possible yet.,Define new types/predicates; formalize in Lean 4 or Coq.


1	(*
2	  CENTILLION CUBIE Q — QUANTUM CONTEXTUAL CONSENT MODULE
3	  Formalizes Theorems T5-T8 from the Quantum Contextual Consent
4	  Information Percolation framework.
5
6	  - T5: Measurement collapse changes consent (post-measurement
7	    agreement = 1.0 vs classical agreement = 0.5).
8	  - T6: Entanglement-enhanced threshold p_c(f_ent) = 0.5 - f_ent/4.
9	  - T7: Context-dependent quantum consent — non-commutative algebra
10	    [A, B] != [B, A].
11	  - T8: Holevo bound limits extraction I(S; Access) <= S(rho_consent).
12
13	  Constructive only. No Classical. No sorry. No propext.
14	*)
15
16	Require Import Coq.Arith.PeanoNat.
17	Require Import Coq.Init.Nat.
18	Require Import Lia.
19
20	Set Implicit Arguments.
21	Unset Strict Implicit.
22	Unset Printing Implicit Defensive.
23	Open Scope nat_scope.
24
25	Module CubieQuantumConsent.
26
27	(* ============================================================ *)
28	(* 1. Measurement bases (the requesters' contexts)              *)
29	(* ============================================================ *)
30
31	(* Two non-commuting measurement bases. *)
32	Inductive MeasurementBasis : Type :=
33	  | Computational     (* {|0⟩, |1⟩}, the Z basis *)
34	  | Hadamard.         (* {|+⟩, |−⟩}, the X basis *)
35
36	(* Consent outcomes from a measurement. *)
37	Inductive ConsentOutcome : Type :=
38	  | Grant
39	  | Deny.
40
41	(* Quantum consent state — abstract carrier. The actual Hilbert  *)
42	(* space is opaque; we postulate the measurement function.       *)
43	Parameter ConsentState : Type.
44
45	(* The |+⟩ superposition state: half-grant, half-deny in        *)
46	(* computational basis; deterministic-grant in Hadamard basis.   *)
47	Parameter PlusState : ConsentState.
48
49	(* Measurement function. In a classical model this would be     *)
50	(* deterministic; in the quantum model the outcome depends on   *)
51	(* the measurement basis (T7 non-commutativity).                *)
52	Parameter measure : ConsentState -> MeasurementBasis -> ConsentOutcome.
53
54	(* ============================================================ *)
55	(* 2. Theorem T7 axioms — the measurement basis discriminates    *)
56	(* ============================================================ *)
57
58	(* The plus state in the computational basis has a 50/50 outcome *)
59	(* — modeled here by stating only that the outcome can be either, *)
60	(* without privileging one. We use a sealed-state abstraction.    *)
61
62	Parameter measure_plus_computational_can_deny :
63	  measure PlusState Computational = Deny.
64
65	(* The plus state in the Hadamard basis is deterministically      *)
66	(* a grant (it is the +1 eigenstate of X).                        *)
67	Parameter measure_plus_hadamard_grants :
68	  measure PlusState Hadamard = Grant.
69
70	(* T7 — Same state, different measurement bases, different        *)
71	(* outcomes. This is the non-commutativity result: the order of   *)
72	(* measurement matters because the bases don't commute.           *)
73	Theorem T7_context_dependent_consent :
74	  measure PlusState Computational <> measure PlusState Hadamard.
75	Proof.
76	  rewrite measure_plus_computational_can_deny.
77	  rewrite measure_plus_hadamard_grants.
78	  discriminate.
79	Qed.
80
81	(* ============================================================ *)
82	(* 3. Non-commutative consent algebra                            *)
83	(* ============================================================ *)
84
85	(* Composition of two measurements. The order of composition     *)
86	(* affects the outcome — this is the core T7 result.             *)
87
88	Parameter measure_after :
89	  ConsentState -> MeasurementBasis -> MeasurementBasis -> ConsentOutcome.
90
91	(* [A, B] applies A first, then B to the post-A state.           *)
92	Definition commutator_AB (s : ConsentState) :
93	  ConsentOutcome := measure_after s Computational Hadamard.
94
95	(* [B, A] applies B first, then A to the post-B state.           *)
96	Definition commutator_BA (s : ConsentState) :
97	  ConsentOutcome := measure_after s Hadamard Computational.
98
99	(* The two orderings can disagree, witnessing non-commutativity. *)
100	Parameter non_commutativity_witness :
101	  exists s : ConsentState, commutator_AB s <> commutator_BA s.
102
103	Theorem non_commutativity_holds : exists s, commutator_AB s <> commutator_BA s.
104	Proof. exact non_commutativity_witness. Qed.
105
106	(* ============================================================ *)
107	(* 4. Theorem T6 — Entanglement-enhanced threshold               *)
108	(* ============================================================ *)
109
110	(* Entanglement fraction f_ent is modeled as a value in {0..100}. *)
111	(* We work in nat with f_ent representing percentage points.     *)
112	(* The classical critical threshold is 50 (representing 0.5).    *)
113	(* The entanglement-enhanced threshold is 50 - f_ent/4.          *)
114
115	Definition entanglement_fraction := nat.  (* 0..100 *)
116	Definition critical_threshold_classical : nat := 50.
117
118	Definition critical_threshold_quantum (f_ent : nat) : nat :=
119	  critical_threshold_classical - f_ent / 4.
120
121	(* T6 — Entanglement strictly lowers the critical threshold     *)
122	(* when f_ent >= 4 (one quarter of an entanglement bit).         *)
123	Theorem T6_entanglement_lowers_threshold :
124	  forall f_ent : nat, f_ent >= 4 ->
125	  critical_threshold_quantum f_ent < critical_threshold_classical.
126	Proof.
127	  intros f_ent Hf. unfold critical_threshold_quantum, critical_threshold_classical.
128	  assert (f_ent / 4 >= 1).
129	  { apply Nat.div_le_lower_bound; lia. }
130	  lia.
131	Qed.
132
133	(* At f_ent = 100% (full entanglement), threshold drops by 25.   *)
134	Theorem T6_full_entanglement_threshold :
135	  critical_threshold_quantum 100 = 25.
136	Proof. reflexivity. Qed.
137
138	(* At f_ent = 50%, threshold drops by 12 (integer division).    *)
139	Theorem T6_half_entanglement_threshold :
140	  critical_threshold_quantum 50 = 38.
141	Proof. reflexivity. Qed.
142
143	(* ============================================================ *)
144	(* 5. Theorem T8 — Holevo bound on extractable information       *)
145	(* ============================================================ *)
146
147	(* The Holevo bound states that classical information accessible *)
148	(* from a quantum source S is bounded above by the von Neumann   *)
149	(* entropy of the consent state. We model this as an inequality  *)
150	(* between two opaque numerics.                                  *)
151
152	Parameter accessible_information : nat.  (* I(S; Access)        *)
153	Parameter consent_state_entropy : nat.   (* S(rho_consent)      *)
154
155	(* T8 — Holevo bound: extractable info bounded by entropy.       *)
156	Parameter T8_holevo_bound :
157	  accessible_information <= consent_state_entropy.
158
159	Theorem T8_holevo_bound_holds :
160	  accessible_information <= consent_state_entropy.
161	Proof. exact T8_holevo_bound. Qed.
162
163	(* Information gap: the difference between the bound and the    *)
164	(* actual extractable information. This is the "blindness"      *)
165	(* margin the framework guarantees.                             *)
166	Definition information_gap : nat :=
167	  consent_state_entropy - accessible_information.
168
169	Theorem information_gap_nonneg :
170	  consent_state_entropy >= accessible_information.
171	Proof. apply T8_holevo_bound. Qed.
172
173	(* ============================================================ *)
174	(* 6. Theorem T5 — Measurement collapse changes consent         *)
175	(* ============================================================ *)
176
177	(* Once a quantum state is measured, subsequent measurements in   *)
178	(* the same basis yield the same outcome (collapse). This is the *)
179	(* "checking consent changes it" property.                        *)
180
181	Parameter post_measurement_state :
182	  ConsentState -> MeasurementBasis -> ConsentState.
183
184	(* After measuring s in basis b, re-measuring in the same basis  *)
185	(* yields the same outcome. *)
186	Parameter T5_collapse_idempotent :
187	  forall s : ConsentState, forall b : MeasurementBasis,
188	  measure (post_measurement_state s b) b = measure s b.
189
190	Theorem T5_collapse_idempotent_holds :
191	  forall s : ConsentState, forall b : MeasurementBasis,
192	  measure (post_measurement_state s b) b = measure s b.
193	Proof. exact T5_collapse_idempotent. Qed.
194
195	(* Post-measurement agreement rate. After collapse, two           *)
196	(* requesters using the same basis always agree.                  *)
197	Definition post_measurement_agreement (s : ConsentState) (b : MeasurementBasis) : Prop :=
198	  measure (post_measurement_state s b) b = measure s b.
199
200	Theorem T5_post_measurement_agreement_universal :
201	  forall s b, post_measurement_agreement s b.
202	Proof.
203	  intros s b. unfold post_measurement_agreement.
204	  apply T5_collapse_idempotent.
205	Qed.
206
207	End CubieQuantumConsent.
208

(*
  CENTILLION CUBIE Q — QUANTUM CONTEXTUAL CONSENT MODULE
  Formalizes Theorems T5-T8 from the Quantum Contextual Consent
  Information Percolation framework.

  - T5: Measurement collapse changes consent (post-measurement
    agreement = 1.0 vs classical agreement = 0.5).
  - T6: Entanglement-enhanced threshold p_c(f_ent) = 0.5 - f_ent/4.
  - T7: Context-dependent quantum consent — non-commutative algebra
    [A, B] != [B, A].
  - T8: Holevo bound limits extraction I(S; Access) <= S(rho_consent).

  Constructive only. No Classical. No sorry. No propext.
*)

Require Import Coq.Arith.PeanoNat.
Require Import Coq.Init.Nat.
Require Import Lia.

Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
Open Scope nat_scope.

Module CubieQuantumConsent.

(* ============================================================ *)
(* 1. Measurement bases (the requesters' contexts)              *)
(* ============================================================ *)

(* Two non-commuting measurement bases. *)
Inductive MeasurementBasis : Type :=
  | Computational     (* {|0⟩, |1⟩}, the Z basis *)
  | Hadamard.         (* {|+⟩, |−⟩}, the X basis *)

(* Consent outcomes from a measurement. *)
Inductive ConsentOutcome : Type :=
  | Grant
  | Deny.

(* Quantum consent state — abstract carrier. The actual Hilbert  *)
(* space is opaque; we postulate the measurement function.       *)
Parameter ConsentState : Type.

(* The |+⟩ superposition state: half-grant, half-deny in        *)
(* computational basis; deterministic-grant in Hadamard basis.   *)
Parameter PlusState : ConsentState.

(* Measurement function. In a classical model this would be     *)
(* deterministic; in the quantum model the outcome depends on   *)
(* the measurement basis (T7 non-commutativity).                *)
Parameter measure : ConsentState -> MeasurementBasis -> ConsentOutcome.

(* ============================================================ *)
(* 2. Theorem T7 axioms — the measurement basis discriminates    *)
(* ============================================================ *)

(* The plus state in the computational basis has a 50/50 outcome *)
(* — modeled here by stating only that the outcome can be either, *)
(* without privileging one. We use a sealed-state abstraction.    *)

Parameter measure_plus_computational_can_deny :
  measure PlusState Computational = Deny.

(* The plus state in the Hadamard basis is deterministically      *)
(* a grant (it is the +1 eigenstate of X).                        *)
Parameter measure_plus_hadamard_grants :
  measure PlusState Hadamard = Grant.

(* T7 — Same state, different measurement bases, different        *)
(* outcomes. This is the non-commutativity result: the order of   *)
(* measurement matters because the bases don't commute.           *)
Theorem T7_context_dependent_consent :
  measure PlusState Computational <> measure PlusState Hadamard.
Proof.
  rewrite measure_plus_computational_can_deny.
  rewrite measure_plus_hadamard_grants.
  discriminate.
Qed.

(* ============================================================ *)
(* 3. Non-commutative consent algebra                            *)
(* ============================================================ *)

(* Composition of two measurements. The order of composition     *)
(* affects the outcome — this is the core T7 result.             *)

Parameter measure_after :
  ConsentState -> MeasurementBasis -> MeasurementBasis -> ConsentOutcome.

(* [A, B] applies A first, then B to the post-A state.           *)
Definition commutator_AB (s : ConsentState) :
  ConsentOutcome := measure_after s Computational Hadamard.

(* [B, A] applies B first, then A to the post-B state.           *)
Definition commutator_BA (s : ConsentState) :
  ConsentOutcome := measure_after s Hadamard Computational.

(* The two orderings can disagree, witnessing non-commutativity. *)
Parameter non_commutativity_witness :
  exists s : ConsentState, commutator_AB s <> commutator_BA s.

Theorem non_commutativity_holds : exists s, commutator_AB s <> commutator_BA s.
Proof. exact non_commutativity_witness. Qed.

(* ============================================================ *)
(* 4. Theorem T6 — Entanglement-enhanced threshold               *)
(* ============================================================ *)

(* Entanglement fraction f_ent is modeled as a value in {0..100}. *)
(* We work in nat with f_ent representing percentage points.     *)
(* The classical critical threshold is 50 (representing 0.5).    *)
(* The entanglement-enhanced threshold is 50 - f_ent/4.          *)

Definition entanglement_fraction := nat.  (* 0..100 *)
Definition critical_threshold_classical : nat := 50.

Definition critical_threshold_quantum (f_ent : nat) : nat :=
  critical_threshold_classical - f_ent / 4.

(* T6 — Entanglement strictly lowers the critical threshold     *)
(* when f_ent >= 4 (one quarter of an entanglement bit).         *)
Theorem T6_entanglement_lowers_threshold :
  forall f_ent : nat, f_ent >= 4 ->
  critical_threshold_quantum f_ent < critical_threshold_classical.
Proof.
  intros f_ent Hf. unfold critical_threshold_quantum, critical_threshold_classical.
  assert (f_ent / 4 >= 1).
  { apply Nat.div_le_lower_bound; lia. }
  lia.
Qed.

(* At f_ent = 100% (full entanglement), threshold drops by 25.   *)
Theorem T6_full_entanglement_threshold :
  critical_threshold_quantum 100 = 25.
Proof. reflexivity. Qed.

(* At f_ent = 50%, threshold drops by 12 (integer division).    *)
Theorem T6_half_entanglement_threshold :
  critical_threshold_quantum 50 = 38.
Proof. reflexivity. Qed.

(* ============================================================ *)
(* 5. Theorem T8 — Holevo bound on extractable information       *)
(* ============================================================ *)

(* The Holevo bound states that classical information accessible *)
(* from a quantum source S is bounded above by the von Neumann   *)
(* entropy of the consent state. We model this as an inequality  *)
(* between two opaque numerics.                                  *)

Parameter accessible_information : nat.  (* I(S; Access)        *)
Parameter consent_state_entropy : nat.   (* S(rho_consent)      *)

(* T8 — Holevo bound: extractable info bounded by entropy.       *)
Parameter T8_holevo_bound :
  accessible_information <= consent_state_entropy.

Theorem T8_holevo_bound_holds :
  accessible_information <= consent_state_entropy.
Proof. exact T8_holevo_bound. Qed.

(* Information gap: the difference between the bound and the    *)
(* actual extractable information. This is the "blindness"      *)
(* margin the framework guarantees.                             *)
Definition information_gap : nat :=
  consent_state_entropy - accessible_information.

Theorem information_gap_nonneg :
  consent_state_entropy >= accessible_information.
Proof. apply T8_holevo_bound. Qed.

(* ============================================================ *)
(* 6. Theorem T5 — Measurement collapse changes consent         *)
(* ============================================================ *)

(* Once a quantum state is measured, subsequent measurements in   *)
(* the same basis yield the same outcome (collapse). This is the *)
(* "checking consent changes it" property.                        *)

Parameter post_measurement_state :
  ConsentState -> MeasurementBasis -> ConsentState.

(* After measuring s in basis b, re-measuring in the same basis  *)
(* yields the same outcome. *)
Parameter T5_collapse_idempotent :
  forall s : ConsentState, forall b : MeasurementBasis,
  measure (post_measurement_state s b) b = measure s b.

Theorem T5_collapse_idempotent_holds :
  forall s : ConsentState, forall b : MeasurementBasis,
  measure (post_measurement_state s b) b = measure s b.
Proof. exact T5_collapse_idempotent. Qed.

(* Post-measurement agreement rate. After collapse, two           *)
(* requesters using the same basis always agree.                  *)
Definition post_measurement_agreement (s : ConsentState) (b : MeasurementBasis) : Prop :=
  measure (post_measurement_state s b) b = measure s b.

Theorem T5_post_measurement_agreement_universal :
  forall s b, post_measurement_agreement s b.
Proof.
  intros s b. unfold post_measurement_agreement.
  apply T5_collapse_idempotent.
Qed.

End CubieQuantumConsent.


1	// cubie_delegation_spec.rs — Verus spec for delegated permission model
2	//
3	// Corresponds to: CubieTrustCompilerV1_50 / V2_0 delegation chain
4	// ENGINEERING_INVARIANT: bounded delegation depth, HMAC presence gate
5	//
6	// Design constraints:
7	//   - capability_hmac_valid is an UNINTERPRETED trusted predicate.
8	//     Correctness of HMAC computation is NOT attempted here.
9	//     The only claim: if it returns false, the request is denied.
10	//   - Delegation depth must not exceed MAX_DELEGATION_DEPTH.
11	//   - parent_request_hash and parent_chain_hash must be preserved
12	//     across the delegation chain (continuity invariants).
13	//   - No asymmetric crypto in hot path.
14
15	#![allow(unused_imports)]
16	use vstd::prelude::*;
17
18	verus! {
19
20	// ---------------------------------------------------------------------------
21	// Constants
22	// ---------------------------------------------------------------------------
23
24	/// Maximum allowed delegation depth.
25	/// Requests at depth > MAX_DELEGATION_DEPTH must receive DENY_DEPTH.
26	pub const MAX_DELEGATION_DEPTH: u8 = 8u8;
27
28	// ---------------------------------------------------------------------------
29	// Structs
30	// ---------------------------------------------------------------------------
31
32	/// A delegated CubieRequest with parent chain fields.
33	pub struct DelegatedRequest {
34	    /// Hash of the immediate parent request (continuity invariant).
35	    pub parent_request_hash: u64,
36	    /// Hash of the entire parent chain (continuity invariant).
37	    pub parent_chain_hash:   u64,
38	    /// Depth in the delegation chain (0 = root, max = MAX_DELEGATION_DEPTH).
39	    pub delegation_depth:    u8,
40	    /// Structural flag: HMAC was present in the envelope (not validated here).
41	    pub capability_hmac_present: bool,
42	}
43
44	/// Denial codes for delegation violations.
45	pub enum DelegationDenyCode {
46	    DenyDepth,
47	    DenyHmacMissing,
48	    DenyChainHashMismatch,
49	}
50
51	// ---------------------------------------------------------------------------
52	// Uninterpreted trusted predicate
53	// ---------------------------------------------------------------------------
54
55	/// HMAC validity predicate — UNINTERPRETED.
56	///
57	/// This predicate is declared but not defined. In the production runtime it
58	/// wraps the result of a constant-time HMAC-SHA256 verification.
59	///
60	/// The Verus proofs only claim: if this is false, the request is denied.
61	/// Cryptographic correctness is a FUTURE_OBLIGATION (Verus crypto library needed).
62	pub spec fn capability_hmac_valid(req: &DelegatedRequest) -> bool;
63
64	// ---------------------------------------------------------------------------
65	// Spec functions
66	// ---------------------------------------------------------------------------
67
68	/// True iff delegation depth is within the allowed bound.
69	pub open spec fn depth_within_bound(req: &DelegatedRequest) -> bool {
70	    req.delegation_depth <= MAX_DELEGATION_DEPTH
71	}
72
73	/// True iff the HMAC is present (structural envelope check).
74	/// Note: presence ≠ validity. validity is capability_hmac_valid().
75	pub open spec fn hmac_present(req: &DelegatedRequest) -> bool {
76	    req.capability_hmac_present
77	}
78
79	/// True iff all delegation invariants pass (depth + HMAC + structural).
80	pub open spec fn delegation_ok(req: &DelegatedRequest) -> bool {
81	    depth_within_bound(req) && capability_hmac_valid(req) && hmac_present(req)
82	}
83
84	// ---------------------------------------------------------------------------
85	// Invariant proofs
86	// ---------------------------------------------------------------------------
87
88	/// Theorem: depth exceeded implies denial.
89	/// ENGINEERING_INVARIANT: any request at depth > MAX_DELEGATION_DEPTH must be denied.
90	proof fn deny_on_depth_exceeded(req: &DelegatedRequest)
91	    requires req.delegation_depth > MAX_DELEGATION_DEPTH
92	    ensures  !depth_within_bound(req) && !delegation_ok(req)
93	{
94	    // depth_within_bound = (depth <= MAX) = false when depth > MAX
95	}
96
97	/// Theorem: if HMAC validity predicate fails, delegation_ok fails.
98	/// This is the key safety claim: invalid HMAC always produces deny.
99	proof fn deny_on_invalid_hmac(req: &DelegatedRequest)
100	    requires !capability_hmac_valid(req)
101	    ensures  !delegation_ok(req)
102	{
103	    // delegation_ok = ... && capability_hmac_valid && ...
104	    // If capability_hmac_valid is false, conjunction is false.
105	}
106
107	/// Theorem: if HMAC is structurally absent, delegation_ok fails.
108	proof fn deny_on_hmac_missing(req: &DelegatedRequest)
109	    requires !hmac_present(req)
110	    ensures  !delegation_ok(req)
111	{
112	    // delegation_ok = ... && hmac_present && ...
113	}
114
115	/// Theorem: parent_request_hash continuity.
116	/// The parent hash must equal the value established at the delegation boundary.
117	/// This is a structural invariant: the runtime must not mutate parent_request_hash
118	/// after the envelope is sealed.
119	proof fn parent_request_hash_continuity(req: &DelegatedRequest, original_hash: u64)
120	    requires req.parent_request_hash == original_hash
121	    ensures  req.parent_request_hash == original_hash
122	{
123	    // Trivial structural invariant — documented for audit trail
124	}
125
126	/// Theorem: parent_chain_hash continuity.
127	/// The chain hash accumulates all parent hashes. Must not be modified
128	/// after sealing. The runtime must treat it as read-only.
129	proof fn parent_chain_hash_continuity(req: &DelegatedRequest, expected_chain: u64)
130	    requires req.parent_chain_hash == expected_chain
131	    ensures  req.parent_chain_hash == expected_chain
132	{
133	    // Structural invariant — enforces immutability of sealed chain hash
134	}
135
136	/// Theorem: depth monotone — a child's depth is strictly greater than its parent's.
137	/// Prevents cycles and depth inflation.
138	proof fn depth_is_monotone(parent_depth: u8, child_depth: u8)
139	    requires child_depth == parent_depth + 1u8
140	    ensures  child_depth > parent_depth
141	{
142	    // child_depth = parent_depth + 1 > parent_depth
143	}
144
145	/// Theorem: root request has depth 0.
146	proof fn root_has_zero_depth(req: &DelegatedRequest)
147	    requires req.delegation_depth == 0u8
148	    ensures  depth_within_bound(req)
149	{
150	    // 0 <= MAX_DELEGATION_DEPTH (8)
151	}
152
153	/// Theorem: delegation chain bounded — after MAX_DELEGATION_DEPTH steps,
154	/// any further child is denied at depth gate before other checks.
155	proof fn chain_is_bounded(req: &DelegatedRequest)
156	    requires req.delegation_depth == MAX_DELEGATION_DEPTH
157	    ensures  depth_within_bound(req)
158	{
159	    // MAX_DELEGATION_DEPTH <= MAX_DELEGATION_DEPTH ✓
160	}
161
162	// ---------------------------------------------------------------------------
163	// Active-active split-brain safety
164	// ---------------------------------------------------------------------------
165
166	/// Theorem: deterministic decision — same request, same epoch, same state
167	/// produces the same delegation_ok result on any appliance.
168	///
169	/// VERIFIED_EXACT: CubieTrustCompilerV2_0.ha_split_brain_fail_closed (partial)
170	///
171	/// The full split-brain theorem requires distributed state assumptions.
172	/// This Verus fragment proves the spec function is pure (deterministic).
173	proof fn delegation_ok_is_deterministic(req: &DelegatedRequest)
174	    ensures delegation_ok(req) == delegation_ok(req)
175	{
176	    // Pure spec function: same input => same output
177	}
178
179	/// EXEC: delegation gate — hmac_result is the output of the hardware HMAC verifier.
180	pub fn exec_delegation_ok(req: &DelegatedRequest, hmac_result: bool) -> (result: bool)
181	    requires capability_hmac_valid(req) == hmac_result,
182	    ensures  result == delegation_ok(req),
183	{
184	    req.delegation_depth <= MAX_DELEGATION_DEPTH && hmac_result && req.capability_hmac_present
185	}
186
187	} // verus!
188

// cubie_delegation_spec.rs — Verus spec for delegated permission model
//
// Corresponds to: CubieTrustCompilerV1_50 / V2_0 delegation chain
// ENGINEERING_INVARIANT: bounded delegation depth, HMAC presence gate
//
// Design constraints:
//   - capability_hmac_valid is an UNINTERPRETED trusted predicate.
//     Correctness of HMAC computation is NOT attempted here.
//     The only claim: if it returns false, the request is denied.
//   - Delegation depth must not exceed MAX_DELEGATION_DEPTH.
//   - parent_request_hash and parent_chain_hash must be preserved
//     across the delegation chain (continuity invariants).
//   - No asymmetric crypto in hot path.

#![allow(unused_imports)]
use vstd::prelude::*;

verus! {

// ---------------------------------------------------------------------------
// Constants
// ---------------------------------------------------------------------------

/// Maximum allowed delegation depth.
/// Requests at depth > MAX_DELEGATION_DEPTH must receive DENY_DEPTH.
pub const MAX_DELEGATION_DEPTH: u8 = 8u8;

// ---------------------------------------------------------------------------
// Structs
// ---------------------------------------------------------------------------

/// A delegated CubieRequest with parent chain fields.
pub struct DelegatedRequest {
    /// Hash of the immediate parent request (continuity invariant).
    pub parent_request_hash: u64,
    /// Hash of the entire parent chain (continuity invariant).
    pub parent_chain_hash:   u64,
    /// Depth in the delegation chain (0 = root, max = MAX_DELEGATION_DEPTH).
    pub delegation_depth:    u8,
    /// Structural flag: HMAC was present in the envelope (not validated here).
    pub capability_hmac_present: bool,
}

/// Denial codes for delegation violations.
pub enum DelegationDenyCode {
    DenyDepth,
    DenyHmacMissing,
    DenyChainHashMismatch,
}

// ---------------------------------------------------------------------------
// Uninterpreted trusted predicate
// ---------------------------------------------------------------------------

/// HMAC validity predicate — UNINTERPRETED.
///
/// This predicate is declared but not defined. In the production runtime it
/// wraps the result of a constant-time HMAC-SHA256 verification.
///
/// The Verus proofs only claim: if this is false, the request is denied.
/// Cryptographic correctness is a FUTURE_OBLIGATION (Verus crypto library needed).
pub spec fn capability_hmac_valid(req: &DelegatedRequest) -> bool;

// ---------------------------------------------------------------------------
// Spec functions
// ---------------------------------------------------------------------------

/// True iff delegation depth is within the allowed bound.
pub open spec fn depth_within_bound(req: &DelegatedRequest) -> bool {
    req.delegation_depth <= MAX_DELEGATION_DEPTH
}

/// True iff the HMAC is present (structural envelope check).
/// Note: presence ≠ validity. validity is capability_hmac_valid().
pub open spec fn hmac_present(req: &DelegatedRequest) -> bool {
    req.capability_hmac_present
}

/// True iff all delegation invariants pass (depth + HMAC + structural).
pub open spec fn delegation_ok(req: &DelegatedRequest) -> bool {
    depth_within_bound(req) && capability_hmac_valid(req) && hmac_present(req)
}

// ---------------------------------------------------------------------------
// Invariant proofs
// ---------------------------------------------------------------------------

/// Theorem: depth exceeded implies denial.
/// ENGINEERING_INVARIANT: any request at depth > MAX_DELEGATION_DEPTH must be denied.
proof fn deny_on_depth_exceeded(req: &DelegatedRequest)
    requires req.delegation_depth > MAX_DELEGATION_DEPTH
    ensures  !depth_within_bound(req) && !delegation_ok(req)
{
    // depth_within_bound = (depth <= MAX) = false when depth > MAX
}

/// Theorem: if HMAC validity predicate fails, delegation_ok fails.
/// This is the key safety claim: invalid HMAC always produces deny.
proof fn deny_on_invalid_hmac(req: &DelegatedRequest)
    requires !capability_hmac_valid(req)
    ensures  !delegation_ok(req)
{
    // delegation_ok = ... && capability_hmac_valid && ...
    // If capability_hmac_valid is false, conjunction is false.
}

/// Theorem: if HMAC is structurally absent, delegation_ok fails.
proof fn deny_on_hmac_missing(req: &DelegatedRequest)
    requires !hmac_present(req)
    ensures  !delegation_ok(req)
{
    // delegation_ok = ... && hmac_present && ...
}

/// Theorem: parent_request_hash continuity.
/// The parent hash must equal the value established at the delegation boundary.
/// This is a structural invariant: the runtime must not mutate parent_request_hash
/// after the envelope is sealed.
proof fn parent_request_hash_continuity(req: &DelegatedRequest, original_hash: u64)
    requires req.parent_request_hash == original_hash
    ensures  req.parent_request_hash == original_hash
{
    // Trivial structural invariant — documented for audit trail
}

/// Theorem: parent_chain_hash continuity.
/// The chain hash accumulates all parent hashes. Must not be modified
/// after sealing. The runtime must treat it as read-only.
proof fn parent_chain_hash_continuity(req: &DelegatedRequest, expected_chain: u64)
    requires req.parent_chain_hash == expected_chain
    ensures  req.parent_chain_hash == expected_chain
{
    // Structural invariant — enforces immutability of sealed chain hash
}

/// Theorem: depth monotone — a child's depth is strictly greater than its parent's.
/// Prevents cycles and depth inflation.
proof fn depth_is_monotone(parent_depth: u8, child_depth: u8)
    requires child_depth == parent_depth + 1u8
    ensures  child_depth > parent_depth
{
    // child_depth = parent_depth + 1 > parent_depth
}

/// Theorem: root request has depth 0.
proof fn root_has_zero_depth(req: &DelegatedRequest)
    requires req.delegation_depth == 0u8
    ensures  depth_within_bound(req)
{
    // 0 <= MAX_DELEGATION_DEPTH (8)
}

/// Theorem: delegation chain bounded — after MAX_DELEGATION_DEPTH steps,
/// any further child is denied at depth gate before other checks.
proof fn chain_is_bounded(req: &DelegatedRequest)
    requires req.delegation_depth == MAX_DELEGATION_DEPTH
    ensures  depth_within_bound(req)
{
    // MAX_DELEGATION_DEPTH <= MAX_DELEGATION_DEPTH ✓
}

// ---------------------------------------------------------------------------
// Active-active split-brain safety
// ---------------------------------------------------------------------------

/// Theorem: deterministic decision — same request, same epoch, same state
/// produces the same delegation_ok result on any appliance.
///
/// VERIFIED_EXACT: CubieTrustCompilerV2_0.ha_split_brain_fail_closed (partial)
///
/// The full split-brain theorem requires distributed state assumptions.
/// This Verus fragment proves the spec function is pure (deterministic).
proof fn delegation_ok_is_deterministic(req: &DelegatedRequest)
    ensures delegation_ok(req) == delegation_ok(req)
{
    // Pure spec function: same input => same output
}

/// EXEC: delegation gate — hmac_result is the output of the hardware HMAC verifier.
pub fn exec_delegation_ok(req: &DelegatedRequest, hmac_result: bool) -> (result: bool)
    requires capability_hmac_valid(req) == hmac_result,
    ensures  result == delegation_ok(req),
{
    req.delegation_depth <= MAX_DELEGATION_DEPTH && hmac_result && req.capability_hmac_present
}

} // verus!


Let me also check existing Lean patterns and the bare-metal HMAC code that we'll reference.


No files found


1	//! HMAC-SHA256 per FIPS 198-1 — no_std, no heap, no external crates.
2	//!
3	//! hmac_sha256(key: &[u8; 32], msg: &[u8]) -> [u8; 32]
4	//!
5	//! Key is always 32 bytes (eFuse slot output). Block-size key = key padded
6	//! with 0x00 bytes to 64 bytes.  Inner and outer hash inputs are stacked
7	//! on the call-frame as fixed-size arrays — no allocations.
8
9	use crate::sha256::sha256;
10
11	/// HMAC-SHA256 (FIPS 198-1).
12	///
13	/// `key` — 32-byte symmetric key (e.g. read from eFuse slot).
14	/// `msg` — message bytes (up to 64 bytes for single outer-block; longer
15	///          messages still work via sha256's multi-block path).
16	pub fn hmac_sha256(key: &[u8; 32], msg: &[u8]) -> [u8; 32] {
17	    // ------------------------------------------------------------------
18	    // Inner hash: H( (K ⊕ ipad) ∥ msg )
19	    //   K padded to 64 bytes: key[0..32] ⊕ 0x36, zeros[32..64] ⊕ 0x36
20	    // ------------------------------------------------------------------
21	    // Buffer is 64 (ipad key) + 64 (max msg) = 128 bytes.
22	    // For capability_hmac_verify the message is always 8 bytes (u64).
23	    let mlen = msg.len();
24	    let mut inner = [0u8; 128];
25	    for i in 0..32 {
26	        inner[i] = key[i] ^ 0x36;
27	    }
28	    for i in 32..64 {
29	        inner[i] = 0x36; // zero-pad ^ ipad
30	    }
31	    inner[64..64 + mlen].copy_from_slice(msg);
32	    let inner_hash = sha256(&inner[..64 + mlen]);
33
34	    // ------------------------------------------------------------------
35	    // Outer hash: H( (K ⊕ opad) ∥ inner_hash )
36	    //   K padded to 64 bytes: key[0..32] ⊕ 0x5c, zeros[32..64] ⊕ 0x5c
37	    //   Outer input is always exactly 64 + 32 = 96 bytes.
38	    // ------------------------------------------------------------------
39	    let mut outer = [0u8; 96];
40	    for i in 0..32 {
41	        outer[i] = key[i] ^ 0x5c;
42	    }
43	    for i in 32..64 {
44	        outer[i] = 0x5c;
45	    }
46	    outer[64..96].copy_from_slice(&inner_hash);
47	    sha256(&outer)
48	}
49
50	/// Constant-time 32-byte equality — avoids early-exit timing oracle.
51	pub fn ct_eq_32(a: &[u8; 32], b: &[u8; 32]) -> bool {
52	    let mut diff = 0u8;
53	    for i in 0..32 {
54	        diff |= a[i] ^ b[i];
55	    }
56	    diff == 0
57	}
58

//! HMAC-SHA256 per FIPS 198-1 — no_std, no heap, no external crates.
//!
//! hmac_sha256(key: &[u8; 32], msg: &[u8]) -> [u8; 32]
//!
//! Key is always 32 bytes (eFuse slot output). Block-size key = key padded
//! with 0x00 bytes to 64 bytes.  Inner and outer hash inputs are stacked
//! on the call-frame as fixed-size arrays — no allocations.

use crate::sha256::sha256;

/// HMAC-SHA256 (FIPS 198-1).
///
/// `key` — 32-byte symmetric key (e.g. read from eFuse slot).
/// `msg` — message bytes (up to 64 bytes for single outer-block; longer
///          messages still work via sha256's multi-block path).
pub fn hmac_sha256(key: &[u8; 32], msg: &[u8]) -> [u8; 32] {
    // ------------------------------------------------------------------
    // Inner hash: H( (K ⊕ ipad) ∥ msg )
    //   K padded to 64 bytes: key[0..32] ⊕ 0x36, zeros[32..64] ⊕ 0x36
    // ------------------------------------------------------------------
    // Buffer is 64 (ipad key) + 64 (max msg) = 128 bytes.
    // For capability_hmac_verify the message is always 8 bytes (u64).
    let mlen = msg.len();
    let mut inner = [0u8; 128];
    for i in 0..32 {
        inner[i] = key[i] ^ 0x36;
    }
    for i in 32..64 {
        inner[i] = 0x36; // zero-pad ^ ipad
    }
    inner[64..64 + mlen].copy_from_slice(msg);
    let inner_hash = sha256(&inner[..64 + mlen]);

    // ------------------------------------------------------------------
    // Outer hash: H( (K ⊕ opad) ∥ inner_hash )
    //   K padded to 64 bytes: key[0..32] ⊕ 0x5c, zeros[32..64] ⊕ 0x5c
    //   Outer input is always exactly 64 + 32 = 96 bytes.
    // ------------------------------------------------------------------
    let mut outer = [0u8; 96];
    for i in 0..32 {
        outer[i] = key[i] ^ 0x5c;
    }
    for i in 32..64 {
        outer[i] = 0x5c;
    }
    outer[64..96].copy_from_slice(&inner_hash);
    sha256(&outer)
}

/// Constant-time 32-byte equality — avoids early-exit timing oracle.
pub fn ct_eq_32(a: &[u8; 32], b: &[u8; 32]) -> bool {
    let mut diff = 0u8;
    for i in 0..32 {
        diff |= a[i] ^ b[i];
    }
    diff == 0
}


1	//! HMAC-SHA256 capability verifier — hardware-backed implementation.
2	//!
3	//! Replaces the previous all-deny stub.  Key material is read from
4	//! eFuse MMIO registers at the slot index carried in CubieRequest.key_slot.
5	//!
6	//! Verification steps:
7	//!   1. Read 32-byte symmetric key from eFuse slot `key_slot`  (MMIO)
8	//!   2. Compute HMAC-SHA256(key, request_hash.to_be_bytes())
9	//!   3. Compare first 8 bytes of HMAC with capability_hmac (big-endian u64)
10	//!   4. Return true iff they match (constant-time comparison)
11	//!
12	//! Key derivation: each eFuse slot holds an independent 256-bit key.
13	//! Slot 0 is reserved for the platform root key.
14	//! Slots 1–7 are capability-tier keys (provisioned at manufacturing).
15
16	use crate::hmac::{hmac_sha256, ct_eq_32};
17	use crate::mmio;
18
19	/// Verify a capability HMAC against a hardware eFuse key.
20	///
21	/// # Arguments
22	/// * `request_hash`   — 64-bit hash of the CubieRequest content fields
23	/// * `capability_hmac`— first 8 bytes of the expected HMAC (big-endian u64)
24	/// * `key_slot`       — eFuse key slot index (0–7; 0 = platform root)
25	///
26	/// # Returns
27	/// `true`  — HMAC verified: capability is authentic.
28	/// `false` — HMAC mismatch or key unreadable: deny.
29	///
30	/// # Safety
31	/// Reads from eFuse MMIO registers.  The firmware must map the eFuse
32	/// region before calling `cubie_admit`.
33	pub fn capability_hmac_verify(
34	    request_hash:    u64,
35	    capability_hmac: u64,
36	    key_slot:        u8,
37	) -> bool {
38	    // Step 1: Read key material from eFuse hardware.
39	    // SAFETY: key_slot is carried in the request; out-of-range slots read
40	    // from unmapped memory and will fault — the firmware is responsible for
41	    // providing a valid slot (0–7).
42	    let key = unsafe { mmio::read_efuse_key(key_slot) };
43
44	    // Step 2: Compute HMAC-SHA256(key, request_hash as 8 big-endian bytes).
45	    let msg = request_hash.to_be_bytes();
46	    let mac = hmac_sha256(&key, &msg);
47
48	    // Step 3: Build expected 32-byte comparison buffer.
49	    // Upper 8 bytes match capability_hmac; remaining bytes must be zero
50	    // (truncated MAC comparison — only the first 8 bytes are transmitted).
51	    let mut expected = [0u8; 32];
52	    expected[0..8].copy_from_slice(&capability_hmac.to_be_bytes());
53
54	    // Step 4: Constant-time compare to prevent timing oracle.
55	    // We compare the full 32 bytes: mac[0..8] vs capability_hmac bytes,
56	    // mac[8..32] vs zeros.  Both sides are included in ct_eq_32.
57	    let mut mac_truncated = [0u8; 32];
58	    mac_truncated[0..8].copy_from_slice(&mac[0..8]);
59
60	    ct_eq_32(&mac_truncated, &expected)
61	}
62

//! HMAC-SHA256 capability verifier — hardware-backed implementation.
//!
//! Replaces the previous all-deny stub.  Key material is read from
//! eFuse MMIO registers at the slot index carried in CubieRequest.key_slot.
//!
//! Verification steps:
//!   1. Read 32-byte symmetric key from eFuse slot `key_slot`  (MMIO)
//!   2. Compute HMAC-SHA256(key, request_hash.to_be_bytes())
//!   3. Compare first 8 bytes of HMAC with capability_hmac (big-endian u64)
//!   4. Return true iff they match (constant-time comparison)
//!
//! Key derivation: each eFuse slot holds an independent 256-bit key.
//! Slot 0 is reserved for the platform root key.
//! Slots 1–7 are capability-tier keys (provisioned at manufacturing).

use crate::hmac::{hmac_sha256, ct_eq_32};
use crate::mmio;

/// Verify a capability HMAC against a hardware eFuse key.
///
/// # Arguments
/// * `request_hash`   — 64-bit hash of the CubieRequest content fields
/// * `capability_hmac`— first 8 bytes of the expected HMAC (big-endian u64)
/// * `key_slot`       — eFuse key slot index (0–7; 0 = platform root)
///
/// # Returns
/// `true`  — HMAC verified: capability is authentic.
/// `false` — HMAC mismatch or key unreadable: deny.
///
/// # Safety
/// Reads from eFuse MMIO registers.  The firmware must map the eFuse
/// region before calling `cubie_admit`.
pub fn capability_hmac_verify(
    request_hash:    u64,
    capability_hmac: u64,
    key_slot:        u8,
) -> bool {
    // Step 1: Read key material from eFuse hardware.
    // SAFETY: key_slot is carried in the request; out-of-range slots read
    // from unmapped memory and will fault — the firmware is responsible for
    // providing a valid slot (0–7).
    let key = unsafe { mmio::read_efuse_key(key_slot) };

    // Step 2: Compute HMAC-SHA256(key, request_hash as 8 big-endian bytes).
    let msg = request_hash.to_be_bytes();
    let mac = hmac_sha256(&key, &msg);

    // Step 3: Build expected 32-byte comparison buffer.
    // Upper 8 bytes match capability_hmac; remaining bytes must be zero
    // (truncated MAC comparison — only the first 8 bytes are transmitted).
    let mut expected = [0u8; 32];
    expected[0..8].copy_from_slice(&capability_hmac.to_be_bytes());

    // Step 4: Constant-time compare to prevent timing oracle.
    // We compare the full 32 bytes: mac[0..8] vs capability_hmac bytes,
    // mac[8..32] vs zeros.  Both sides are included in ct_eq_32.
    let mut mac_truncated = [0u8; 32];
    mac_truncated[0..8].copy_from_slice(&mac[0..8]);

    ct_eq_32(&mac_truncated, &expected)
}


Bash

List lean directory contents


CubieAttentionGeometry_v7.lean
CubieBridgeV1_40.lean
CubieDelegationRecursion_v6.lean
CubieEngineeringPhysics_v7.lean
CubieNonQuantum_v1_10.lean
CubieOmegaBridgeV2_3.lean
CubieOmegaStage2V2_3.lean
CubieQApex.lean
CubieQGeometric.lean
CubieQuantumConsent.lean
CubieQv14.lean
CubieSiteTopology_v4.lean
CubieTrustCompilerV1_50.lean
CubieTrustCompilerV2_0.lean
CubieTrustCompilerV2_0_PerPredicate.lean
CubieTrustCompilerV2_1.lean
OAI_Cubie_TrustCompiler_Theorems.lean
OmegaEight.lean
OmegaSeven.lean
RamenCornerConsensusV1191.lean
RamenCornerConsensusV1192.lean
RamenCornerConsensusV1193.lean
RamenCornerConsensus_v1_19_addon.lean
Ramen_v1_17_1.lean
Ramen_v1_18.lean
Ramen_v1_19.lean
SemanticCalculus_v1_11.lean
TheoremOmega4.lean
TheoremOmega6.lean
TheoremOmega_v4_3.lean
TheoremOmega_v5_0.lean
TheoremOmega_v6_0.lean
ToRAdmissionCompilerV1_30.lean
ToRCornerSpoofingV1_31.lean


1	Require Import Bool List Nat Lia PeanoNat.
2	Import ListNotations.
3	Section CubieAttentionGeometry_v7.
4	(* ============================================================================== *)
5	(* 1. HEAD-SHAPE AGREEMENT PREDICATE (CUB-0722)                                  *)
6	(* ============================================================================== *)
7
8	(* AttentionManifest: the shape parameters that must agree across manifest,
9	   engine, and runtime for a valid attention configuration. *)
10	Record AttentionManifest := {
11	  manifest_layers : nat;
12	  manifest_h_q    : nat;
13	  manifest_h_kv   : nat;
14	  manifest_d_head : nat;
15	  manifest_tp     : nat;
16	  manifest_pp     : nat;
17	  manifest_use_fp16 : bool;
18	}.
19
20	(* HeadShapeOK: manifest, engine, and runtime must agree on L, H_q, H_kv, D_head.
21	   This is an 8-field equality predicate across 3 sources = 8 comparisons. *)
22	Definition HeadShapeOK (manifest engine runtime : AttentionManifest) : bool :=
23	  Nat.eqb (manifest_layers manifest) (manifest_layers engine)   &&
24	  Nat.eqb (manifest_layers engine)   (manifest_layers runtime)  &&
25	  Nat.eqb (manifest_h_q manifest)    (manifest_h_q engine)      &&
26	  Nat.eqb (manifest_h_q engine)      (manifest_h_q runtime)     &&
27	  Nat.eqb (manifest_h_kv manifest)   (manifest_h_kv engine)     &&
28	  Nat.eqb (manifest_h_kv engine)     (manifest_h_kv runtime)    &&
29	  Nat.eqb (manifest_d_head manifest) (manifest_d_head engine)   &&
30	  Nat.eqb (manifest_d_head engine)   (manifest_d_head runtime).
31
32	(* ============================================================================== *)
33	(* 2. WASTE-OK DECOMPOSITION (CUB-0723)                                           *)
34	(* ============================================================================== *)
35
36	(* WasteOKFactors: the 7 orthogonal factors that jointly constitute waste_ok.
37	   V1.40/V2.0 treated waste_ok as atomic; v2.5 decomposes it. *)
38	Record WasteOKFactors := {
39	  roofline_ok          : bool;
40	  kv_heads_ok          : bool;
41	  q_heads_ok           : bool;
42	  adapter_swap_ok_b    : bool;
43	  nvlink_waiter_safe_b : bool;
44	  loop_free            : bool;
45	  target_pool_ok       : bool;
46	}.
47
48	(* waste_ok_decomposition: all 7 factors must hold for waste_ok = true. *)
49	Definition waste_ok_decomposition (w : WasteOKFactors) : bool :=
50	  roofline_ok w          &&
51	  kv_heads_ok w          &&
52	  q_heads_ok w           &&
53	  adapter_swap_ok_b w    &&
54	  nvlink_waiter_safe_b w &&
55	  loop_free w            &&
56	  target_pool_ok w.
57
58	(* ============================================================================== *)
59	(* 3. ADAPTER-SWAP AND NVLINK-WAITER (CUB-0724, CUB-0725)                        *)
60	(* ============================================================================== *)
61
62	(* adapter_swap_ok: ok iff the adapter is already cached OR PCIe has capacity. *)
63	Definition adapter_swap_ok (cached pcie_ok : bool) : bool :=
64	  cached || pcie_ok.
65
66	(* nvlink_waiter_safe: unsafe iff SM activity is zero AND VRAM is allocated.
67	   "Zero SM + allocated VRAM" is the deadlock signature. *)
68	Definition nvlink_waiter_safe (zero_sm alloc_vram : bool) : bool :=
69	  negb (zero_sm && alloc_vram).
70
71	(* ============================================================================== *)
72	(* 4. HEAD-SHAPE MISMATCH IMPLIES WASTE ZERO (CUB-0726)                          *)
73	(* ============================================================================== *)
74
75	(* Design rule: when HeadShapeOK fails AND kv_heads_ok reflects HeadShapeOK,
76	   waste_ok_decomposition is false.
77	   Encoding: kv_heads_ok is set by the runtime to equal HeadShapeOK(m,e,r). *)
78	Theorem head_shape_mismatch_implies_waste_zero :
79	  forall (m e r : AttentionManifest) (w : WasteOKFactors),
80	  HeadShapeOK m e r = false ->
81	  kv_heads_ok w = HeadShapeOK m e r ->
82	  waste_ok_decomposition w = false.
83	Proof.
84	  intros m e r w Hmismatch Hkv.
85	  unfold waste_ok_decomposition.
86	  rewrite Hkv.
87	  rewrite Hmismatch.
88	  destruct (roofline_ok w); reflexivity.
89	Qed.
90
91	(* ============================================================================== *)
92	(* 5. SYMMETRIC-MAC FAST-PATH CONSTRAINT (CUB-0727)                              *)
93	(* ============================================================================== *)
94
95	(* FastPathConfig: fast-path is only valid when symmetric MAC is in use. *)
96	Record FastPathConfig := {
97	  use_symmetric_mac : bool;
98	  fast_path_ok      : bool;
99	}.
100
101	(* symmetric_fast_path_valid: requires both symmetric MAC and fast_path_ok. *)
102	Definition symmetric_fast_path_valid (cfg : FastPathConfig) : bool :=
103	  use_symmetric_mac cfg && fast_path_ok cfg.
104
105	(* symmetric_mac_fast_path_constraint: no symmetric MAC => fast-path invalid.
106	   Subagent delegation chains must use symmetric chained MACs (Macaroons),
107	   not asymmetric nested JWTs. *)
108	Theorem symmetric_mac_fast_path_constraint : forall (cfg : FastPathConfig),
109	  use_symmetric_mac cfg = false ->
110	  symmetric_fast_path_valid cfg = false.
111	Proof.
112	  intros cfg H.
113	  unfold symmetric_fast_path_valid.
114	  rewrite H.
115	  reflexivity.
116	Qed.
117
118	(* Lemma: nvlink deadlock signature is detectable. *)
119	Lemma nvlink_deadlock_detected : forall (zero_sm alloc_vram : bool),
120	  zero_sm = true -> alloc_vram = true ->
121	  nvlink_waiter_safe zero_sm alloc_vram = false.
122	Proof.
123	  intros zero_sm alloc_vram Hz Ha.
124	  unfold nvlink_waiter_safe.
125	  rewrite Hz. rewrite Ha.
126	  reflexivity.
127	Qed.
128
129	(* Lemma: if not cached and PCIe fails, adapter_swap is false. *)
130	Lemma adapter_swap_fails_when_uncached_and_no_pcie :
131	  forall (cached pcie_ok : bool),
132	  cached = false -> pcie_ok = false ->
133	  adapter_swap_ok cached pcie_ok = false.
134	Proof.
135	  intros cached pcie_ok Hc Hp.
136	  unfold adapter_swap_ok.
137	  rewrite Hc. rewrite Hp.
138	  reflexivity.
139	Qed.
140
141	End CubieAttentionGeometry_v7.
142

Require Import Bool List Nat Lia PeanoNat.
Import ListNotations.
Section CubieAttentionGeometry_v7.
(* ============================================================================== *)
(* 1. HEAD-SHAPE AGREEMENT PREDICATE (CUB-0722)                                  *)
(* ============================================================================== *)

(* AttentionManifest: the shape parameters that must agree across manifest,
   engine, and runtime for a valid attention configuration. *)
Record AttentionManifest := {
  manifest_layers : nat;
  manifest_h_q    : nat;
  manifest_h_kv   : nat;
  manifest_d_head : nat;
  manifest_tp     : nat;
  manifest_pp     : nat;
  manifest_use_fp16 : bool;
}.

(* HeadShapeOK: manifest, engine, and runtime must agree on L, H_q, H_kv, D_head.
   This is an 8-field equality predicate across 3 sources = 8 comparisons. *)
Definition HeadShapeOK (manifest engine runtime : AttentionManifest) : bool :=
  Nat.eqb (manifest_layers manifest) (manifest_layers engine)   &&
  Nat.eqb (manifest_layers engine)   (manifest_layers runtime)  &&
  Nat.eqb (manifest_h_q manifest)    (manifest_h_q engine)      &&
  Nat.eqb (manifest_h_q engine)      (manifest_h_q runtime)     &&
  Nat.eqb (manifest_h_kv manifest)   (manifest_h_kv engine)     &&
  Nat.eqb (manifest_h_kv engine)     (manifest_h_kv runtime)    &&
  Nat.eqb (manifest_d_head manifest) (manifest_d_head engine)   &&
  Nat.eqb (manifest_d_head engine)   (manifest_d_head runtime).

(* ============================================================================== *)
(* 2. WASTE-OK DECOMPOSITION (CUB-0723)                                           *)
(* ============================================================================== *)

(* WasteOKFactors: the 7 orthogonal factors that jointly constitute waste_ok.
   V1.40/V2.0 treated waste_ok as atomic; v2.5 decomposes it. *)
Record WasteOKFactors := {
  roofline_ok          : bool;
  kv_heads_ok          : bool;
  q_heads_ok           : bool;
  adapter_swap_ok_b    : bool;
  nvlink_waiter_safe_b : bool;
  loop_free            : bool;
  target_pool_ok       : bool;
}.

(* waste_ok_decomposition: all 7 factors must hold for waste_ok = true. *)
Definition waste_ok_decomposition (w : WasteOKFactors) : bool :=
  roofline_ok w          &&
  kv_heads_ok w          &&
  q_heads_ok w           &&
  adapter_swap_ok_b w    &&
  nvlink_waiter_safe_b w &&
  loop_free w            &&
  target_pool_ok w.

(* ============================================================================== *)
(* 3. ADAPTER-SWAP AND NVLINK-WAITER (CUB-0724, CUB-0725)                        *)
(* ============================================================================== *)

(* adapter_swap_ok: ok iff the adapter is already cached OR PCIe has capacity. *)
Definition adapter_swap_ok (cached pcie_ok : bool) : bool :=
  cached || pcie_ok.

(* nvlink_waiter_safe: unsafe iff SM activity is zero AND VRAM is allocated.
   "Zero SM + allocated VRAM" is the deadlock signature. *)
Definition nvlink_waiter_safe (zero_sm alloc_vram : bool) : bool :=
  negb (zero_sm && alloc_vram).

(* ============================================================================== *)
(* 4. HEAD-SHAPE MISMATCH IMPLIES WASTE ZERO (CUB-0726)                          *)
(* ============================================================================== *)

(* Design rule: when HeadShapeOK fails AND kv_heads_ok reflects HeadShapeOK,
   waste_ok_decomposition is false.
   Encoding: kv_heads_ok is set by the runtime to equal HeadShapeOK(m,e,r). *)
Theorem head_shape_mismatch_implies_waste_zero :
  forall (m e r : AttentionManifest) (w : WasteOKFactors),
  HeadShapeOK m e r = false ->
  kv_heads_ok w = HeadShapeOK m e r ->
  waste_ok_decomposition w = false.
Proof.
  intros m e r w Hmismatch Hkv.
  unfold waste_ok_decomposition.
  rewrite Hkv.
  rewrite Hmismatch.
  destruct (roofline_ok w); reflexivity.
Qed.

(* ============================================================================== *)
(* 5. SYMMETRIC-MAC FAST-PATH CONSTRAINT (CUB-0727)                              *)
(* ============================================================================== *)

(* FastPathConfig: fast-path is only valid when symmetric MAC is in use. *)
Record FastPathConfig := {
  use_symmetric_mac : bool;
  fast_path_ok      : bool;
}.

(* symmetric_fast_path_valid: requires both symmetric MAC and fast_path_ok. *)
Definition symmetric_fast_path_valid (cfg : FastPathConfig) : bool :=
  use_symmetric_mac cfg && fast_path_ok cfg.

(* symmetric_mac_fast_path_constraint: no symmetric MAC => fast-path invalid.
   Subagent delegation chains must use symmetric chained MACs (Macaroons),
   not asymmetric nested JWTs. *)
Theorem symmetric_mac_fast_path_constraint : forall (cfg : FastPathConfig),
  use_symmetric_mac cfg = false ->
  symmetric_fast_path_valid cfg = false.
Proof.
  intros cfg H.
  unfold symmetric_fast_path_valid.
  rewrite H.
  reflexivity.
Qed.

(* Lemma: nvlink deadlock signature is detectable. *)
Lemma nvlink_deadlock_detected : forall (zero_sm alloc_vram : bool),
  zero_sm = true -> alloc_vram = true ->
  nvlink_waiter_safe zero_sm alloc_vram = false.
Proof.
  intros zero_sm alloc_vram Hz Ha.
  unfold nvlink_waiter_safe.
  rewrite Hz. rewrite Ha.
  reflexivity.
Qed.

(* Lemma: if not cached and PCIe fails, adapter_swap is false. *)
Lemma adapter_swap_fails_when_uncached_and_no_pcie :
  forall (cached pcie_ok : bool),
  cached = false -> pcie_ok = false ->
  adapter_swap_ok cached pcie_ok = false.
Proof.
  intros cached pcie_ok Hc Hp.
  unfold adapter_swap_ok.
  rewrite Hc. rewrite Hp.
  reflexivity.
Qed.

End CubieAttentionGeometry_v7.


1	-- ============================================================
2	--  CENTILLION AI INC. -- QUANTUM CONTEXTUAL CONSENT
3	--  T5/T6/T7/T8: measurement collapse, entanglement-enhanced
4	--  threshold, non-commutative consent algebra, Holevo bound
5	--  (Lean 4 mirror of CubieQuantumConsent.v)
6	--
7	--  File:        Centillion/CubieQuantumConsent.lean
8	--  Lean:        4.15.0
9	--  Status:      Closed proof. Zero `sorry`. Constructive.
10	--  Patent:      US20240195628A1, Patent 18/005,497
11	--  Date:        April 27, 2026
12	--  CNDA:        Intel CNDA Number 083697
13	-- ============================================================
14
15	namespace Centillion.CubieQuantumConsent
16
17	-- ============================================================
18	-- 1. Measurement bases (the requesters' contexts)
19	-- ============================================================
20
21	/-- Two non-commuting measurement bases. -/
22	inductive MeasurementBasis where
23	  | Computational  -- {|0⟩, |1⟩}, the Z basis
24	  | Hadamard       -- {|+⟩, |−⟩}, the X basis
25	  deriving DecidableEq, Repr
26
27	/-- Consent outcomes from a measurement. -/
28	inductive ConsentOutcome where
29	  | Grant
30	  | Deny
31	  deriving DecidableEq, Repr
32
33	/-- Quantum consent state — abstract carrier. -/
34	axiom ConsentState : Type
35
36	/-- The |+⟩ superposition state. -/
37	axiom PlusState : ConsentState
38
39	/-- Measurement function. The outcome depends on the basis (T7). -/
40	axiom measure : ConsentState → MeasurementBasis → ConsentOutcome
41
42	-- ============================================================
43	-- 2. Theorem T7 axioms — non-commutative consent algebra
44	-- ============================================================
45
46	axiom measurePlus_computational_can_deny :
47	  measure PlusState MeasurementBasis.Computational = ConsentOutcome.Deny
48
49	axiom measurePlus_hadamard_grants :
50	  measure PlusState MeasurementBasis.Hadamard = ConsentOutcome.Grant
51
52	/-- T7 — Same state, different bases, different outcomes.
53	    The non-commutativity of consent measurement. -/
54	theorem T7_context_dependent_consent :
55	    measure PlusState MeasurementBasis.Computational ≠
56	    measure PlusState MeasurementBasis.Hadamard := by
57	  rw [measurePlus_computational_can_deny, measurePlus_hadamard_grants]
58	  decide
59
60	-- ============================================================
61	-- 3. Non-commutative consent algebra
62	-- ============================================================
63
64	axiom measure_after :
65	  ConsentState → MeasurementBasis → MeasurementBasis → ConsentOutcome
66
67	noncomputable def commutator_AB (s : ConsentState) : ConsentOutcome :=
68	  measure_after s MeasurementBasis.Computational MeasurementBasis.Hadamard
69
70	noncomputable def commutator_BA (s : ConsentState) : ConsentOutcome :=
71	  measure_after s MeasurementBasis.Hadamard MeasurementBasis.Computational
72
73	axiom non_commutativity_witness :
74	  ∃ s : ConsentState, commutator_AB s ≠ commutator_BA s
75
76	theorem non_commutativity_holds :
77	    ∃ s, commutator_AB s ≠ commutator_BA s :=
78	  non_commutativity_witness
79
80	-- ============================================================
81	-- 4. Theorem T6 — Entanglement-enhanced threshold
82	-- ============================================================
83
84	abbrev EntanglementFraction := Nat  -- 0..100
85	def critical_threshold_classical : Nat := 50
86
87	def critical_threshold_quantum (f_ent : Nat) : Nat :=
88	  critical_threshold_classical - f_ent / 4
89
90	/-- T6 — Entanglement strictly lowers the critical threshold when f_ent ≥ 4. -/
91	theorem T6_entanglement_lowers_threshold :
92	    ∀ (f_ent : Nat), f_ent ≥ 4 →
93	    critical_threshold_quantum f_ent < critical_threshold_classical := by
94	  intro f_ent hf
95	  unfold critical_threshold_quantum critical_threshold_classical
96	  -- Need 50 - f_ent/4 < 50, equivalently f_ent/4 ≥ 1.
97	  have hdiv : 1 ≤ f_ent / 4 := by
98	    -- f_ent = 4 * (f_ent/4) + (f_ent%4), and f_ent%4 < 4, so if f_ent ≥ 4 then f_ent/4 ≥ 1.
99	    have hdivmod := Nat.div_add_mod f_ent 4
100	    have hmod : f_ent % 4 < 4 := Nat.mod_lt f_ent (by decide)
101	    omega
102	  omega
103
104	theorem T6_full_entanglement_threshold :
105	    critical_threshold_quantum 100 = 25 := by decide
106
107	theorem T6_half_entanglement_threshold :
108	    critical_threshold_quantum 50 = 38 := by decide
109
110	-- ============================================================
111	-- 5. Theorem T8 — Holevo bound on extractable information
112	-- ============================================================
113
114	axiom accessible_information : Nat
115	axiom consent_state_entropy : Nat
116
117	axiom T8_holevo_bound : accessible_information ≤ consent_state_entropy
118
119	theorem T8_holevo_bound_holds :
120	    accessible_information ≤ consent_state_entropy := T8_holevo_bound
121
122	noncomputable def information_gap : Nat := consent_state_entropy - accessible_information
123
124	theorem information_gap_nonneg :
125	    consent_state_entropy ≥ accessible_information := T8_holevo_bound
126
127	-- ============================================================
128	-- 6. Theorem T5 — Measurement collapse changes consent
129	-- ============================================================
130
131	axiom post_measurement_state :
132	  ConsentState → MeasurementBasis → ConsentState
133
134	axiom T5_collapse_idempotent :
135	  ∀ (s : ConsentState) (b : MeasurementBasis),
136	    measure (post_measurement_state s b) b = measure s b
137
138	theorem T5_collapse_idempotent_holds :
139	    ∀ (s : ConsentState) (b : MeasurementBasis),
140	      measure (post_measurement_state s b) b = measure s b := T5_collapse_idempotent
141
142	def post_measurement_agreement (s : ConsentState) (b : MeasurementBasis) : Prop :=
143	  measure (post_measurement_state s b) b = measure s b
144
145	theorem T5_post_measurement_agreement_universal :
146	    ∀ s b, post_measurement_agreement s b := by
147	  intro s b
148	  unfold post_measurement_agreement
149	  exact T5_collapse_idempotent s b
150
151	end Centillion.CubieQuantumConsent
152

-- ============================================================
--  CENTILLION AI INC. -- QUANTUM CONTEXTUAL CONSENT
--  T5/T6/T7/T8: measurement collapse, entanglement-enhanced
--  threshold, non-commutative consent algebra, Holevo bound
--  (Lean 4 mirror of CubieQuantumConsent.v)
--
--  File:        Centillion/CubieQuantumConsent.lean
--  Lean:        4.15.0
--  Status:      Closed proof. Zero `sorry`. Constructive.
--  Patent:      US20240195628A1, Patent 18/005,497
--  Date:        April 27, 2026
--  CNDA:        Intel CNDA Number 083697
-- ============================================================

namespace Centillion.CubieQuantumConsent

-- ============================================================
-- 1. Measurement bases (the requesters' contexts)
-- ============================================================

/-- Two non-commuting measurement bases. -/
inductive MeasurementBasis where
  | Computational  -- {|0⟩, |1⟩}, the Z basis
  | Hadamard       -- {|+⟩, |−⟩}, the X basis
  deriving DecidableEq, Repr

/-- Consent outcomes from a measurement. -/
inductive ConsentOutcome where
  | Grant
  | Deny
  deriving DecidableEq, Repr

/-- Quantum consent state — abstract carrier. -/
axiom ConsentState : Type

/-- The |+⟩ superposition state. -/
axiom PlusState : ConsentState

/-- Measurement function. The outcome depends on the basis (T7). -/
axiom measure : ConsentState → MeasurementBasis → ConsentOutcome

-- ============================================================
-- 2. Theorem T7 axioms — non-commutative consent algebra
-- ============================================================

axiom measurePlus_computational_can_deny :
  measure PlusState MeasurementBasis.Computational = ConsentOutcome.Deny

axiom measurePlus_hadamard_grants :
  measure PlusState MeasurementBasis.Hadamard = ConsentOutcome.Grant

/-- T7 — Same state, different bases, different outcomes.
    The non-commutativity of consent measurement. -/
theorem T7_context_dependent_consent :
    measure PlusState MeasurementBasis.Computational ≠
    measure PlusState MeasurementBasis.Hadamard := by
  rw [measurePlus_computational_can_deny, measurePlus_hadamard_grants]
  decide

-- ============================================================
-- 3. Non-commutative consent algebra
-- ============================================================

axiom measure_after :
  ConsentState → MeasurementBasis → MeasurementBasis → ConsentOutcome

noncomputable def commutator_AB (s : ConsentState) : ConsentOutcome :=
  measure_after s MeasurementBasis.Computational MeasurementBasis.Hadamard

noncomputable def commutator_BA (s : ConsentState) : ConsentOutcome :=
  measure_after s MeasurementBasis.Hadamard MeasurementBasis.Computational

axiom non_commutativity_witness :
  ∃ s : ConsentState, commutator_AB s ≠ commutator_BA s

theorem non_commutativity_holds :
    ∃ s, commutator_AB s ≠ commutator_BA s :=
  non_commutativity_witness

-- ============================================================
-- 4. Theorem T6 — Entanglement-enhanced threshold
-- ============================================================

abbrev EntanglementFraction := Nat  -- 0..100
def critical_threshold_classical : Nat := 50

def critical_threshold_quantum (f_ent : Nat) : Nat :=
  critical_threshold_classical - f_ent / 4

/-- T6 — Entanglement strictly lowers the critical threshold when f_ent ≥ 4. -/
theorem T6_entanglement_lowers_threshold :
    ∀ (f_ent : Nat), f_ent ≥ 4 →
    critical_threshold_quantum f_ent < critical_threshold_classical := by
  intro f_ent hf
  unfold critical_threshold_quantum critical_threshold_classical
  -- Need 50 - f_ent/4 < 50, equivalently f_ent/4 ≥ 1.
  have hdiv : 1 ≤ f_ent / 4 := by
    -- f_ent = 4 * (f_ent/4) + (f_ent%4), and f_ent%4 < 4, so if f_ent ≥ 4 then f_ent/4 ≥ 1.
    have hdivmod := Nat.div_add_mod f_ent 4
    have hmod : f_ent % 4 < 4 := Nat.mod_lt f_ent (by decide)
    omega
  omega

theorem T6_full_entanglement_threshold :
    critical_threshold_quantum 100 = 25 := by decide

theorem T6_half_entanglement_threshold :
    critical_threshold_quantum 50 = 38 := by decide

-- ============================================================
-- 5. Theorem T8 — Holevo bound on extractable information
-- ============================================================

axiom accessible_information : Nat
axiom consent_state_entropy : Nat

axiom T8_holevo_bound : accessible_information ≤ consent_state_entropy

theorem T8_holevo_bound_holds :
    accessible_information ≤ consent_state_entropy := T8_holevo_bound

noncomputable def information_gap : Nat := consent_state_entropy - accessible_information

theorem information_gap_nonneg :
    consent_state_entropy ≥ accessible_information := T8_holevo_bound

-- ============================================================
-- 6. Theorem T5 — Measurement collapse changes consent
-- ============================================================

axiom post_measurement_state :
  ConsentState → MeasurementBasis → ConsentState

axiom T5_collapse_idempotent :
  ∀ (s : ConsentState) (b : MeasurementBasis),
    measure (post_measurement_state s b) b = measure s b

theorem T5_collapse_idempotent_holds :
    ∀ (s : ConsentState) (b : MeasurementBasis),
      measure (post_measurement_state s b) b = measure s b := T5_collapse_idempotent

def post_measurement_agreement (s : ConsentState) (b : MeasurementBasis) : Prop :=
  measure (post_measurement_state s b) b = measure s b

theorem T5_post_measurement_agreement_universal :
    ∀ s b, post_measurement_agreement s b := by
  intro s b
  unfold post_measurement_agreement
  exact T5_collapse_idempotent s b

end Centillion.CubieQuantumConsent


ToolSearch

Question: select:TaskUpdate


1	-- CubieAttentionGeometry_v7.lean
2	-- Lean 4 mirror of CubieAttentionGeometry_v7.v
3	-- Covers: HeadShapeOK (CUB-0722), waste_ok_decomposition (CUB-0723),
4	--         adapter_swap_ok (CUB-0724), nvlink_waiter_safe (CUB-0725),
5	--         head_shape_mismatch_implies_waste_zero (CUB-0726),
6	--         symmetric_mac_fast_path_constraint (CUB-0727)
7	namespace CubieAttentionGeometry_v7
8
9	-- ==============================================================================
10	-- 1. ATTENTION MANIFEST AND HEAD-SHAPE OK (CUB-0722)
11	-- ==============================================================================
12
13	structure AttentionManifest where
14	  manifest_layers   : Nat
15	  manifest_h_q      : Nat
16	  manifest_h_kv     : Nat
17	  manifest_d_head   : Nat
18	  manifest_tp       : Nat
19	  manifest_pp       : Nat
20	  manifest_use_fp16 : Bool
21	  deriving Repr, DecidableEq
22
23	-- HeadShapeOK: 8-field agreement predicate across manifest, engine, runtime
24	def HeadShapeOK (manifest engine runtime : AttentionManifest) : Bool :=
25	  (manifest.manifest_layers == engine.manifest_layers)   &&
26	  (engine.manifest_layers   == runtime.manifest_layers)  &&
27	  (manifest.manifest_h_q    == engine.manifest_h_q)      &&
28	  (engine.manifest_h_q      == runtime.manifest_h_q)     &&
29	  (manifest.manifest_h_kv   == engine.manifest_h_kv)     &&
30	  (engine.manifest_h_kv     == runtime.manifest_h_kv)    &&
31	  (manifest.manifest_d_head == engine.manifest_d_head)   &&
32	  (engine.manifest_d_head   == runtime.manifest_d_head)
33
34	-- ==============================================================================
35	-- 2. WASTE-OK DECOMPOSITION (CUB-0723)
36	-- ==============================================================================
37
38	structure WasteOKFactors where
39	  roofline_ok          : Bool
40	  kv_heads_ok          : Bool
41	  q_heads_ok           : Bool
42	  adapter_swap_ok_b    : Bool
43	  nvlink_waiter_safe_b : Bool
44	  loop_free            : Bool
45	  target_pool_ok       : Bool
46	  deriving Repr, DecidableEq
47
48	-- waste_ok_decomposition: all 7 factors must hold
49	def waste_ok_decomposition (w : WasteOKFactors) : Bool :=
50	  w.roofline_ok          &&
51	  w.kv_heads_ok          &&
52	  w.q_heads_ok           &&
53	  w.adapter_swap_ok_b    &&
54	  w.nvlink_waiter_safe_b &&
55	  w.loop_free            &&
56	  w.target_pool_ok
57
58	-- ==============================================================================
59	-- 3. ADAPTER-SWAP AND NVLINK-WAITER (CUB-0724, CUB-0725)
60	-- ==============================================================================
61
62	-- adapter_swap_ok: ok iff cached OR PCIe has capacity
63	def adapter_swap_ok (cached pcie_ok : Bool) : Bool :=
64	  cached || pcie_ok
65
66	-- nvlink_waiter_safe: unsafe iff zero SM activity AND VRAM allocated (deadlock)
67	def nvlink_waiter_safe (zero_sm alloc_vram : Bool) : Bool :=
68	  !(zero_sm && alloc_vram)
69
70	-- ==============================================================================
71	-- 4. HEAD-SHAPE MISMATCH IMPLIES WASTE ZERO (CUB-0726)
72	-- ==============================================================================
73
74	-- Design rule: if HeadShapeOK fails and kv_heads_ok reflects HeadShapeOK,
75	-- then waste_ok_decomposition = false.
76	theorem head_shape_mismatch_implies_waste_zero
77	    (m e r : AttentionManifest) (w : WasteOKFactors)
78	    (hmismatch : HeadShapeOK m e r = false)
79	    (hkv : w.kv_heads_ok = HeadShapeOK m e r) :
80	    waste_ok_decomposition w = false := by
81	  simp [waste_ok_decomposition, hkv, hmismatch]
82
83	-- ==============================================================================
84	-- 5. SYMMETRIC-MAC FAST-PATH CONSTRAINT (CUB-0727)
85	-- ==============================================================================
86
87	structure FastPathConfig where
88	  use_symmetric_mac : Bool
89	  fast_path_ok      : Bool
90	  deriving Repr, DecidableEq
91
92	-- symmetric_fast_path_valid: requires both symmetric MAC and fast_path_ok
93	def symmetric_fast_path_valid (cfg : FastPathConfig) : Bool :=
94	  cfg.use_symmetric_mac && cfg.fast_path_ok
95
96	-- symmetric_mac_fast_path_constraint: no symmetric MAC => fast-path invalid
97	theorem symmetric_mac_fast_path_constraint (cfg : FastPathConfig)
98	    (h : cfg.use_symmetric_mac = false) :
99	    symmetric_fast_path_valid cfg = false := by
100	  simp [symmetric_fast_path_valid, h]
101
102	-- Lemma: NVLink deadlock is detectable
103	theorem nvlink_deadlock_detected (zero_sm alloc_vram : Bool)
104	    (hz : zero_sm = true) (ha : alloc_vram = true) :
105	    nvlink_waiter_safe zero_sm alloc_vram = false := by
106	  simp [nvlink_waiter_safe, hz, ha]
107
108	end CubieAttentionGeometry_v7
109

-- CubieAttentionGeometry_v7.lean
-- Lean 4 mirror of CubieAttentionGeometry_v7.v
-- Covers: HeadShapeOK (CUB-0722), waste_ok_decomposition (CUB-0723),
--         adapter_swap_ok (CUB-0724), nvlink_waiter_safe (CUB-0725),
--         head_shape_mismatch_implies_waste_zero (CUB-0726),
--         symmetric_mac_fast_path_constraint (CUB-0727)
namespace CubieAttentionGeometry_v7

-- ==============================================================================
-- 1. ATTENTION MANIFEST AND HEAD-SHAPE OK (CUB-0722)
-- ==============================================================================

structure AttentionManifest where
  manifest_layers   : Nat
  manifest_h_q      : Nat
  manifest_h_kv     : Nat
  manifest_d_head   : Nat
  manifest_tp       : Nat
  manifest_pp       : Nat
  manifest_use_fp16 : Bool
  deriving Repr, DecidableEq

-- HeadShapeOK: 8-field agreement predicate across manifest, engine, runtime
def HeadShapeOK (manifest engine runtime : AttentionManifest) : Bool :=
  (manifest.manifest_layers == engine.manifest_layers)   &&
  (engine.manifest_layers   == runtime.manifest_layers)  &&
  (manifest.manifest_h_q    == engine.manifest_h_q)      &&
  (engine.manifest_h_q      == runtime.manifest_h_q)     &&
  (manifest.manifest_h_kv   == engine.manifest_h_kv)     &&
  (engine.manifest_h_kv     == runtime.manifest_h_kv)    &&
  (manifest.manifest_d_head == engine.manifest_d_head)   &&
  (engine.manifest_d_head   == runtime.manifest_d_head)

-- ==============================================================================
-- 2. WASTE-OK DECOMPOSITION (CUB-0723)
-- ==============================================================================

structure WasteOKFactors where
  roofline_ok          : Bool
  kv_heads_ok          : Bool
  q_heads_ok           : Bool
  adapter_swap_ok_b    : Bool
  nvlink_waiter_safe_b : Bool
  loop_free            : Bool
  target_pool_ok       : Bool
  deriving Repr, DecidableEq

-- waste_ok_decomposition: all 7 factors must hold
def waste_ok_decomposition (w : WasteOKFactors) : Bool :=
  w.roofline_ok          &&
  w.kv_heads_ok          &&
  w.q_heads_ok           &&
  w.adapter_swap_ok_b    &&
  w.nvlink_waiter_safe_b &&
  w.loop_free            &&
  w.target_pool_ok

-- ==============================================================================
-- 3. ADAPTER-SWAP AND NVLINK-WAITER (CUB-0724, CUB-0725)
-- ==============================================================================

-- adapter_swap_ok: ok iff cached OR PCIe has capacity
def adapter_swap_ok (cached pcie_ok : Bool) : Bool :=
  cached || pcie_ok

-- nvlink_waiter_safe: unsafe iff zero SM activity AND VRAM allocated (deadlock)
def nvlink_waiter_safe (zero_sm alloc_vram : Bool) : Bool :=
  !(zero_sm && alloc_vram)

-- ==============================================================================
-- 4. HEAD-SHAPE MISMATCH IMPLIES WASTE ZERO (CUB-0726)
-- ==============================================================================

-- Design rule: if HeadShapeOK fails and kv_heads_ok reflects HeadShapeOK,
-- then waste_ok_decomposition = false.
theorem head_shape_mismatch_implies_waste_zero
    (m e r : AttentionManifest) (w : WasteOKFactors)
    (hmismatch : HeadShapeOK m e r = false)
    (hkv : w.kv_heads_ok = HeadShapeOK m e r) :
    waste_ok_decomposition w = false := by
  simp [waste_ok_decomposition, hkv, hmismatch]

-- ==============================================================================
-- 5. SYMMETRIC-MAC FAST-PATH CONSTRAINT (CUB-0727)
-- ==============================================================================

structure FastPathConfig where
  use_symmetric_mac : Bool
  fast_path_ok      : Bool
  deriving Repr, DecidableEq

-- symmetric_fast_path_valid: requires both symmetric MAC and fast_path_ok
def symmetric_fast_path_valid (cfg : FastPathConfig) : Bool :=
  cfg.use_symmetric_mac && cfg.fast_path_ok

-- symmetric_mac_fast_path_constraint: no symmetric MAC => fast-path invalid
theorem symmetric_mac_fast_path_constraint (cfg : FastPathConfig)
    (h : cfg.use_symmetric_mac = false) :
    symmetric_fast_path_valid cfg = false := by
  simp [symmetric_fast_path_valid, h]

-- Lemma: NVLink deadlock is detectable
theorem nvlink_deadlock_detected (zero_sm alloc_vram : Bool)
    (hz : zero_sm = true) (ha : alloc_vram = true) :
    nvlink_waiter_safe zero_sm alloc_vram = false := by
  simp [nvlink_waiter_safe, hz, ha]

end CubieAttentionGeometry_v7


Question: select:TaskUpdate