<persisted-output>
Output too large (217.3KB). Full output saved to: C:\Users\NickV\.claude\projects\C--Users-NickV\bfc2bfbf-6683-4826-bf18-edd758f725bb\tool-results\b5067899l.txt

Preview (first 2KB):
[notice] A new release of pip is available: 26.0.1 -> 26.1
[notice] To update, run: python.exe -m pip install --upgrade pip
Pages: 77

--- PAGE 1 ---
Cubie Trust Compiler – Master Theorem Stack
v1.0_CubieMasterStack_0430.md
Field Value
Author Nicholas M Venezia
Organization Centillion AI Inc.
Date 2026-04-30
Verification protocol Triple-kernel (Coq 8.18.0 + coqchk + Lean 4.30.0-rc2)
Lean configuration Lean 4 Core (no Mathlib)
Patent family US11956363B2, US12073439B2, US20240195628A1
CNDA Intel CNDA 083697
Total deliverables 7
Total theorems 163 (146 unique; V2.0 subsumes V1.50)
Status SPEC_LOCKED across all deliverables
This document is the canonical bundle of every approved theorem and machine-checked proof in the Cubie Trust Compiler verification stack. Each
deliverable section contains the full Coq source, the full Lean 4 source, and the SHA-256 hash of each source file. Every theorem has been independently
verified by both kernels under the constraints of Lean 4 Core (no Mathlib) and Coq’s standard library.
The stack is the formal substrate for the TrustFortress BNN gate, the Blue Shield kernel-bypass security appliance, and the patent claims listed above.
Section A: Stack Index and SHA Manifest
The seven deliverables, in build order, with primary source SHA-256 hashes:
ID Title Theorems Coq SHA-256 Lean SHA-256
Ramen
V1.19.2 Corner 53 d564c4830fc9030bff0f9c6ed14dbde1c382a3bf04ad601d7e953548d206206b 0f269cb03e2b30069cfb4a7b757c4c34dd15dc56ce204071061dd8f3bc7787b5
Consensus
ToR
V1.30 Admission 5 a73a6b7586a865057d587b02f2fe06dd1d5d53b002ebc070ce3d55efbba3ba8c 34fa586a7c161f330ea3b5d1ed6c550c39986803ec99bdaa8b5141944280cd2a
Compiler
ToR
V1.31 Corner 2 2d306870d199b2aa402b9bf521776517bc80ff8cf251d4252864b2bb09b0529d 6c3b1772caa9de2986bd0e715eddef5622ef41f91b83b6cafb7492e8b36f38df
Spoofing
Cubie
...
</persisted-output>

[notice] A new release of pip is available: 26.0.1 -> 26.1
[notice] To update, run: python.exe -m pip install --upgrade pip
Pages: 77

--- PAGE 1 ---
Cubie Trust Compiler – Master Theorem Stack
v1.0_CubieMasterStack_0430.md
Field Value
Author Nicholas M Venezia
Organization Centillion AI Inc.
Date 2026-04-30
Verification protocol Triple-kernel (Coq 8.18.0 + coqchk + Lean 4.30.0-rc2)
Lean configuration Lean 4 Core (no Mathlib)
Patent family US11956363B2, US12073439B2, US20240195628A1
CNDA Intel CNDA 083697
Total deliverables 7
Total theorems 163 (146 unique; V2.0 subsumes V1.50)
Status SPEC_LOCKED across all deliverables
This document is the canonical bundle of every approved theorem and machine-checked proof in the Cubie Trust Compiler verification stack. Each
deliverable section contains the full Coq source, the full Lean 4 source, and the SHA-256 hash of each source file. Every theorem has been independently
verified by both kernels under the constraints of Lean 4 Core (no Mathlib) and Coq’s standard library.
The stack is the formal substrate for the TrustFortress BNN gate, the Blue Shield kernel-bypass security appliance, and the patent claims listed above.
Section A: Stack Index and SHA Manifest
The seven deliverables, in build order, with primary source SHA-256 hashes:
ID Title Theorems Coq SHA-256 Lean SHA-256
Ramen
V1.19.2 Corner 53 d564c4830fc9030bff0f9c6ed14dbde1c382a3bf04ad601d7e953548d206206b 0f269cb03e2b30069cfb4a7b757c4c34dd15dc56ce204071061dd8f3bc7787b5
Consensus
ToR
V1.30 Admission 5 a73a6b7586a865057d587b02f2fe06dd1d5d53b002ebc070ce3d55efbba3ba8c 34fa586a7c161f330ea3b5d1ed6c550c39986803ec99bdaa8b5141944280cd2a
Compiler
ToR
V1.31 Corner 2 2d306870d199b2aa402b9bf521776517bc80ff8cf251d4252864b2bb09b0529d 6c3b1772caa9de2986bd0e715eddef5622ef41f91b83b6cafb7492e8b36f38df
Spoofing
Cubie
V1.40 6 815bfcf12627f5c1bc2bef702092cf6dda85a5ab69e0fe29e9d0c18ea4ca5340 f14cd1ae1e8eb6a2dc0df9175246ce64f5994c9bf03a4cd9b74e632945338d6b
Bridge
Cubie
Trust
V1.50 17 5dd9197339549a0b289bad6c4532a422387b2b385f8d2acfb67a654832f4117b fcf1132144f46f104a1a41699297c99a35d07b9d345b75f4d329d5b7d553cc50
Compiler
(Track B)
Cubie
Trust
V2.0 Compiler 26 17af5b3f2cc3d6648eba08d8e0aa94557a250430f454a53454396439ed02c31e c9d1d80c75e93df6af0c868fce1936a393b4e6af40afd0ce1de8ddceefedd436
(Track C,
canonical)
Cubie
Trust
Compiler
V2.0
V2.0 Per- 54 91f31a74c1675dde7b6857050f68f5c8049afab7115f5ae5cdc17e605ecb4a36 98a99b8e9438277c85d20675b6f18c3bf47b76ad681a260c0bde8c9a80a93d36
PerPredicate

--- PAGE 2 ---
Predicate
Addendum
Section B: Deliverable Summaries
V1.19.2 – Ramen Corner Consensus
Track: Tier Two
Theorem count: 53
Status: DELIVERED
Axiom profile: Coq: 53/53 closed under the global context. Lean: 4 axiom-free, 46 [propext], 3 [propext, Quot.sound].
Tier Two of the Ramen Corner Consensus stack. Fifty-three theorems across the 23 diagnostic predicates plus three denial-counting theorems plus the
corner-consensus iff equivalence. Establishes the foundational corner-level admission semantics that all subsequent compilers (V1.30, V1.40, V1.50, V2.0)
inherit.
V1.30 – ToR Admission Compiler
Track: GPU rack-edge admission
Theorem count: 5
Status: DELIVERED
Axiom profile: Coq: 5/5 closed under the global context. Lean: all 5 axiom-free or [propext].
Rack-edge GPU admission control with seven-dimensional ToR seam, explainable corner consensus, in-rack bypass rejection, epoch staleness rejection,
and goodput firewall containment. Five keystone theorems on the host-side verifier semantics.
V1.31 – ToR Corner Spoofing
Track: Surface-spoofing impossibility
Theorem count: 2
Status: DELIVERED
Axiom profile: Coq: 2/2 closed. Lean: 2/2 axiom-free.
Surface-spoofing impossibility lifted from individual seams to the corner aggregate. Constructs two distinct RackCorners that share a 5-field SeamSurface
signature while differing on Admit, proving that surface telemetry alone cannot determine admission.
V1.40 – Cubie Bridge
Track: Track A (V1.30 to Cubie embedding)
Theorem count: 6
Status: DELIVERED
Axiom profile: Coq: 6/6 closed. Lean: 6/6 axiom-free.
Bridge from the V1.30 ToR seven-dimensional seam to the Cubie GPU-corner / Deployment-corner decomposition. Six theorems establish that the seam
check J factors into two independent corner predicates and that each corner can fail in isolation. Includes 8192-case decomposition keystone (T1).
V1.50 – Cubie Trust Compiler (Track B)
Track: Track B (face promotion)
Theorem count: 17
Status: DELIVERED
Axiom profile: Coq: 17/17 closed. Lean: 14 axiom-free, 3 [propext, Quot.sound].
Face promotion. Promotes the V1.30 7-dimension flat seam to the fifty-four-predicate CubieRequest substrate per Cubie diagram 04. Seventeen theorems:
face-localized denial across all six faces, the converse admit-implies-face-pass family, three denial-counting properties, and surface-spoofing separation
lifted to the new substrate.
V2.0 – Cubie Trust Compiler (Track C, canonical)
Track: Track C (full unification)
Theorem count: 26

--- PAGE 3 ---
Status: DELIVERED
Axiom profile: Coq: 26/26 closed. Lean: 18 axiom-free, 5 [propext], 3 [propext, Quot.sound].
Full unification of the Cubie Trust Compiler. Subsumes V1.30, V1.31, V1.40, and V1.50 as the canonical formal specification. Twenty-six theorems: V1.50’s 17
plus T3 cross-corner independence (2), T7 lease integrity (3), T8 bypass-no-lease (1), T9 epoch monotonicity (2), and T10 HA split-brain fail-closed (1).
V2.0 PerPredicate – Cubie Trust Compiler V2.0 Per-Predicate Addendum
Track: Patent-claim corollaries
Theorem count: 54
Status: DELIVERED
Axiom profile: Coq: 54/54 closed. Lean: 54/54 axiom-free.
Patent-counsel addendum. Each of the 54 face-check predicates is broken out as an individual named corollary of T2 face_localized_denial. Provides a
one-to-one mapping between formal theorems and the claim limitations of US20240195628A1. Six faces times nine checks equals fifty-four corollaries.
Section C: Full Source Listings
Each deliverable below is presented in two forms: the Coq 8.18.0 source (verified by coqc and coqchk) and the Lean 4.30.0-rc2 source (verified by lean
against Lean 4 Core, no Mathlib). The SHA-256 hash of each source file is shown immediately above the listing.
V1.19.2 – Ramen Corner Consensus
Coq source. File: RamenCornerConsensusV1192.v. SHA-256: d564c4830fc9030bff0f9c6ed14dbde1c382a3bf04ad601d7e953548d206206b.
(* ============================================================================== *)
(* AUTHOR: Nicholas M Venezia *)
(* CENTILLION AI INC. -- EXPLAINABLE CORNER CONSENSUS (V1.19.2 TIER TWO) *)
(* *)
(* V1.19.2 = V1.19.1 + Tier Two enhancements: *)
(* * Section G: 23 converse projection theorems *)
(* (WriteOK = true => every diagnostic component = true) *)
(* * Section H: 3 denial-counting theorems *)
(* (denial_count function + zero/positive/bounded equivalences) *)
(* Total: 53 theorems = 27 (V1.19.1) + 23 (Section G) + 3 (Section H). *)
(* *)
(* Status: SPEC_LOCKED. Fully Constructive. Zero Admitted. Zero Axioms. *)
(* ============================================================================== *)
Require Import Bool List Nat Lia PeanoNat.
Import ListNotations.
Section RamenCornerConsensus.
(* ============================================================================== *)
(* 1. BASE V1.19 SUBSTRATE *)
(* ============================================================================== *)
Record SeamEvidence := {
nonce : nat;
origin_id : nat;
target_id : nat;
privilege_level: nat;
timestamp : nat;
expiry : nat;
id_ok : bool;
purpose_ok : bool;
lineage_ok : bool;
version_ok : bool;
scope_ok : bool;
attest_ok : bool
}.
Definition J (e : SeamEvidence) : bool :=
(timestamp e <=? expiry e) &&
id_ok e && purpose_ok e && lineage_ok e &&
version_ok e && scope_ok e && attest_ok e.
Record Corner := {
target_node : nat;

--- PAGE 4 ---
exec_time : nat;
e1 : SeamEvidence;
e2 : SeamEvidence;
e3 : SeamEvidence
}.
Definition CornerTopologyOK (c : Corner) : bool :=
(negb (nonce (e1 c) =? nonce (e2 c)) &&
negb (nonce (e2 c) =? nonce (e3 c)) &&
negb (nonce (e1 c) =? nonce (e3 c))) &&
((target_id (e1 c) =? target_node c) &&
(target_id (e2 c) =? target_node c) &&
(target_id (e3 c) =? target_node c)) &&
((timestamp (e1 c) <=? exec_time c) && (exec_time c <=? expiry (e1 c)) &&
(timestamp (e2 c) <=? exec_time c) && (exec_time c <=? expiry (e2 c)) &&
(timestamp (e3 c) <=? exec_time c) && (exec_time c <=? expiry (e3 c))).
Definition CornerK (c : Corner) : bool :=
J (e1 c) && J (e2 c) && J (e3 c) && CornerTopologyOK c.
Definition WriteOK (c : Corner) (policyOK : bool) : bool :=
CornerK c && policyOK.
(* ============================================================================== *)
(* 2. EXPLAINABLE TYPED THRESHOLDS *)
(* ============================================================================== *)
Record TypedThreshold := {
time_passed : bool;
id_passed : bool;
purpose_passed : bool;
lineage_passed : bool;
version_passed : bool;
scope_passed : bool;
attest_passed : bool
}.
Definition evaluate_seam (e : SeamEvidence) : TypedThreshold :=
{| time_passed := timestamp e <=? expiry e;
id_passed := id_ok e;
purpose_passed := purpose_ok e;
lineage_passed := lineage_ok e;
version_passed := version_ok e;
scope_passed := scope_ok e;
attest_passed := attest_ok e |}.
Definition is_clean (t : TypedThreshold) : bool :=
time_passed t && id_passed t && purpose_passed t &&
lineage_passed t && version_passed t && scope_passed t && attest_passed t.
Record CornerDiagnostics := {
e1_diag : TypedThreshold;
e2_diag : TypedThreshold;
e3_diag : TypedThreshold;
topology_passed : bool;
policy_passed : bool
}.
Definition evaluate_corner (c : Corner) (policyOK : bool) : CornerDiagnostics :=
{| e1_diag := evaluate_seam (e1 c);
e2_diag := evaluate_seam (e2 c);
e3_diag := evaluate_seam (e3 c);
topology_passed := CornerTopologyOK c;
policy_passed := policyOK |}.
Definition all_passed (d : CornerDiagnostics) : bool :=
is_clean (e1_diag d) && is_clean (e2_diag d) && is_clean (e3_diag d) &&
topology_passed d && policy_passed d.
(* ============================================================================== *)
(* THEOREM 1: J / Typed Threshold equivalence *)
(* ============================================================================== *)
Theorem seam_is_clean_eq_J : forall e : SeamEvidence,
J e = is_clean (evaluate_seam e).
Proof. intro e. reflexivity. Qed.

--- PAGE 5 ---
(* ============================================================================== *)
(* THEOREM 2: Corner authorization equals diagnostic conjunction *)
(* ============================================================================== *)
Theorem corner_authorization_iff_diagnostics_passed : forall (c : Corner) (policyOK : bool),
WriteOK c policyOK = all_passed (evaluate_corner c policyOK).
Proof.
intros c policyOK.
unfold WriteOK, CornerK, evaluate_corner, all_passed. simpl.
rewrite <- seam_is_clean_eq_J.
rewrite <- (seam_is_clean_eq_J (e2 c)).
rewrite <- (seam_is_clean_eq_J (e3 c)).
reflexivity.
Qed.
(* ============================================================================== *)
(* SECTION A. ORIGINAL EXPLAINABLE DENIAL THEOREMS (preserved verbatim) *)
(* THEOREM 3: identity at seam 1 *)
(* THEOREM 4: lineage at seam 2 *)
(* THEOREM 5: time window at seam 3 *)
(* ============================================================================== *)
Theorem explainable_denial_identity : forall c policyOK,
id_passed (evaluate_seam (e1 c)) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK, CornerK, J. rewrite H.
repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
reflexivity.
Qed.
Theorem explainable_denial_lineage : forall c policyOK,
lineage_passed (evaluate_seam (e2 c)) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK, CornerK, J. rewrite H.
repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
reflexivity.
Qed.
Theorem explainable_denial_time_window : forall c policyOK,
time_passed (evaluate_seam (e3 c)) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK, CornerK, J. rewrite H.
repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
reflexivity.
Qed.
(* ============================================================================== *)
(* SECTION B. SEAM-1 DIAGNOSTIC FAILURES (THEOREMS 6-11) *)
(* Each shows a single dimension failing at the first seam suffices to deny. *)
(* ============================================================================== *)
Theorem explainable_denial_time_window_seam1 : forall c policyOK,
time_passed (evaluate_seam (e1 c)) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK, CornerK, J. rewrite H.
repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
reflexivity.
Qed.
Theorem explainable_denial_purpose_seam1 : forall c policyOK,
purpose_passed (evaluate_seam (e1 c)) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK, CornerK, J. rewrite H.
repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
reflexivity.
Qed.

--- PAGE 6 ---
Theorem explainable_denial_lineage_seam1 : forall c policyOK,
lineage_passed (evaluate_seam (e1 c)) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK, CornerK, J. rewrite H.
repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
reflexivity.
Qed.
Theorem explainable_denial_version_seam1 : forall c policyOK,
version_passed (evaluate_seam (e1 c)) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK, CornerK, J. rewrite H.
repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
reflexivity.
Qed.
Theorem explainable_denial_scope_seam1 : forall c policyOK,
scope_passed (evaluate_seam (e1 c)) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK, CornerK, J. rewrite H.
repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
reflexivity.
Qed.
Theorem explainable_denial_attest_seam1 : forall c policyOK,
attest_passed (evaluate_seam (e1 c)) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK, CornerK, J. rewrite H.
repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
reflexivity.
Qed.
(* ============================================================================== *)
(* SECTION C. SEAM-2 DIAGNOSTIC FAILURES (THEOREMS 12-17) *)
(* ============================================================================== *)
Theorem explainable_denial_time_window_seam2 : forall c policyOK,
time_passed (evaluate_seam (e2 c)) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK, CornerK, J. rewrite H.
repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
reflexivity.
Qed.
Theorem explainable_denial_identity_seam2 : forall c policyOK,
id_passed (evaluate_seam (e2 c)) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK, CornerK, J. rewrite H.
repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
reflexivity.
Qed.
Theorem explainable_denial_purpose_seam2 : forall c policyOK,
purpose_passed (evaluate_seam (e2 c)) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK, CornerK, J. rewrite H.
repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
reflexivity.
Qed.

--- PAGE 7 ---
Theorem explainable_denial_version_seam2 : forall c policyOK,
version_passed (evaluate_seam (e2 c)) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK, CornerK, J. rewrite H.
repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
reflexivity.
Qed.
Theorem explainable_denial_scope_seam2 : forall c policyOK,
scope_passed (evaluate_seam (e2 c)) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK, CornerK, J. rewrite H.
repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
reflexivity.
Qed.
Theorem explainable_denial_attest_seam2 : forall c policyOK,
attest_passed (evaluate_seam (e2 c)) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK, CornerK, J. rewrite H.
repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
reflexivity.
Qed.
(* ============================================================================== *)
(* SECTION D. SEAM-3 DIAGNOSTIC FAILURES (THEOREMS 18-23) *)
(* ============================================================================== *)
Theorem explainable_denial_identity_seam3 : forall c policyOK,
id_passed (evaluate_seam (e3 c)) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK, CornerK, J. rewrite H.
repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
reflexivity.
Qed.
Theorem explainable_denial_purpose_seam3 : forall c policyOK,
purpose_passed (evaluate_seam (e3 c)) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK, CornerK, J. rewrite H.
repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
reflexivity.
Qed.
Theorem explainable_denial_lineage_seam3 : forall c policyOK,
lineage_passed (evaluate_seam (e3 c)) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK, CornerK, J. rewrite H.
repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
reflexivity.
Qed.
Theorem explainable_denial_version_seam3 : forall c policyOK,
version_passed (evaluate_seam (e3 c)) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK, CornerK, J. rewrite H.
repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
reflexivity.
Qed.
Theorem explainable_denial_scope_seam3 : forall c policyOK,

--- PAGE 8 ---
scope_passed (evaluate_seam (e3 c)) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK, CornerK, J. rewrite H.
repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
reflexivity.
Qed.
Theorem explainable_denial_attest_seam3 : forall c policyOK,
attest_passed (evaluate_seam (e3 c)) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK, CornerK, J. rewrite H.
repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
reflexivity.
Qed.
(* ============================================================================== *)
(* SECTION E. STRUCTURAL DENIAL THEOREMS (THEOREMS 24-25) *)
(* ============================================================================== *)
Theorem explainable_denial_topology : forall c policyOK,
topology_passed (evaluate_corner c policyOK) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK, CornerK. rewrite H.
repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
reflexivity.
Qed.
Theorem explainable_denial_policy : forall c policyOK,
policy_passed (evaluate_corner c policyOK) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK. rewrite H.
repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
reflexivity.
Qed.
(* ============================================================================== *)
(* SECTION F. WITNESS-EXISTENCE THEOREMS (THEOREMS 26-27) *)
(* Establish that the predicate is non-trivial: at least one corner *)
(* authorizes and at least one denies under its respective policy. *)
(* ============================================================================== *)
Definition wit_seam_a : SeamEvidence := {|
nonce := 1; origin_id := 1; target_id := 5; privilege_level := 50;
timestamp := 100; expiry := 200;
id_ok := true; purpose_ok := true; lineage_ok := true;
version_ok := true; scope_ok := true; attest_ok := true |}.
Definition wit_seam_b : SeamEvidence := {|
nonce := 2; origin_id := 2; target_id := 5; privilege_level := 50;
timestamp := 110; expiry := 200;
id_ok := true; purpose_ok := true; lineage_ok := true;
version_ok := true; scope_ok := true; attest_ok := true |}.
Definition wit_seam_c : SeamEvidence := {|
nonce := 3; origin_id := 3; target_id := 5; privilege_level := 50;
timestamp := 120; expiry := 200;
id_ok := true; purpose_ok := true; lineage_ok := true;
version_ok := true; scope_ok := true; attest_ok := true |}.
Definition wit_corner : Corner := {|
target_node := 5; exec_time := 150;
e1 := wit_seam_a; e2 := wit_seam_b; e3 := wit_seam_c |}.
Theorem good_corner_exists :
exists (c : Corner) (policyOK : bool), WriteOK c policyOK = true.
Proof.
exists wit_corner. exists true. reflexivity.

--- PAGE 9 ---
Qed.
Theorem bad_corner_exists :
exists (c : Corner) (policyOK : bool), WriteOK c policyOK = false.
Proof.
exists wit_corner. exists false. reflexivity.
Qed.
(* ============================================================================== *)
(* SECTION G. CONVERSE PROJECTION THEOREMS (THEOREMS 28-50) *)
(* *)
(* For every diagnostic component, WriteOK = true implies that component = true. *)
(* Establishes the reverse direction of the keystone equivalence on a per-field *)
(* basis: granted authorization guarantees every individual diagnostic passed. *)
(* ============================================================================== *)
(* Decomposition helpers *)
Lemma all_passed_decomp : forall d : CornerDiagnostics,
all_passed d = true ->
is_clean (e1_diag d) = true /\
is_clean (e2_diag d) = true /\
is_clean (e3_diag d) = true /\
topology_passed d = true /\
policy_passed d = true.
Proof.
intros d H. unfold all_passed in H.
rewrite !Bool.andb_true_iff in H. tauto.
Qed.
Lemma is_clean_decomp : forall t : TypedThreshold,
is_clean t = true ->
time_passed t = true /\ id_passed t = true /\ purpose_passed t = true /\
lineage_passed t = true /\ version_passed t = true /\ scope_passed t = true /\
attest_passed t = true.
Proof.
intros t H. unfold is_clean in H.
rewrite !Bool.andb_true_iff in H. tauto.
Qed.
(* SEAM 1 -- Theorems 28-34 *)
Theorem authorization_implies_time_window_seam1 : forall c policyOK,
WriteOK c policyOK = true -> time_passed (evaluate_seam (e1 c)) = true.
Proof.
intros c policyOK H.
rewrite corner_authorization_iff_diagnostics_passed in H.
apply all_passed_decomp in H. destruct H as [H _].
apply is_clean_decomp in H. destruct H as [H _]. exact H.
Qed.
Theorem authorization_implies_identity_seam1 : forall c policyOK,
WriteOK c policyOK = true -> id_passed (evaluate_seam (e1 c)) = true.
Proof.
intros c policyOK H.
rewrite corner_authorization_iff_diagnostics_passed in H.
apply all_passed_decomp in H. destruct H as [H _].
apply is_clean_decomp in H. destruct H as [_ [H _]]. exact H.
Qed.
Theorem authorization_implies_purpose_seam1 : forall c policyOK,
WriteOK c policyOK = true -> purpose_passed (evaluate_seam (e1 c)) = true.
Proof.
intros c policyOK H.
rewrite corner_authorization_iff_diagnostics_passed in H.
apply all_passed_decomp in H. destruct H as [H _].
apply is_clean_decomp in H. destruct H as [_ [_ [H _]]]. exact H.
Qed.
Theorem authorization_implies_lineage_seam1 : forall c policyOK,
WriteOK c policyOK = true -> lineage_passed (evaluate_seam (e1 c)) = true.
Proof.
intros c policyOK H.
rewrite corner_authorization_iff_diagnostics_passed in H.
apply all_passed_decomp in H. destruct H as [H _].
apply is_clean_decomp in H. destruct H as [_ [_ [_ [H _]]]]. exact H.
Qed.

--- PAGE 10 ---
Theorem authorization_implies_version_seam1 : forall c policyOK,
WriteOK c policyOK = true -> version_passed (evaluate_seam (e1 c)) = true.
Proof.
intros c policyOK H.
rewrite corner_authorization_iff_diagnostics_passed in H.
apply all_passed_decomp in H. destruct H as [H _].
apply is_clean_decomp in H. destruct H as [_ [_ [_ [_ [H _]]]]]. exact H.
Qed.
Theorem authorization_implies_scope_seam1 : forall c policyOK,
WriteOK c policyOK = true -> scope_passed (evaluate_seam (e1 c)) = true.
Proof.
intros c policyOK H.
rewrite corner_authorization_iff_diagnostics_passed in H.
apply all_passed_decomp in H. destruct H as [H _].
apply is_clean_decomp in H. destruct H as [_ [_ [_ [_ [_ [H _]]]]]]. exact H.
Qed.
Theorem authorization_implies_attest_seam1 : forall c policyOK,
WriteOK c policyOK = true -> attest_passed (evaluate_seam (e1 c)) = true.
Proof.
intros c policyOK H.
rewrite corner_authorization_iff_diagnostics_passed in H.
apply all_passed_decomp in H. destruct H as [H _].
apply is_clean_decomp in H. destruct H as [_ [_ [_ [_ [_ [_ H]]]]]]. exact H.
Qed.
(* SEAM 2 -- Theorems 35-41 *)
Theorem authorization_implies_time_window_seam2 : forall c policyOK,
WriteOK c policyOK = true -> time_passed (evaluate_seam (e2 c)) = true.
Proof.
intros c policyOK H.
rewrite corner_authorization_iff_diagnostics_passed in H.
apply all_passed_decomp in H. destruct H as [_ [H _]].
apply is_clean_decomp in H. destruct H as [H _]. exact H.
Qed.
Theorem authorization_implies_identity_seam2 : forall c policyOK,
WriteOK c policyOK = true -> id_passed (evaluate_seam (e2 c)) = true.
Proof.
intros c policyOK H.
rewrite corner_authorization_iff_diagnostics_passed in H.
apply all_passed_decomp in H. destruct H as [_ [H _]].
apply is_clean_decomp in H. destruct H as [_ [H _]]. exact H.
Qed.
Theorem authorization_implies_purpose_seam2 : forall c policyOK,
WriteOK c policyOK = true -> purpose_passed (evaluate_seam (e2 c)) = true.
Proof.
intros c policyOK H.
rewrite corner_authorization_iff_diagnostics_passed in H.
apply all_passed_decomp in H. destruct H as [_ [H _]].
apply is_clean_decomp in H. destruct H as [_ [_ [H _]]]. exact H.
Qed.
Theorem authorization_implies_lineage_seam2 : forall c policyOK,
WriteOK c policyOK = true -> lineage_passed (evaluate_seam (e2 c)) = true.
Proof.
intros c policyOK H.
rewrite corner_authorization_iff_diagnostics_passed in H.
apply all_passed_decomp in H. destruct H as [_ [H _]].
apply is_clean_decomp in H. destruct H as [_ [_ [_ [H _]]]]. exact H.
Qed.
Theorem authorization_implies_version_seam2 : forall c policyOK,
WriteOK c policyOK = true -> version_passed (evaluate_seam (e2 c)) = true.
Proof.
intros c policyOK H.
rewrite corner_authorization_iff_diagnostics_passed in H.
apply all_passed_decomp in H. destruct H as [_ [H _]].
apply is_clean_decomp in H. destruct H as [_ [_ [_ [_ [H _]]]]]. exact H.
Qed.
Theorem authorization_implies_scope_seam2 : forall c policyOK,

--- PAGE 11 ---
WriteOK c policyOK = true -> scope_passed (evaluate_seam (e2 c)) = true.
Proof.
intros c policyOK H.
rewrite corner_authorization_iff_diagnostics_passed in H.
apply all_passed_decomp in H. destruct H as [_ [H _]].
apply is_clean_decomp in H. destruct H as [_ [_ [_ [_ [_ [H _]]]]]]. exact H.
Qed.
Theorem authorization_implies_attest_seam2 : forall c policyOK,
WriteOK c policyOK = true -> attest_passed (evaluate_seam (e2 c)) = true.
Proof.
intros c policyOK H.
rewrite corner_authorization_iff_diagnostics_passed in H.
apply all_passed_decomp in H. destruct H as [_ [H _]].
apply is_clean_decomp in H. destruct H as [_ [_ [_ [_ [_ [_ H]]]]]]. exact H.
Qed.
(* SEAM 3 -- Theorems 42-48 *)
Theorem authorization_implies_time_window_seam3 : forall c policyOK,
WriteOK c policyOK = true -> time_passed (evaluate_seam (e3 c)) = true.
Proof.
intros c policyOK H.
rewrite corner_authorization_iff_diagnostics_passed in H.
apply all_passed_decomp in H. destruct H as [_ [_ [H _]]].
apply is_clean_decomp in H. destruct H as [H _]. exact H.
Qed.
Theorem authorization_implies_identity_seam3 : forall c policyOK,
WriteOK c policyOK = true -> id_passed (evaluate_seam (e3 c)) = true.
Proof.
intros c policyOK H.
rewrite corner_authorization_iff_diagnostics_passed in H.
apply all_passed_decomp in H. destruct H as [_ [_ [H _]]].
apply is_clean_decomp in H. destruct H as [_ [H _]]. exact H.
Qed.
Theorem authorization_implies_purpose_seam3 : forall c policyOK,
WriteOK c policyOK = true -> purpose_passed (evaluate_seam (e3 c)) = true.
Proof.
intros c policyOK H.
rewrite corner_authorization_iff_diagnostics_passed in H.
apply all_passed_decomp in H. destruct H as [_ [_ [H _]]].
apply is_clean_decomp in H. destruct H as [_ [_ [H _]]]. exact H.
Qed.
Theorem authorization_implies_lineage_seam3 : forall c policyOK,
WriteOK c policyOK = true -> lineage_passed (evaluate_seam (e3 c)) = true.
Proof.
intros c policyOK H.
rewrite corner_authorization_iff_diagnostics_passed in H.
apply all_passed_decomp in H. destruct H as [_ [_ [H _]]].
apply is_clean_decomp in H. destruct H as [_ [_ [_ [H _]]]]. exact H.
Qed.
Theorem authorization_implies_version_seam3 : forall c policyOK,
WriteOK c policyOK = true -> version_passed (evaluate_seam (e3 c)) = true.
Proof.
intros c policyOK H.
rewrite corner_authorization_iff_diagnostics_passed in H.
apply all_passed_decomp in H. destruct H as [_ [_ [H _]]].
apply is_clean_decomp in H. destruct H as [_ [_ [_ [_ [H _]]]]]. exact H.
Qed.
Theorem authorization_implies_scope_seam3 : forall c policyOK,
WriteOK c policyOK = true -> scope_passed (evaluate_seam (e3 c)) = true.
Proof.
intros c policyOK H.
rewrite corner_authorization_iff_diagnostics_passed in H.
apply all_passed_decomp in H. destruct H as [_ [_ [H _]]].
apply is_clean_decomp in H. destruct H as [_ [_ [_ [_ [_ [H _]]]]]]. exact H.
Qed.
Theorem authorization_implies_attest_seam3 : forall c policyOK,
W


0
1	[notice] A new release of pip is available: 26.0.1 -> 26.1
2	[notice] To update, run: python.exe -m pip install --upgrade pip
3	Pages: 77
4
5	--- PAGE 1 ---
6	Cubie Trust Compiler – Master Theorem Stack
7	v1.0_CubieMasterStack_0430.md
8	Field Value
9	Author Nicholas M Venezia
10	Organization Centillion AI Inc.
11	Date 2026-04-30
12	Verification protocol Triple-kernel (Coq 8.18.0 + coqchk + Lean 4.30.0-rc2)
13	Lean configuration Lean 4 Core (no Mathlib)
14	Patent family US11956363B2, US12073439B2, US20240195628A1
15	CNDA Intel CNDA 083697
16	Total deliverables 7
17	Total theorems 163 (146 unique; V2.0 subsumes V1.50)
18	Status SPEC_LOCKED across all deliverables
19	This document is the canonical bundle of every approved theorem and machine-checked proof in the Cubie Trust Compiler verification stack. Each
20	deliverable section contains the full Coq source, the full Lean 4 source, and the SHA-256 hash of each source file. Every theorem has been independently
21	verified by both kernels under the constraints of Lean 4 Core (no Mathlib) and Coq’s standard library.
22	The stack is the formal substrate for the TrustFortress BNN gate, the Blue Shield kernel-bypass security appliance, and the patent claims listed above.
23	Section A: Stack Index and SHA Manifest
24	The seven deliverables, in build order, with primary source SHA-256 hashes:
25	ID Title Theorems Coq SHA-256 Lean SHA-256
26	Ramen
27	V1.19.2 Corner 53 d564c4830fc9030bff0f9c6ed14dbde1c382a3bf04ad601d7e953548d206206b 0f269cb03e2b30069cfb4a7b757c4c34dd15dc56ce204071061dd8f3bc7787b5
28	Consensus
29	ToR
30	V1.30 Admission 5 a73a6b7586a865057d587b02f2fe06dd1d5d53b002ebc070ce3d55efbba3ba8c 34fa586a7c161f330ea3b5d1ed6c550c39986803ec99bdaa8b5141944280cd2a
31	Compiler
32	ToR
33	V1.31 Corner 2 2d306870d199b2aa402b9bf521776517bc80ff8cf251d4252864b2bb09b0529d 6c3b1772caa9de2986bd0e715eddef5622ef41f91b83b6cafb7492e8b36f38df
34	Spoofing
35	Cubie
36	V1.40 6 815bfcf12627f5c1bc2bef702092cf6dda85a5ab69e0fe29e9d0c18ea4ca5340 f14cd1ae1e8eb6a2dc0df9175246ce64f5994c9bf03a4cd9b74e632945338d6b
37	Bridge
38	Cubie
39	Trust
40	V1.50 17 5dd9197339549a0b289bad6c4532a422387b2b385f8d2acfb67a654832f4117b fcf1132144f46f104a1a41699297c99a35d07b9d345b75f4d329d5b7d553cc50
41	Compiler
42	(Track B)
43	Cubie
44	Trust
45	V2.0 Compiler 26 17af5b3f2cc3d6648eba08d8e0aa94557a250430f454a53454396439ed02c31e c9d1d80c75e93df6af0c868fce1936a393b4e6af40afd0ce1de8ddceefedd436
46	(Track C,
47	canonical)
48	Cubie
49	Trust
50	Compiler
51	V2.0
52	V2.0 Per- 54 91f31a74c1675dde7b6857050f68f5c8049afab7115f5ae5cdc17e605ecb4a36 98a99b8e9438277c85d20675b6f18c3bf47b76ad681a260c0bde8c9a80a93d36
53	PerPredicate
54
55	--- PAGE 2 ---
56	Predicate
57	Addendum
58	Section B: Deliverable Summaries
59	V1.19.2 – Ramen Corner Consensus
60	Track: Tier Two
61	Theorem count: 53
62	Status: DELIVERED
63	Axiom profile: Coq: 53/53 closed under the global context. Lean: 4 axiom-free, 46 [propext], 3 [propext, Quot.sound].
64	Tier Two of the Ramen Corner Consensus stack. Fifty-three theorems across the 23 diagnostic predicates plus three denial-counting theorems plus the
65	corner-consensus iff equivalence. Establishes the foundational corner-level admission semantics that all subsequent compilers (V1.30, V1.40, V1.50, V2.0)
66	inherit.
67	V1.30 – ToR Admission Compiler
68	Track: GPU rack-edge admission
69	Theorem count: 5
70	Status: DELIVERED
71	Axiom profile: Coq: 5/5 closed under the global context. Lean: all 5 axiom-free or [propext].
72	Rack-edge GPU admission control with seven-dimensional ToR seam, explainable corner consensus, in-rack bypass rejection, epoch staleness rejection,
73	and goodput firewall containment. Five keystone theorems on the host-side verifier semantics.
74	V1.31 – ToR Corner Spoofing
75	Track: Surface-spoofing impossibility
76	Theorem count: 2
77	Status: DELIVERED
78	Axiom profile: Coq: 2/2 closed. Lean: 2/2 axiom-free.
79	Surface-spoofing impossibility lifted from individual seams to the corner aggregate. Constructs two distinct RackCorners that share a 5-field SeamSurface
80	signature while differing on Admit, proving that surface telemetry alone cannot determine admission.
81	V1.40 – Cubie Bridge
82	Track: Track A (V1.30 to Cubie embedding)
83	Theorem count: 6
84	Status: DELIVERED
85	Axiom profile: Coq: 6/6 closed. Lean: 6/6 axiom-free.
86	Bridge from the V1.30 ToR seven-dimensional seam to the Cubie GPU-corner / Deployment-corner decomposition. Six theorems establish that the seam
87	check J factors into two independent corner predicates and that each corner can fail in isolation. Includes 8192-case decomposition keystone (T1).
88	V1.50 – Cubie Trust Compiler (Track B)
89	Track: Track B (face promotion)
90	Theorem count: 17
91	Status: DELIVERED
92	Axiom profile: Coq: 17/17 closed. Lean: 14 axiom-free, 3 [propext, Quot.sound].
93	Face promotion. Promotes the V1.30 7-dimension flat seam to the fifty-four-predicate CubieRequest substrate per Cubie diagram 04. Seventeen theorems:
94	face-localized denial across all six faces, the converse admit-implies-face-pass family, three denial-counting properties, and surface-spoofing separation
95	lifted to the new substrate.
96	V2.0 – Cubie Trust Compiler (Track C, canonical)
97	Track: Track C (full unification)
98	Theorem count: 26
99
100	--- PAGE 3 ---
101	Status: DELIVERED
102	Axiom profile: Coq: 26/26 closed. Lean: 18 axiom-free, 5 [propext], 3 [propext, Quot.sound].
103	Full unification of the Cubie Trust Compiler. Subsumes V1.30, V1.31, V1.40, and V1.50 as the canonical formal specification. Twenty-six theorems: V1.50’s 17
104	plus T3 cross-corner independence (2), T7 lease integrity (3), T8 bypass-no-lease (1), T9 epoch monotonicity (2), and T10 HA split-brain fail-closed (1).
105	V2.0 PerPredicate – Cubie Trust Compiler V2.0 Per-Predicate Addendum
106	Track: Patent-claim corollaries
107	Theorem count: 54
108	Status: DELIVERED
109	Axiom profile: Coq: 54/54 closed. Lean: 54/54 axiom-free.
110	Patent-counsel addendum. Each of the 54 face-check predicates is broken out as an individual named corollary of T2 face_localized_denial. Provides a
111	one-to-one mapping between formal theorems and the claim limitations of US20240195628A1. Six faces times nine checks equals fifty-four corollaries.
112	Section C: Full Source Listings
113	Each deliverable below is presented in two forms: the Coq 8.18.0 source (verified by coqc and coqchk) and the Lean 4.30.0-rc2 source (verified by lean
114	against Lean 4 Core, no Mathlib). The SHA-256 hash of each source file is shown immediately above the listing.
115	V1.19.2 – Ramen Corner Consensus
116	Coq source. File: RamenCornerConsensusV1192.v. SHA-256: d564c4830fc9030bff0f9c6ed14dbde1c382a3bf04ad601d7e953548d206206b.
117	(* ============================================================================== *)
118	(* AUTHOR: Nicholas M Venezia *)
119	(* CENTILLION AI INC. -- EXPLAINABLE CORNER CONSENSUS (V1.19.2 TIER TWO) *)
120	(* *)
121	(* V1.19.2 = V1.19.1 + Tier Two enhancements: *)
122	(* * Section G: 23 converse projection theorems *)
123	(* (WriteOK = true => every diagnostic component = true) *)
124	(* * Section H: 3 denial-counting theorems *)
125	(* (denial_count function + zero/positive/bounded equivalences) *)
126	(* Total: 53 theorems = 27 (V1.19.1) + 23 (Section G) + 3 (Section H). *)
127	(* *)
128	(* Status: SPEC_LOCKED. Fully Constructive. Zero Admitted. Zero Axioms. *)
129	(* ============================================================================== *)
130	Require Import Bool List Nat Lia PeanoNat.
131	Import ListNotations.
132	Section RamenCornerConsensus.
133	(* ============================================================================== *)
134	(* 1. BASE V1.19 SUBSTRATE *)
135	(* ============================================================================== *)
136	Record SeamEvidence := {
137	nonce : nat;
138	origin_id : nat;
139	target_id : nat;
140	privilege_level: nat;
141	timestamp : nat;
142	expiry : nat;
143	id_ok : bool;
144	purpose_ok : bool;
145	lineage_ok : bool;
146	version_ok : bool;
147	scope_ok : bool;
148	attest_ok : bool
149	}.
150	Definition J (e : SeamEvidence) : bool :=
151	(timestamp e <=? expiry e) &&
152	id_ok e && purpose_ok e && lineage_ok e &&
153	version_ok e && scope_ok e && attest_ok e.
154	Record Corner := {
155	target_node : nat;
156
157	--- PAGE 4 ---
158	exec_time : nat;
159	e1 : SeamEvidence;
160	e2 : SeamEvidence;
161	e3 : SeamEvidence
162	}.
163	Definition CornerTopologyOK (c : Corner) : bool :=
164	(negb (nonce (e1 c) =? nonce (e2 c)) &&
165	negb (nonce (e2 c) =? nonce (e3 c)) &&
166	negb (nonce (e1 c) =? nonce (e3 c))) &&
167	((target_id (e1 c) =? target_node c) &&
168	(target_id (e2 c) =? target_node c) &&
169	(target_id (e3 c) =? target_node c)) &&
170	((timestamp (e1 c) <=? exec_time c) && (exec_time c <=? expiry (e1 c)) &&
171	(timestamp (e2 c) <=? exec_time c) && (exec_time c <=? expiry (e2 c)) &&
172	(timestamp (e3 c) <=? exec_time c) && (exec_time c <=? expiry (e3 c))).
173	Definition CornerK (c : Corner) : bool :=
174	J (e1 c) && J (e2 c) && J (e3 c) && CornerTopologyOK c.
175	Definition WriteOK (c : Corner) (policyOK : bool) : bool :=
176	CornerK c && policyOK.
177	(* ============================================================================== *)
178	(* 2. EXPLAINABLE TYPED THRESHOLDS *)
179	(* ============================================================================== *)
180	Record TypedThreshold := {
181	time_passed : bool;
182	id_passed : bool;
183	purpose_passed : bool;
184	lineage_passed : bool;
185	version_passed : bool;
186	scope_passed : bool;
187	attest_passed : bool
188	}.
189	Definition evaluate_seam (e : SeamEvidence) : TypedThreshold :=
190	{| time_passed := timestamp e <=? expiry e;
191	id_passed := id_ok e;
192	purpose_passed := purpose_ok e;
193	lineage_passed := lineage_ok e;
194	version_passed := version_ok e;
195	scope_passed := scope_ok e;
196	attest_passed := attest_ok e |}.
197	Definition is_clean (t : TypedThreshold) : bool :=
198	time_passed t && id_passed t && purpose_passed t &&
199	lineage_passed t && version_passed t && scope_passed t && attest_passed t.
200	Record CornerDiagnostics := {
201	e1_diag : TypedThreshold;
202	e2_diag : TypedThreshold;
203	e3_diag : TypedThreshold;
204	topology_passed : bool;
205	policy_passed : bool
206	}.
207	Definition evaluate_corner (c : Corner) (policyOK : bool) : CornerDiagnostics :=
208	{| e1_diag := evaluate_seam (e1 c);
209	e2_diag := evaluate_seam (e2 c);
210	e3_diag := evaluate_seam (e3 c);
211	topology_passed := CornerTopologyOK c;
212	policy_passed := policyOK |}.
213	Definition all_passed (d : CornerDiagnostics) : bool :=
214	is_clean (e1_diag d) && is_clean (e2_diag d) && is_clean (e3_diag d) &&
215	topology_passed d && policy_passed d.
216	(* ============================================================================== *)
217	(* THEOREM 1: J / Typed Threshold equivalence *)
218	(* ============================================================================== *)
219	Theorem seam_is_clean_eq_J : forall e : SeamEvidence,
220	J e = is_clean (evaluate_seam e).
221	Proof. intro e. reflexivity. Qed.
222
223	--- PAGE 5 ---
224	(* ============================================================================== *)
225	(* THEOREM 2: Corner authorization equals diagnostic conjunction *)
226	(* ============================================================================== *)
227	Theorem corner_authorization_iff_diagnostics_passed : forall (c : Corner) (policyOK : bool),
228	WriteOK c policyOK = all_passed (evaluate_corner c policyOK).
229	Proof.
230	intros c policyOK.
231	unfold WriteOK, CornerK, evaluate_corner, all_passed. simpl.
232	rewrite <- seam_is_clean_eq_J.
233	rewrite <- (seam_is_clean_eq_J (e2 c)).
234	rewrite <- (seam_is_clean_eq_J (e3 c)).
235	reflexivity.
236	Qed.
237	(* ============================================================================== *)
238	(* SECTION A. ORIGINAL EXPLAINABLE DENIAL THEOREMS (preserved verbatim) *)
239	(* THEOREM 3: identity at seam 1 *)
240	(* THEOREM 4: lineage at seam 2 *)
241	(* THEOREM 5: time window at seam 3 *)
242	(* ============================================================================== *)
243	Theorem explainable_denial_identity : forall c policyOK,
244	id_passed (evaluate_seam (e1 c)) = false -> WriteOK c policyOK = false.
245	Proof.
246	intros c policyOK H.
247	simpl in H.
248	unfold WriteOK, CornerK, J. rewrite H.
249	repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
250	reflexivity.
251	Qed.
252	Theorem explainable_denial_lineage : forall c policyOK,
253	lineage_passed (evaluate_seam (e2 c)) = false -> WriteOK c policyOK = false.
254	Proof.
255	intros c policyOK H.
256	simpl in H.
257	unfold WriteOK, CornerK, J. rewrite H.
258	repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
259	reflexivity.
260	Qed.
261	Theorem explainable_denial_time_window : forall c policyOK,
262	time_passed (evaluate_seam (e3 c)) = false -> WriteOK c policyOK = false.
263	Proof.
264	intros c policyOK H.
265	simpl in H.
266	unfold WriteOK, CornerK, J. rewrite H.
267	repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
268	reflexivity.
269	Qed.
270	(* ============================================================================== *)
271	(* SECTION B. SEAM-1 DIAGNOSTIC FAILURES (THEOREMS 6-11) *)
272	(* Each shows a single dimension failing at the first seam suffices to deny. *)
273	(* ============================================================================== *)
274	Theorem explainable_denial_time_window_seam1 : forall c policyOK,
275	time_passed (evaluate_seam (e1 c)) = false -> WriteOK c policyOK = false.
276	Proof.
277	intros c policyOK H.
278	simpl in H.
279	unfold WriteOK, CornerK, J. rewrite H.
280	repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
281	reflexivity.
282	Qed.
283	Theorem explainable_denial_purpose_seam1 : forall c policyOK,
284	purpose_passed (evaluate_seam (e1 c)) = false -> WriteOK c policyOK = false.
285	Proof.
286	intros c policyOK H.
287	simpl in H.
288	unfold WriteOK, CornerK, J. rewrite H.
289	repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
290	reflexivity.
291	Qed.
292
293	--- PAGE 6 ---
294	Theorem explainable_denial_lineage_seam1 : forall c policyOK,
295	lineage_passed (evaluate_seam (e1 c)) = false -> WriteOK c policyOK = false.
296	Proof.
297	intros c policyOK H.
298	simpl in H.
299	unfold WriteOK, CornerK, J. rewrite H.

[notice] A new release of pip is available: 26.0.1 -> 26.1
[notice] To update, run: python.exe -m pip install --upgrade pip
Pages: 77

--- PAGE 1 ---
Cubie Trust Compiler – Master Theorem Stack
v1.0_CubieMasterStack_0430.md
Field Value
Author Nicholas M Venezia
Organization Centillion AI Inc.
Date 2026-04-30
Verification protocol Triple-kernel (Coq 8.18.0 + coqchk + Lean 4.30.0-rc2)
Lean configuration Lean 4 Core (no Mathlib)
Patent family US11956363B2, US12073439B2, US20240195628A1
CNDA Intel CNDA 083697
Total deliverables 7
Total theorems 163 (146 unique; V2.0 subsumes V1.50)
Status SPEC_LOCKED across all deliverables
This document is the canonical bundle of every approved theorem and machine-checked proof in the Cubie Trust Compiler verification stack. Each
deliverable section contains the full Coq source, the full Lean 4 source, and the SHA-256 hash of each source file. Every theorem has been independently
verified by both kernels under the constraints of Lean 4 Core (no Mathlib) and Coq’s standard library.
The stack is the formal substrate for the TrustFortress BNN gate, the Blue Shield kernel-bypass security appliance, and the patent claims listed above.
Section A: Stack Index and SHA Manifest
The seven deliverables, in build order, with primary source SHA-256 hashes:
ID Title Theorems Coq SHA-256 Lean SHA-256
Ramen
V1.19.2 Corner 53 d564c4830fc9030bff0f9c6ed14dbde1c382a3bf04ad601d7e953548d206206b 0f269cb03e2b30069cfb4a7b757c4c34dd15dc56ce204071061dd8f3bc7787b5
Consensus
ToR
V1.30 Admission 5 a73a6b7586a865057d587b02f2fe06dd1d5d53b002ebc070ce3d55efbba3ba8c 34fa586a7c161f330ea3b5d1ed6c550c39986803ec99bdaa8b5141944280cd2a
Compiler
ToR
V1.31 Corner 2 2d306870d199b2aa402b9bf521776517bc80ff8cf251d4252864b2bb09b0529d 6c3b1772caa9de2986bd0e715eddef5622ef41f91b83b6cafb7492e8b36f38df
Spoofing
Cubie
V1.40 6 815bfcf12627f5c1bc2bef702092cf6dda85a5ab69e0fe29e9d0c18ea4ca5340 f14cd1ae1e8eb6a2dc0df9175246ce64f5994c9bf03a4cd9b74e632945338d6b
Bridge
Cubie
Trust
V1.50 17 5dd9197339549a0b289bad6c4532a422387b2b385f8d2acfb67a654832f4117b fcf1132144f46f104a1a41699297c99a35d07b9d345b75f4d329d5b7d553cc50
Compiler
(Track B)
Cubie
Trust
V2.0 Compiler 26 17af5b3f2cc3d6648eba08d8e0aa94557a250430f454a53454396439ed02c31e c9d1d80c75e93df6af0c868fce1936a393b4e6af40afd0ce1de8ddceefedd436
(Track C,
canonical)
Cubie
Trust
Compiler
V2.0
V2.0 Per- 54 91f31a74c1675dde7b6857050f68f5c8049afab7115f5ae5cdc17e605ecb4a36 98a99b8e9438277c85d20675b6f18c3bf47b76ad681a260c0bde8c9a80a93d36
PerPredicate

--- PAGE 2 ---
Predicate
Addendum
Section B: Deliverable Summaries
V1.19.2 – Ramen Corner Consensus
Track: Tier Two
Theorem count: 53
Status: DELIVERED
Axiom profile: Coq: 53/53 closed under the global context. Lean: 4 axiom-free, 46 [propext], 3 [propext, Quot.sound].
Tier Two of the Ramen Corner Consensus stack. Fifty-three theorems across the 23 diagnostic predicates plus three denial-counting theorems plus the
corner-consensus iff equivalence. Establishes the foundational corner-level admission semantics that all subsequent compilers (V1.30, V1.40, V1.50, V2.0)
inherit.
V1.30 – ToR Admission Compiler
Track: GPU rack-edge admission
Theorem count: 5
Status: DELIVERED
Axiom profile: Coq: 5/5 closed under the global context. Lean: all 5 axiom-free or [propext].
Rack-edge GPU admission control with seven-dimensional ToR seam, explainable corner consensus, in-rack bypass rejection, epoch staleness rejection,
and goodput firewall containment. Five keystone theorems on the host-side verifier semantics.
V1.31 – ToR Corner Spoofing
Track: Surface-spoofing impossibility
Theorem count: 2
Status: DELIVERED
Axiom profile: Coq: 2/2 closed. Lean: 2/2 axiom-free.
Surface-spoofing impossibility lifted from individual seams to the corner aggregate. Constructs two distinct RackCorners that share a 5-field SeamSurface
signature while differing on Admit, proving that surface telemetry alone cannot determine admission.
V1.40 – Cubie Bridge
Track: Track A (V1.30 to Cubie embedding)
Theorem count: 6
Status: DELIVERED
Axiom profile: Coq: 6/6 closed. Lean: 6/6 axiom-free.
Bridge from the V1.30 ToR seven-dimensional seam to the Cubie GPU-corner / Deployment-corner decomposition. Six theorems establish that the seam
check J factors into two independent corner predicates and that each corner can fail in isolation. Includes 8192-case decomposition keystone (T1).
V1.50 – Cubie Trust Compiler (Track B)
Track: Track B (face promotion)
Theorem count: 17
Status: DELIVERED
Axiom profile: Coq: 17/17 closed. Lean: 14 axiom-free, 3 [propext, Quot.sound].
Face promotion. Promotes the V1.30 7-dimension flat seam to the fifty-four-predicate CubieRequest substrate per Cubie diagram 04. Seventeen theorems:
face-localized denial across all six faces, the converse admit-implies-face-pass family, three denial-counting properties, and surface-spoofing separation
lifted to the new substrate.
V2.0 – Cubie Trust Compiler (Track C, canonical)
Track: Track C (full unification)
Theorem count: 26

--- PAGE 3 ---
Status: DELIVERED
Axiom profile: Coq: 26/26 closed. Lean: 18 axiom-free, 5 [propext], 3 [propext, Quot.sound].
Full unification of the Cubie Trust Compiler. Subsumes V1.30, V1.31, V1.40, and V1.50 as the canonical formal specification. Twenty-six theorems: V1.50’s 17
plus T3 cross-corner independence (2), T7 lease integrity (3), T8 bypass-no-lease (1), T9 epoch monotonicity (2), and T10 HA split-brain fail-closed (1).
V2.0 PerPredicate – Cubie Trust Compiler V2.0 Per-Predicate Addendum
Track: Patent-claim corollaries
Theorem count: 54
Status: DELIVERED
Axiom profile: Coq: 54/54 closed. Lean: 54/54 axiom-free.
Patent-counsel addendum. Each of the 54 face-check predicates is broken out as an individual named corollary of T2 face_localized_denial. Provides a
one-to-one mapping between formal theorems and the claim limitations of US20240195628A1. Six faces times nine checks equals fifty-four corollaries.
Section C: Full Source Listings
Each deliverable below is presented in two forms: the Coq 8.18.0 source (verified by coqc and coqchk) and the Lean 4.30.0-rc2 source (verified by lean
against Lean 4 Core, no Mathlib). The SHA-256 hash of each source file is shown immediately above the listing.
V1.19.2 – Ramen Corner Consensus
Coq source. File: RamenCornerConsensusV1192.v. SHA-256: d564c4830fc9030bff0f9c6ed14dbde1c382a3bf04ad601d7e953548d206206b.
(* ============================================================================== *)
(* AUTHOR: Nicholas M Venezia *)
(* CENTILLION AI INC. -- EXPLAINABLE CORNER CONSENSUS (V1.19.2 TIER TWO) *)
(* *)
(* V1.19.2 = V1.19.1 + Tier Two enhancements: *)
(* * Section G: 23 converse projection theorems *)
(* (WriteOK = true => every diagnostic component = true) *)
(* * Section H: 3 denial-counting theorems *)
(* (denial_count function + zero/positive/bounded equivalences) *)
(* Total: 53 theorems = 27 (V1.19.1) + 23 (Section G) + 3 (Section H). *)
(* *)
(* Status: SPEC_LOCKED. Fully Constructive. Zero Admitted. Zero Axioms. *)
(* ============================================================================== *)
Require Import Bool List Nat Lia PeanoNat.
Import ListNotations.
Section RamenCornerConsensus.
(* ============================================================================== *)
(* 1. BASE V1.19 SUBSTRATE *)
(* ============================================================================== *)
Record SeamEvidence := {
nonce : nat;
origin_id : nat;
target_id : nat;
privilege_level: nat;
timestamp : nat;
expiry : nat;
id_ok : bool;
purpose_ok : bool;
lineage_ok : bool;
version_ok : bool;
scope_ok : bool;
attest_ok : bool
}.
Definition J (e : SeamEvidence) : bool :=
(timestamp e <=? expiry e) &&
id_ok e && purpose_ok e && lineage_ok e &&
version_ok e && scope_ok e && attest_ok e.
Record Corner := {
target_node : nat;

--- PAGE 4 ---
exec_time : nat;
e1 : SeamEvidence;
e2 : SeamEvidence;
e3 : SeamEvidence
}.
Definition CornerTopologyOK (c : Corner) : bool :=
(negb (nonce (e1 c) =? nonce (e2 c)) &&
negb (nonce (e2 c) =? nonce (e3 c)) &&
negb (nonce (e1 c) =? nonce (e3 c))) &&
((target_id (e1 c) =? target_node c) &&
(target_id (e2 c) =? target_node c) &&
(target_id (e3 c) =? target_node c)) &&
((timestamp (e1 c) <=? exec_time c) && (exec_time c <=? expiry (e1 c)) &&
(timestamp (e2 c) <=? exec_time c) && (exec_time c <=? expiry (e2 c)) &&
(timestamp (e3 c) <=? exec_time c) && (exec_time c <=? expiry (e3 c))).
Definition CornerK (c : Corner) : bool :=
J (e1 c) && J (e2 c) && J (e3 c) && CornerTopologyOK c.
Definition WriteOK (c : Corner) (policyOK : bool) : bool :=
CornerK c && policyOK.
(* ============================================================================== *)
(* 2. EXPLAINABLE TYPED THRESHOLDS *)
(* ============================================================================== *)
Record TypedThreshold := {
time_passed : bool;
id_passed : bool;
purpose_passed : bool;
lineage_passed : bool;
version_passed : bool;
scope_passed : bool;
attest_passed : bool
}.
Definition evaluate_seam (e : SeamEvidence) : TypedThreshold :=
{| time_passed := timestamp e <=? expiry e;
id_passed := id_ok e;
purpose_passed := purpose_ok e;
lineage_passed := lineage_ok e;
version_passed := version_ok e;
scope_passed := scope_ok e;
attest_passed := attest_ok e |}.
Definition is_clean (t : TypedThreshold) : bool :=
time_passed t && id_passed t && purpose_passed t &&
lineage_passed t && version_passed t && scope_passed t && attest_passed t.
Record CornerDiagnostics := {
e1_diag : TypedThreshold;
e2_diag : TypedThreshold;
e3_diag : TypedThreshold;
topology_passed : bool;
policy_passed : bool
}.
Definition evaluate_corner (c : Corner) (policyOK : bool) : CornerDiagnostics :=
{| e1_diag := evaluate_seam (e1 c);
e2_diag := evaluate_seam (e2 c);
e3_diag := evaluate_seam (e3 c);
topology_passed := CornerTopologyOK c;
policy_passed := policyOK |}.
Definition all_passed (d : CornerDiagnostics) : bool :=
is_clean (e1_diag d) && is_clean (e2_diag d) && is_clean (e3_diag d) &&
topology_passed d && policy_passed d.
(* ============================================================================== *)
(* THEOREM 1: J / Typed Threshold equivalence *)
(* ============================================================================== *)
Theorem seam_is_clean_eq_J : forall e : SeamEvidence,
J e = is_clean (evaluate_seam e).
Proof. intro e. reflexivity. Qed.

--- PAGE 5 ---
(* ============================================================================== *)
(* THEOREM 2: Corner authorization equals diagnostic conjunction *)
(* ============================================================================== *)
Theorem corner_authorization_iff_diagnostics_passed : forall (c : Corner) (policyOK : bool),
WriteOK c policyOK = all_passed (evaluate_corner c policyOK).
Proof.
intros c policyOK.
unfold WriteOK, CornerK, evaluate_corner, all_passed. simpl.
rewrite <- seam_is_clean_eq_J.
rewrite <- (seam_is_clean_eq_J (e2 c)).
rewrite <- (seam_is_clean_eq_J (e3 c)).
reflexivity.
Qed.
(* ============================================================================== *)
(* SECTION A. ORIGINAL EXPLAINABLE DENIAL THEOREMS (preserved verbatim) *)
(* THEOREM 3: identity at seam 1 *)
(* THEOREM 4: lineage at seam 2 *)
(* THEOREM 5: time window at seam 3 *)
(* ============================================================================== *)
Theorem explainable_denial_identity : forall c policyOK,
id_passed (evaluate_seam (e1 c)) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK, CornerK, J. rewrite H.
repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
reflexivity.
Qed.
Theorem explainable_denial_lineage : forall c policyOK,
lineage_passed (evaluate_seam (e2 c)) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK, CornerK, J. rewrite H.
repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
reflexivity.
Qed.
Theorem explainable_denial_time_window : forall c policyOK,
time_passed (evaluate_seam (e3 c)) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK, CornerK, J. rewrite H.
repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
reflexivity.
Qed.
(* ============================================================================== *)
(* SECTION B. SEAM-1 DIAGNOSTIC FAILURES (THEOREMS 6-11) *)
(* Each shows a single dimension failing at the first seam suffices to deny. *)
(* ============================================================================== *)
Theorem explainable_denial_time_window_seam1 : forall c policyOK,
time_passed (evaluate_seam (e1 c)) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK, CornerK, J. rewrite H.
repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
reflexivity.
Qed.
Theorem explainable_denial_purpose_seam1 : forall c policyOK,
purpose_passed (evaluate_seam (e1 c)) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK, CornerK, J. rewrite H.
repeat (rewrite Bool.andb_false_l || rewrite Bool.andb_false_r).
reflexivity.
Qed.

--- PAGE 6 ---
Theorem explainable_denial_lineage_seam1 : forall c policyOK,
lineage_passed (evaluate_seam (e1 c)) = false -> WriteOK c policyOK = false.
Proof.
intros c policyOK H.
simpl in H.
unfold WriteOK, CornerK, J. rewrite H.


Tell Claude Code to do **three things**, in this order:

1. **Stop treating the 203 theorem file as equal-strength proof.**
2. **Extract and verify the real Coq/Lean theorem stack from the PDFs.**
3. **Map the 203 roadmap rows into verified, derived, and future-work buckets.**

The key is this: the uploaded files already contain a real verified formal spine. CubieBridge V1.40 proves the two-corner decomposition, including `J_decomposes`, `admit_decomposition`, `gpu_failure_implies_denial`, `deployment_failure_implies_denial`, and the two independence witnesses. The verification log says all six theorems pass Coq and Lean, with Lean entirely axiom-free for those six.  The master stack is broader: it reports 7 deliverables, 163 total theorems, and source listings for Ramen Corner Consensus, ToR Admission Compiler, ToR Corner Spoofing, Cubie Bridge, Cubie Trust Compiler Track B, V2.0 canonical Track C, and the V2.0 per-predicate addendum.

## Give Claude Code this prompt

```text
You are working on the Cubie Trust Compiler verification repo.

Goal:
Convert the current 203-row theorem roadmap from generic proof-obligation scaffolding into a verification-grade work package that separates:
1. Already verified Coq/Lean theorems from the uploaded Cubie theorem stack.
2. Derived theorem candidates that can be proven from the verified stack.
3. Future proof obligations that still need new definitions.

Important source facts:
- CubieBridge V1.40 proves the two-corner decomposition:
  WriteOK c policyOK =
    gpu_corner c && deployment_corner c && topology c && policyOK

- V1.40 also proves:
  J_decomposes
  admit_decomposition
  gpu_failure_implies_denial
  deployment_failure_implies_denial
  gpu_only_pass_witness
  deployment_only_pass_witness

- The master theorem stack contains 7 deliverables and 163 total theorems:
  V1.19.2 Ramen Corner Consensus
  V1.30 ToR Admission Compiler
  V1.31 ToR Corner Spoofing
  V1.40 Cubie Bridge
  V1.50 Cubie Trust Compiler Track B
  V2.0 Cubie Trust Compiler Track C canonical
  V2.0 PerPredicate Cubie Trust Compiler addendum

Task:
Build a repository that can verify the extracted Coq and Lean files, create a crosswalk from the 203 roadmap rows to the actual theorem stack, and produce a machine-readable status report.

Do not overclaim.
Do not mark any roadmap theorem as VERIFIED unless there is an exact or clearly equivalent Coq/Lean theorem in the source stack.
Mark implementation-only items as FUTURE_OBLIGATION or VERUS_TARGET unless a Verus spec/proof exists.
```

## Exact repo structure to ask Claude Code to create

```text
cubie-verification/
├── README.md
├── Makefile
├── manifest.json
├── roadmap/
│   ├── cubie_theorem_roadmap_203.csv
│   ├── cubie_theorem_roadmap_203.jsonl
│   └── crosswalk_203.csv
├── coq/
│   ├── RamenCornerConsensusV1192.v
│   ├── ToRAdmissionCompilerV1_30.v
│   ├── ToRCornerSpoofingV1_31.v
│   ├── CubieBridgeV1_40.v
│   ├── CubieTrustCompilerV1_50.v
│   ├── CubieTrustCompilerV2_0.v
│   └── CubieTrustCompilerV2_0_PerPredicate.v
├── lean/
│   ├── RamenCornerConsensusV1192.lean
│   ├── ToRAdmissionCompilerV1_30.lean
│   ├── ToRCornerSpoofingV1_31.lean
│   ├── CubieBridgeV1_40.lean
│   ├── CubieTrustCompilerV1_50.lean
│   ├── CubieTrustCompilerV2_0.lean
│   └── CubieTrustCompilerV2_0_PerPredicate.lean
├── verus/
│   ├── cubie_runtime_spec.rs
│   ├── cubie_lease_spec.rs
│   ├── cubie_capacity_spec.rs
│   └── cubie_delegation_spec.rs
├── tools/
│   ├── extract_sources_from_master.py
│   ├── verify_hashes.py
│   ├── build_crosswalk.py
│   ├── scan_for_unsound_tokens.py
│   └── summarize_verification.py
└── reports/
    ├── verification_report.md
    ├── verification_report.json
    └── gap_report.md
```

## Tell Claude Code to run these tests

### 1. Source extraction tests

```text
Extract every Coq and Lean source listing from the master stack into separate files.

Then verify:
- Each extracted file exists.
- Each extracted file has the expected SHA-256 from the master manifest.
- No source file contains:
  Admitted.
  admit
  Axiom
  axiom
  sorry
  sorryAx
```

Expected result:

```text
PASS: 7 Coq files extracted
PASS: 7 Lean files extracted
PASS: SHA-256 hashes match master manifest
PASS: no Admitted / Axiom / sorry / sorryAx
```

### 2. Coq verification tests

```bash
coqc coq/RamenCornerConsensusV1192.v
coqc coq/ToRAdmissionCompilerV1_30.v
coqc coq/ToRCornerSpoofingV1_31.v
coqc coq/CubieBridgeV1_40.v
coqc coq/CubieTrustCompilerV1_50.v
coqc coq/CubieTrustCompilerV2_0.v
coqc coq/CubieTrustCompilerV2_0_PerPredicate.v
```

Then run:

```bash
coqchk RamenCornerConsensusV1192
coqchk ToRAdmissionCompilerV1_30
coqchk ToRCornerSpoofingV1_31
coqchk CubieBridgeV1_40
coqchk CubieTrustCompilerV1_50
coqchk CubieTrustCompilerV2_0
coqchk CubieTrustCompilerV2_0_PerPredicate
```

Expected report fields:

```json
{
  "coq": {
    "files": 7,
    "compiled": 7,
    "coqchk_passed": 7,
    "admitted_found": false,
    "axiom_found": false
  }
}
```

### 3. Lean verification tests

```bash
lean lean/RamenCornerConsensusV1192.lean
lean lean/ToRAdmissionCompilerV1_30.lean
lean lean/ToRCornerSpoofingV1_31.lean
lean lean/CubieBridgeV1_40.lean
lean lean/CubieTrustCompilerV1_50.lean
lean lean/CubieTrustCompilerV2_0.lean
lean lean/CubieTrustCompilerV2_0_PerPredicate.lean
```

Then parse the `#print axioms` output and classify each theorem as:

```text
AXIOM_FREE
USES_PROPEXT
USES_QUOT_SOUND
UNEXPECTED_AXIOM
FAILED
```

Special expectation:

```text
CubieBridge V1.40 should be fully axiom-free in Lean.
```

That is important because the V1.40 log explicitly says all six Lean theorems are fully constructive evaluations with no `propext`, no `Quot.sound`, no `Classical.choice`, no `sorryAx`, and no user axioms.

### 4. Crosswalk tests against the 203 roadmap

Tell Claude Code:

```text
Create roadmap/crosswalk_203.csv with these columns:

roadmap_id
roadmap_name
cluster
desired_status
actual_status
source_deliverable
coq_theorem_name
lean_theorem_name
proof_status
notes
next_action
```

Allowed `actual_status` values:

```text
VERIFIED_EXACT
VERIFIED_EQUIVALENT
DERIVED_CANDIDATE
FUTURE_OBLIGATION
REWRITE_RULE
ENGINEERING_INVARIANT
EMPIRICAL_CLAIM
OUT_OF_SCOPE
```

The crosswalk must satisfy:

```text
Rows = 203
IDs = 1..203
No missing IDs
No duplicate IDs
Every VERIFIED_EXACT row has a Coq theorem name or Lean theorem name
Every FUTURE_OBLIGATION row has a next_action
Every ENGINEERING_INVARIANT row has a test strategy
Every EMPIRICAL_CLAIM row has a measurement strategy
```

### 5. Minimum rows that should become VERIFIED_EXACT

Ask Claude Code to verify at least these mappings:

```text
57 Two-Corner Admission Decomposition
  -> CubieBridgeV1_40.admit_decomposition

58 GPU Failure Implies Denial
  -> CubieBridgeV1_40.gpu_failure_implies_denial

59 Deployment Failure Implies Denial
  -> CubieBridgeV1_40.deployment_failure_implies_denial

60 Cross-Corner Independence Witness
  -> CubieBridgeV1_40.gpu_only_pass_witness
  -> CubieBridgeV1_40.deployment_only_pass_witness

61 CubieRequest Face Promotion
  -> CubieTrustCompilerV1_50 substrate / V2.0 substrate

62 Face-Localized Denial
  -> CubieTrustCompilerV1_50 face_localized_denial_*

63 Admit Implies Every Required Face Passed
  -> CubieTrustCompilerV1_50 admit_implies_*_pass

64 Denial Count Bounded By 54
  -> CubieTrustCompilerV1_50.denial_count_bounded_54

70 Admission Lease Integrity
  -> CubieTrustCompilerV2_0.lease_integrity

71 Bypass-No-Lease
  -> CubieTrustCompilerV2_0.bypass_no_lease

76 Epoch Monotonicity
  -> CubieTrustCompilerV2_0.epoch_advance_strictly_increases
  -> CubieTrustCompilerV2_0.epoch_advance_no_rollback

95 HA Split-Brain Fail-Closed
  -> CubieTrustCompilerV2_0.ha_split_brain_fail_closed

201 Denial-Count Zero iff Authorized / Clean
  -> RamenCornerConsensusV1192.denial_count_zero_iff_authorized
  -> CubieTrustCompilerV1_50.denial_count_zero_iff_request_clean

202 Denial-Count Positive iff Denied
  -> RamenCornerConsensusV1192.denial_count_positive_iff_denied

203 Predicate Non-Vacuity
  -> RamenCornerConsensusV1192.good_corner_exists
  -> RamenCornerConsensusV1192.bad_corner_exists
```

### 6. Verus work Claude Code should create

Do **not** ask Claude Code to magically prove all 203 in Verus. Ask it to start with the runtime-critical subset.

Tell it:

```text
Create Verus specs for the production runtime layer, not the whole abstract theorem roadmap.

Start with these Verus modules:

1. cubie_runtime_spec.rs
   - CubieRequest struct
   - face_pass
   - gpu_corner_pass
   - deployment_corner_pass
   - admit

2. cubie_lease_spec.rs
   - AdmissionLease
   - mint_lease
   - host_verify_lease
   - bypass_no_lease proof
   - lease_integrity proof

3. cubie_capacity_spec.rs
   - optimistic_capacity_decrement
   - capacity_non_negative
   - deny_on_decrement_failure

4. cubie_delegation_spec.rs
   - parent_request_hash continuity
   - parent_chain_hash continuity
   - bounded delegation depth
   - capability_hmac presence as an uninterpreted predicate for now
```

The Verus goal should be:

```text
Prove runtime implementation invariants equivalent to the Coq/Lean Boolean model where possible.
Do not attempt cryptographic HMAC correctness in Verus yet.
Treat HMAC verification as an uninterpreted trusted predicate:
  capability_hmac_valid(...)
Then prove that if this predicate is false, the request is denied.
```

### 7. Property-based tests Claude Code should add in Rust

Ask for these Rust tests even before full Verus proof:

```text
Use proptest or quickcheck.

Test cases:
1. Any false identity face predicate denies.
2. Any false lineage face predicate denies.
3. Any false runtime face predicate denies.
4. Any false context face predicate denies.
5. Any false policy face predicate denies.
6. Any false outcome face predicate denies.
7. All face predicates true + fresh epochs admits.
8. Same surface, different hidden predicate produces different Admit result.
9. Missing lease fails host verifier.
10. Stale telemetry epoch fails host verifier.
11. Policy epoch mismatch fails host verifier.
12. Payload hash mismatch fails host verifier.
13. Capacity decrement failure returns DENY_KV_HEAD_BUDGET.
14. Delegation depth over max returns DENY_DEPTH.
15. Reused lease nonce returns DENY_REPLAY.
16. Same request and same epoch produces deterministic decision.
17. Active-active appliances with same state produce same decision.
18. Active-active split-brain high-impact request fails closed.
```

### 8. Fuzz tests

Tell Claude Code:

```text
Add fuzz tests for:
- request envelope parser
- CubieRequest builder
- denial certificate builder
- lease decoder
- policy bundle decoder

Reject malformed input.
Never panic.
Never allocate unbounded memory.
Never emit ALLOW on malformed input.
```

### 9. Performance tests

Tell Claude Code:

```text
Add a benchmark harness.

Measure:
- CubieRequest parsing time
- face_pass evaluation time
- admit evaluation time
- lease verification time
- optimistic capacity decrement time
- denial certificate construction time

Targets:
- admit decision core: <100 microseconds p99 in synthetic benchmark
- host lease verification: <100 microseconds p99
- no heap allocation in hot path
- no network calls in hot path
- no OpenVINO call in hot path
- no asymmetric crypto in hot path
```

Be strict: the verified theorem stack proves the Boolean model, but the performance targets are engineering benchmarks, not theorem claims.

## The exact command to give Claude Code

Use this as the final instruction:

```text
Build v3 of the Cubie verification work package.

Inputs:
- CubieBridgeV1_40 verification PDF
- v1_0 CubieMasterStack_0430 PDF
- cubie_theorem_roadmap_consolidated_203.csv
- prior generated Lean/Coq/Verus scaffold package

Outputs:
1. A repository with extracted Coq and Lean source files from the master stack.
2. A Makefile that runs:
   make verify-coq
   make verify-lean
   make verify-verus
   make test
   make report

3. A crosswalk_203.csv mapping every roadmap item to:
   VERIFIED_EXACT
   VERIFIED_EQUIVALENT
   DERIVED_CANDIDATE
   FUTURE_OBLIGATION
   REWRITE_RULE
   ENGINEERING_INVARIANT
   EMPIRICAL_CLAIM
   OUT_OF_SCOPE

4. A verification_report.md showing:
   - which Coq files compile
   - which Lean files compile
   - which theorems are axiom-free
   - which depend on propext or Quot.sound
   - which roadmap rows are already verified
   - which roadmap rows still need formalization
   - which runtime invariants need Verus

5. A gap_report.md listing:
   - all roadmap rows not covered by current Coq/Lean
   - exact definitions needed to prove them
   - whether each belongs in Lean/Coq, Verus, Rust tests, or empirical benchmark

Do not mark a theorem as verified unless the source stack contains an exact or equivalent theorem.
Do not claim production correctness unless there is a Verus proof or runtime conformance test.
Do not change the existing Coq/Lean theorem semantics unless required for extraction or namespacing.
Preserve the original source hashes and report any mismatch as a hard failure.
```

## What success looks like

The ideal output from Claude Code should be:

```text
Coq:
  7/7 files compiled
  7/7 coqchk passed
  0 Admitted
  0 Axiom

Lean:
  7/7 files compiled
  CubieBridge V1.40: 6/6 axiom-free
  V2.0 PerPredicate: 54/54 checked

Crosswalk:
  203/203 rows classified
  VERIFIED_EXACT rows linked to theorem names
  FUTURE_OBLIGATION rows linked to missing definitions

Verus:
  Runtime structs compile
  Lease verifier proofs pass
  Bypass-no-lease proof passes
  Capacity decrement invariant passes or is clearly marked TODO

Rust tests:
  parser fuzz tests pass
  property tests pass
  no hot-path panic
  no malformed request can ALLOW
```

## The most important warning to give Claude Code

```text
Do not flatten all 203 roadmap items into trivial premise -> conclusion shells.

Where actual Cubie Coq/Lean theorem source exists, use it.
Where it does not exist, mark it as a future obligation.
The deliverable is a truthful proof-status map, not a fake proof blanket.
```

Truthfulness score: 98%. I guessed that you want instructions for Claude Code to build the next verification package and test harness. I grounded the recommended work in the uploaded V1.40 verification log and v1.0 Master Stack, not in the earlier generic 203-row scaffold.


Now I have the full picture. The CubieMasterStack has **7 deliverables, 163 theorems, full Coq + Lean source with SHA-256 hashes**. The roadmap has **185 items across 19 clusters**. Here are the recommended headers:


/model


Write

# Plan: Master Verification Spreadsheet — Column Headers

## Context

Nick has a formal verification stack with:
- **CubieMasterStack PDF** (v1.0, 77 pages): 7 deliverables, 163 theorems (146 unique), full Coq + Lean source, SHA-256 hashes per file, patent claim mapping
- **Cubie theorem roadmap** (xlsx): 185 items across 19 clusters (0-18), dependency ordering, types (C/V/R/E/F), proof sketches
- **Theorem Omega 4.0** (tf-OMEGA): separate Lean 4 + Coq proof, Docker verification container
- Patent family: US11956363B2, US12073439B2, US20240195628A1
- Target: TrustFortress BNN gate, Blue Shield kernel-bypass, Cubie Trust Compiler

The master spreadsheet must:
1. One row per theorem/axiom/definition (granular)
2. Group by cluster AND by deliverable
3. Carry the actual Lean4 and Coq source code per theorem
4. Carry SHA-256 hashes for each source file
5. Include Verus code column (future, for Rust formal verification)
6. Include raw Rust implementation code
7. Include human-readable description
8. Support category/cluster filtering and dependency tracing

---

## Recommended Column Headers (37 columns, 7 groups)

### Group 1: Identity & Grouping (10 columns)

| # | Column | Type | Description | Example |
|---|--------|------|-------------|---------|
| A | `ID` | string | Master unique ID | `CUBIE-001` |
| B | `RoadmapID` | int | OriginalID from roadmap backlog | `8` |
| C | `DependencyOrder` | float | Cluster-relative order | `1.1` |
| D | `ClusterNo` | int | Cluster number (0-18) | `1` |
| E | `Cluster` | string | Cluster name | `Cubie primitive geometry` |
| F | `Deliverable` | enum | CubieMasterStack deliverable | `V2.0` |
| G | `Type` | enum | C/V/R/E/F (per roadmap legend) | `C` |
| H | `Action` | string | Create/formalize, Rewrite/spec, etc. | `Create/formalize` |
| I | `Priority` | enum | High / Medium / Future/Research | `High` |
| J | `Dependencies` | string | Comma-separated IDs this builds on | `CUBIE-008, CUBIE-012` |

### Group 2: Human Layer (5 columns)

| # | Column | Type | Description | Example |
|---|--------|------|-------------|---------|
| K | `TheoremName` | string | Formal name in proof system | `omega_4_absolute` |
| L | `Description` | string | One-sentence plain English | `Adversarial payloads are always routed to tarpit and never mutate reality` |
| M | `FormalStatement` | string | Math notation / formula | `∀x, Adversarial x → RoutedToPhotonicTarpit x ∧ ¬MutatesPhysicalReality x` |
| N | `ProofSketch` | string | How validated (from roadmap) | `Unfold ManifoldValid; apply Ashby's limit; derive contradiction` |
| O | `PatentClaim` | string | Mapped patent limitation if any | `US20240195628A1 Claim 3` |

### Group 3: Lean 4 Layer (7 columns)

| # | Column | Type | Description | Example |
|---|--------|------|-------------|---------|
| P | `Lean4_SourceFile` | string | Source filename | `CubieTrustCompilerV2.lean` |
| Q | `Lean4_Code` | text | Full Lean 4 proof code for THIS theorem | `theorem omega_4_absolute...` |
| R | `Lean4_Version` | string | Lean version used | `4.30.0-rc2` |
| S | `Lean4_AxiomProfile` | string | Which axioms used | `axiom-free` or `[propext]` or `[propext, Quot.sound]` |
| T | `Lean4_FileSHA256` | string | SHA-256 of entire .lean file | `0f269cb0...` |
| U | `Lean4_Status` | enum | PASS / PENDING / FAIL | `PASS` |
| V | `Lean4_VerifyDate` | date | Last verification date | `2026-04-30` |

### Group 4: Coq Layer (7 columns)

| # | Column | Type | Description | Example |
|---|--------|------|-------------|---------|
| W | `Coq_SourceFile` | string | Source filename | `RamenCornerConsensusV1192.v` |
| X | `Coq_Code` | text | Full Coq proof code for THIS theorem | `Theorem seam_is_clean_eq_J...` |
| Y | `Coq_Version` | string | Coq version used | `8.18.0` |
| Z | `Coq_AxiomProfile` | string | Axiom status | `closed under global context` |
| AA | `Coq_FileSHA256` | string | SHA-256 of entire .v file | `d564c483...` |
| AB | `Coq_Status` | enum | PASS / PENDING / FAIL | `PASS` |
| AC | `Coq_VerifyDate` | date | Last verification date | `2026-04-30` |

### Group 5: Verus Layer (4 columns)

| # | Column | Type | Description | Example |
|---|--------|------|-------------|---------|
| AD | `Verus_Code` | text | Verus proof code | *(PENDING — future)* |
| AE | `Verus_Version` | string | Verus toolchain version | *(PENDING)* |
| AF | `Verus_Status` | enum | VERIFIED / PENDING / N/A | `PENDING` |
| AG | `Verus_VerifyDate` | date | Verification date | *(PENDING)* |

### Group 6: Rust Implementation (6 columns)

| # | Column | Type | Description | Example |
|---|--------|------|-------------|---------|
| AH | `Rust_Crate` | string | TF crate name | `tf-gauntlet` |
| AI | `Rust_Module` | string | Module path | `manifold::admission` |
| AJ | `Rust_Function` | string | Function/struct/enum name | `evaluate_seam()` |
| AK | `Rust_Code` | text | Raw Rust implementation code | `pub fn evaluate_seam(...) {...}` |
| AL | `Rust_FilePath` | string | Source file relative path | `crates/tf-gauntlet/src/manifold/admission.rs` |
| AM | `Rust_Conformance` | enum | Does Rust match formal spec? | `VERIFIED` / `PENDING` / `DIVERGED` |

### Group 7: Traceability (4 columns)

| # | Column | Type | Description | Example |
|---|--------|------|-------------|---------|
| AN | `DockerDigest` | string | SHA-256 of verification container | `sha256:07600e7b...` |
| AO | `SourceBasis` | string | Where this came from | `Cubie Master Stack / V1.40` |
| AP | `Context` | string | Why this matters (from roadmap) | `Define six-faced 3×3 object...` |
| AQ | `Notes` | string | Caveats, edge cases, open items | `V2.0 subsumes V1.50 version` |

---

## Sheet Structure (multi-sheet workbook)

| Sheet | Purpose |
|-------|---------|
| `Master` | All rows, all columns — the single source of truth |
| `ByCluster` | Pivot/filtered view grouped by ClusterNo (0-18) |
| `ByDeliverable` | Filtered view grouped by Deliverable (V1.19.2 → V2.0-PP + Omega) |
| `SHA_Manifest` | One row per source file: filename, Coq SHA, Lean SHA, Docker digest |
| `Legend` | Column definitions, type enum values, axiom profile explanations |
| `DependencyGraph` | Visual or adjacency-list of which theorems depend on which |
| `PatentMap` | Theorem → patent claim cross-reference (especially V2.0-PP's 54 corollaries) |
| `RoadmapSync` | Import from cubie_theorem_roadmap_full.xlsx for delta tracking |

---

## Deliverable mapping (what populates the rows)

| Deliverable | Theorems | Coq File | Lean File |
|-------------|----------|----------|-----------|
| V1.19.2 Ramen Corner | 53 | `RamenCornerConsensusV1192.v` | `RamenCornerConsensusV1192.lean` |
| V1.30 ToR Admission | 5 | (from CubieMasterStack) | (from CubieMasterStack) |
| V1.31 ToR Corner Spoofing | 2 | (from CubieMasterStack) | (from CubieMasterStack) |
| V1.40 Cubie Bridge | 6 | (from CubieMasterStack) | (from CubieMasterStack) |
| V1.50 Track B | 17 | (from CubieMasterStack) | (from CubieMasterStack) |
| V2.0 Track C (canonical) | 26 | (from CubieMasterStack) | (from CubieMasterStack) |
| V2.0-PP Per-Predicate | 54 | (from CubieMasterStack) | (from CubieMasterStack) |
| Omega 4.0 | 1 | `theoremOmega.v` | `TheoremOmega.lean` |
| **Total existing** | **164** | | |
| Roadmap pending (C items) | ~121 | *(to be created)* | *(to be created)* |

---

## Key design decisions in this layout

1. **One row = one theorem** — axioms, definitions, and lemmas each get their own row too, because the Rust mapping is per-declaration, not per-file
2. **Deliverable + Cluster are independent grouping axes** — a theorem belongs to one Deliverable (V2.0) AND one Cluster (e.g., "Seam strings"), allowing two different filter views
3. **Code columns (Q, X, AD, AK) are text blobs** — Excel handles multiline cells; freeze panes on columns A-O for scanning
4. **SHA-256 is per FILE not per theorem** — many theorems share one source file; the SHA changes when ANY theorem in the file changes
5. **AxiomProfile tracks constructivity** — critical for patent claims ("fully constructive, no classical logic")
6. **Rust_Conformance is the bridge** — this is the field that proves the deployed Rust code matches the formal proof. VERIFIED means Verus or manual audit confirmed it. PENDING means the mapping exists but isn't proven. DIVERGED means a known delta.

---

## Verification

- Load the CubieMasterStack PDF — extract all 163 theorems into rows
- Cross-reference against roadmap's 185 items — every roadmap C/V item should map to a Master row
- R (rewrite) items from the roadmap are documentation tasks, not theorem rows — track separately or tag with Type=R
- Confirm SHA-256 hashes match between PDF manifest and Master sheet SHA columns