1	Cubie Non-Quantum Master Table v1.10 — COMPLETE UNTRUNCATED
2	Row count: 128
3
4	================================================================================
5	ROW 001 —  001 — M1-01 — ALLM Cubie Ontology Primer
6	- Math: \operatorname{Parse}(x)\rightarrow\operatorname{ProjectToCubie}(x)
7	- LLM: Project information/actions into Cubie topology before reasoning over tokens, tables, or graphs.
8	- Human: First ask: what cube, face, nested level, state, and handoff does this belong to?
9
10	================================================================================
11	ROW 002 —  002 — Response 6+5 — Core Definition
12	- Math: \mathcal Q=(F,K,\Gamma,I,M,B,\mu,\chi,\Pi,g,d,\pi,J,h,\ell,\Sigma)
13	- LLM: Cubie is a recursive semantic object with geometry, state, access pattern, lineage, and handoff.
14	- Human: A Cubie is a cube-shaped data object with faces, colors, nested child cubes, visible state, hidden state, access rules, lineage, and handoff history.
15
16	================================================================================
17	ROW 003 —  003 — Response 6+5 — Axiom 0
18	- Math: \forall s\in M,\ \chi(s)\cong\mathcal Q
19	- LLM: Every oriented facelet contains another full Cubie.
20	- Human: Every square on the cube is itself another cube.
21
22	================================================================================
23	ROW 004 —  004 — Response 6+5 — Six Faces
24	- Math: F=\{\text{Who},\text{What},\text{When},\text{Where},\text{Why},\text{How}\}
25	- LLM: The six faces are semantic axes. Handoff is transport/seam logic, not a replacement face.
26	- Human: The cube’s six sides mean Who, What, When, Where, Why, and How.
27
28	================================================================================
29	ROW 005 —  005 — M2-01 — Exact Color-to-Face Canon
30	- Math: \Gamma(Yellow)=Who,\ \Gamma(Blue)=What,\ \Gamma(Green)=When,\ \Gamma(Orange)=Where,\ \Gamma(White)=Why,\ \Gamma(Red)=How
31	- LLM: Lock the color canon to prevent semantic drift.
32	- Human: Yellow = Who, Blue = What, Green = When, Orange = Where, White = Why, Red = How.
33
34	================================================================================
35	ROW 006 —  006 — M1-02 — Context/Handoff as Transport Layer
36	- Math: Handoff\notin F;\quad Handoff=(source,target,flow,depth,lease,scope)
37	- LLM: Context/Handoff is the seam/transport object across cubes, workflows, and nesting levels.
38	- Human: Handoff is how an action moves: upstream, downstream, lateral, return, delegation, or drill-down.
39
40	================================================================================
41	ROW 007 —  007 — Response 4/3 — Color vs Status
42	- Math: \Gamma(f)\ne \sigma_t(f,i,j)
43	- LLM: Face color/type is stable semantic identity; runtime status is mutable.
44	- Human: A Blue/What face can stay Blue while individual cells become active, blocked, authorized, or compromised.
45
46	================================================================================
47	ROW 008 —  008 — M2-02 — Runtime Status Levels
48	- Math: \Sigma=\{0,1,2\}\ \text{or}\ \{\text{locked},\text{partial},\text{full}\}
49	- LLM: Status is distinct from color and Rubik state.
50	- Human: A cubie can be locked, partially unlocked, or fully actionable.

Cubie Non-Quantum Master Table v1.10 — COMPLETE UNTRUNCATED
Row count: 128

================================================================================
ROW 001 —  001 — M1-01 — ALLM Cubie Ontology Primer
- Math: \operatorname{Parse}(x)\rightarrow\operatorname{ProjectToCubie}(x)
- LLM: Project information/actions into Cubie topology before reasoning over tokens, tables, or graphs.
- Human: First ask: what cube, face, nested level, state, and handoff does this belong to?

================================================================================
ROW 002 —  002 — Response 6+5 — Core Definition
- Math: \mathcal Q=(F,K,\Gamma,I,M,B,\mu,\chi,\Pi,g,d,\pi,J,h,\ell,\Sigma)
- LLM: Cubie is a recursive semantic object with geometry, state, access pattern, lineage, and handoff.
- Human: A Cubie is a cube-shaped data object with faces, colors, nested child cubes, visible state, hidden state, access rules, lineage, and handoff history.

================================================================================
ROW 003 —  003 — Response 6+5 — Axiom 0
- Math: \forall s\in M,\ \chi(s)\cong\mathcal Q
- LLM: Every oriented facelet contains another full Cubie.
- Human: Every square on the cube is itself another cube.

================================================================================
ROW 004 —  004 — Response 6+5 — Six Faces
- Math: F=\{\text{Who},\text{What},\text{When},\text{Where},\text{Why},\text{How}\}
- LLM: The six faces are semantic axes. Handoff is transport/seam logic, not a replacement face.
- Human: The cube’s six sides mean Who, What, When, Where, Why, and How.

================================================================================
ROW 005 —  005 — M2-01 — Exact Color-to-Face Canon
- Math: \Gamma(Yellow)=Who,\ \Gamma(Blue)=What,\ \Gamma(Green)=When,\ \Gamma(Orange)=Where,\ \Gamma(White)=Why,\ \Gamma(Red)=How
- LLM: Lock the color canon to prevent semantic drift.
- Human: Yellow = Who, Blue = What, Green = When, Orange = Where, White = Why, Red = How.

================================================================================
ROW 006 —  006 — M1-02 — Context/Handoff as Transport Layer
- Math: Handoff\notin F;\quad Handoff=(source,target,flow,depth,lease,scope)
- LLM: Context/Handoff is the seam/transport object across cubes, workflows, and nesting levels.
- Human: Handoff is how an action moves: upstream, downstream, lateral, return, delegation, or drill-down.

================================================================================
ROW 007 —  007 — Response 4/3 — Color vs Status
- Math: \Gamma(f)\ne \sigma_t(f,i,j)
- LLM: Face color/type is stable semantic identity; runtime status is mutable.
- Human: A Blue/What face can stay Blue while individual cells become active, blocked, authorized, or compromised.

================================================================================
ROW 008 —  008 — M2-02 — Runtime Status Levels
- Math: \Sigma=\{0,1,2\}\ \text{or}\ \{\text{locked},\text{partial},\text{full}\}
- LLM: Status is distinct from color and Rubik state.
- Human: A cubie can be locked, partially unlocked, or fully actionable.


50	- Human: A cubie can be locked, partially unlocked, or fully actionable.
51
52	================================================================================
53	ROW 009 —  009 — Response 6+5 — Surface Geometry
54	- Math: M=F\times\{0,1,2\}^2,\quad \|M\|=54
55	- LLM: Defines 54 oriented visible facelets.
56	- Human: Six sides times nine face positions equals 54.
57
58	================================================================================
59	ROW 010 —  010 — Response 6+5 — Physical Incidence
60	- Math: \|B\|=26,\quad \mu:M\to B
61	- LLM: Distinguish 54 oriented facelets from 26 physical Rubik-style cubies.
62	- Human: A Rubik cube has 54 stickers but 26 visible physical cubies.
63
64	================================================================================
65	ROW 011 —  011 — Response 6+5 — Face Matrix
66	- Math: \operatorname{Face}_f(\mathcal Q)\in\operatorname{Mat}_{3\times3}(\mathcal Q)
67	- LLM: Each face is a matrix of child Cubies, not scalar pixels.
68	- Human: Each side is a 3x3 grid, and every square is another cube.
69
70	================================================================================
71	ROW 012 —  012 — Response 5 — Nested Face Reflection
72	- Math: \operatorname{Face}^{(N)}_f\cong\operatorname{Mat}_{3^N\times3^N}(\mathcal Q)
73	- LLM: Same-face recursive viewing grows as 9^N.
74	- Human: Zooming into one face expands 3x3 to 9x9, then 27x27.
75
76	================================================================================
77	ROW 013 —  013 — M2-04 — Reflective Matrix Counts
78	- Math: \text{depth 1}=9,\quad \text{depth 2}=81,\quad \text{depth 3}=729
79	- LLM: Make visible same-face reflection concrete.
80	- Human: One face becomes 9 visible sites, then 81, then 729.
81
82	================================================================================
83	ROW 014 —  014 — Response 5 — Full Recursion Count
84	- Math: \|M_N\|=54^N
85	- LLM: Full Cubie recursion tracks all six faces at each nested level.
86	- Human: The full cube grows faster than one face because every nested cubie has six sides.
87
88	================================================================================
89	ROW 015 —  015 — Response 3 — q-by-q Resolution
90	- Math: M_q=F\times\{0,\dots,q-1\}^2,\quad \|M_q\|=6q^2
91	- LLM: 3x3 is canonical but not mathematically mandatory.
92	- Human: The model can use larger face grids if needed.
93
94	================================================================================
95	ROW 016 —  016 — Response 3 — q vs d
96	- Math: q=\text{face resolution},\quad d=\text{semantic dimension count}
97	- LLM: q changes grid size; d changes number of semantic axes/dimensions.
98	- Human: A bigger grid is not the same as adding a new meaning dimension.
99

- Human: A cubie can be locked, partially unlocked, or fully actionable.

================================================================================
ROW 009 —  009 — Response 6+5 — Surface Geometry
- Math: M=F\times\{0,1,2\}^2,\quad \|M\|=54
- LLM: Defines 54 oriented visible facelets.
- Human: Six sides times nine face positions equals 54.

================================================================================
ROW 010 —  010 — Response 6+5 — Physical Incidence
- Math: \|B\|=26,\quad \mu:M\to B
- LLM: Distinguish 54 oriented facelets from 26 physical Rubik-style cubies.
- Human: A Rubik cube has 54 stickers but 26 visible physical cubies.

================================================================================
ROW 011 —  011 — Response 6+5 — Face Matrix
- Math: \operatorname{Face}_f(\mathcal Q)\in\operatorname{Mat}_{3\times3}(\mathcal Q)
- LLM: Each face is a matrix of child Cubies, not scalar pixels.
- Human: Each side is a 3x3 grid, and every square is another cube.

================================================================================
ROW 012 —  012 — Response 5 — Nested Face Reflection
- Math: \operatorname{Face}^{(N)}_f\cong\operatorname{Mat}_{3^N\times3^N}(\mathcal Q)
- LLM: Same-face recursive viewing grows as 9^N.
- Human: Zooming into one face expands 3x3 to 9x9, then 27x27.

================================================================================
ROW 013 —  013 — M2-04 — Reflective Matrix Counts
- Math: \text{depth 1}=9,\quad \text{depth 2}=81,\quad \text{depth 3}=729
- LLM: Make visible same-face reflection concrete.
- Human: One face becomes 9 visible sites, then 81, then 729.

================================================================================
ROW 014 —  014 — Response 5 — Full Recursion Count
- Math: \|M_N\|=54^N
- LLM: Full Cubie recursion tracks all six faces at each nested level.
- Human: The full cube grows faster than one face because every nested cubie has six sides.

================================================================================
ROW 015 —  015 — Response 3 — q-by-q Resolution
- Math: M_q=F\times\{0,\dots,q-1\}^2,\quad \|M_q\|=6q^2
- LLM: 3x3 is canonical but not mathematically mandatory.
- Human: The model can use larger face grids if needed.

================================================================================
ROW 016 —  016 — Response 3 — q vs d
- Math: q=\text{face resolution},\quad d=\text{semantic dimension count}
- LLM: q changes grid size; d changes number of semantic axes/dimensions.
- Human: A bigger grid is not the same as adding a new meaning dimension.


Bash

wc -l "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/cubie_theorem_roadmap_full.csv" && head -5 "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/cubie_theorem_roadmap_full.csv"

Check roadmap CSV


186 C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/cubie_theorem_roadmap_full.csv
RowNo,OriginalID,DependencyOrder,ClusterNo,Cluster,Item,Type,Action,Priority,Context,LikelyMathOrFormula,ProofOrValidationSketch,Dependencies,SourceBasis,SequenceCheck
1,121,0.1,0,Claim discipline and terminology guardrails,Claim-boundary classification invariant,R,Rewrite/spec guardrail,High,Prevent overclaiming and keep the paper/proof stack legally and technically defensible.,"Claim ∈ {Formal, Empirical, Engineering, FutureWork}; no promotion across classes without evidence.",Audit each claim and require a support artifact before changing its class.,Builds on prior clusters in dependency order; see DependencyOrder.,Synthesized from this chat roadmap; verified-stack items reference Cubie Master Stack / V1.40 / Ramen logs where applicable.,OK
2,122,0.2,0,Claim discipline and terminology guardrails,Formal claim scope preservation,R,Rewrite/spec guardrail,High,Prevent overclaiming and keep the paper/proof stack legally and technically defensible.,"Theorem P(AbstractModel) ⇏ P(ProductionRuntime) unless RuntimeConforms(R,T)=1.",Separate theorem semantics from implementation evidence.,Builds on prior clusters in dependency order; see DependencyOrder.,Synthesized from this chat roadmap; verified-stack items reference Cubie Master Stack / V1.40 / Ramen logs where applicable.,OK
3,123,0.3,0,Claim discipline and terminology guardrails,Triple-kernel wording correction,R,Rewrite/spec guardrail,High,Prevent overclaiming and keep the paper/proof stack legally and technically defensible.,Use: Coq + coqchk + Lean; do not imply three independent proof assistants.,Terminology correction backed by verification protocol wording.,Builds on prior clusters in dependency order; see DependencyOrder.,Synthesized from this chat roadmap; verified-stack items reference Cubie Master Stack / V1.40 / Ramen logs where applicable.,OK
4,124,0.4,0,Claim discipline and terminology guardrails,Theorem-to-runtime non-substitution,R/C,Create/formalize,High,Prevent overclaiming and keep the paper/proof stack legally and technically defensible.,"T verified ∧ RuntimeConforms(R,T)=0 ⇒ no production-security claim from T alone.",Requires runtime conformance proof or tests before deployment claims.,Builds on prior clusters in dependency order; see DependencyOrder.,Synthesized from this chat roadmap; verified-stack items reference Cubie Master Stack / V1.40 / Ramen logs where applicable.,OK


python -c "
import csv
with open('C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/cubie_theorem_roadmap_full.csv', encoding='utf-8') as f:
    rows = list(csv.DictReader(f))
print(f'Total rows: {len(rows)}')
types = {}
for r in rows:
    t = r['Type']
    types[t] = types.get(t, 0) + 1
print('By Type:', types)
clusters = {}
for r in rows:
    c = r['ClusterNo']
    clusters[c] = clusters.get(c, 0) + 1
print('By Cluster:', sorted(clusters.items(), key=lambda x: float(x[0]) if x[0] else 0))
"

Analyze roadmap CSV breakdown


Total rows: 185
By Type: {'R': 21, 'R/C': 3, 'C': 121, 'V/C': 3, 'C/V': 9, 'V': 5, 'C/R': 7, 'E/C': 1, 'R/E': 1, 'F/C': 14}
By Cluster: [('0', 21), ('1', 7), ('2', 6), ('3', 7), ('4', 3), ('5', 9), ('6', 8), ('7', 19), ('8', 13), ('9', 7), ('10', 7), ('11', 4), ('12', 15), ('13', 20), ('14', 4), ('15', 4), ('16', 7), ('17', 10), ('18', 14)]


python -c "
import csv
with open('C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/cubie_theorem_roadmap_full.csv', encoding='utf-8') as f:
    rows = list(csv.DictReader(f))
# C items = formalize/create theorems
c_items = [r for r in rows if 'C' in r['Type']]
print(f'Items with C (Create/formalize): {len(c_items)}')
# Show cluster names
seen = set()
for r in rows:
    k = (r['ClusterNo'], r['Cluster'])
    if k not in seen:
        seen.add(k)
        print(f'  Cluster {r[\"ClusterNo\"]}: {r[\"Cluster\"]}')
"

Show cluster names and C-type items


Items with C (Create/formalize): 158
  Cluster 0: Claim discipline and terminology guardrails
  Cluster 1: Cubie primitive geometry
  Cluster 2: Base geometric access
  Cluster 3: Recursive Cubie access and noise growth
  Cluster 4: Context, frame, lineage, and unified Golden Path
  Cluster 5: Seam strings, corners, and explainable denial
  Cluster 6: Surface spoofing and face promotion
  Cluster 7: Agentic recursion and delegated permissions
  Cluster 8: Request-to-Cubie construction and struct integrity
  Cluster 9: Two-corner runtime admission core
  Cluster 10: Identity, provenance, attestation, and policy seams
  Cluster 11: Policy compiler and bytecode VM
  Cluster 12: Lease, replay, host verifier, and epoch lifecycle
  Cluster 13: GPU goodput and waste predicates
  Cluster 14: Capacity accounting and TOCTOU protection
  Cluster 15: OpenVINO, cold path, and risk integers
  Cluster 16: HA, split-brain, and degraded availability
  Cluster 17: Regulatory, CAISI, and governance alignment
  Cluster 18: Conditional quantum and advanced research path


python -c "
import csv
# Count existing proven theorems from our master table
import sys
sys.path.insert(0, 'tools')

with open('roadmap/master_theorem_table.csv', encoding='utf-8') as f:
    master = list(csv.DictReader(f))

# Pure theorems/lemmas only (not Definitions/Fixpoints)
proofs = [r for r in master if r['kind'] in ('Theorem','Lemma','Corollary')]
canonical = [r for r in proofs if r['canonical'] == 'YES']
print(f'Master table:')
print(f'  Total named declarations: {len(master)}')
print(f'  Theorem/Lemma/Corollary rows: {len(proofs)}')
print(f'  Canonical proofs: {len(canonical)}')
print(f'  Predecessor proofs: {len(proofs) - len(canonical)}')
print()

# Map roadmap cluster to coq/lean status
with open('C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/cubie_theorem_roadmap_full.csv', encoding='utf-8') as f:
    roadmap = list(csv.DictReader(f))
c_items = [r for r in roadmap if 'C' in r['Type']]
print(f'Roadmap C-items (need formal proofs): {len(c_items)}')
# Already have proofs for clusters covered in master table
covered_clusters = {5,6,7,8,9,10,11,12,13,14,15}  # approximate from MODULE_META
print(f'Roadmap F-items (future research): {len([r for r in roadmap if \"F\" in r[\"Type\"]])}')
"

Compute proof coverage gap


Master table:
  Total named declarations: 716
  Theorem/Lemma/Corollary rows: 412
  Canonical proofs: 339
  Predecessor proofs: 73

Roadmap C-items (need formal proofs): 158
Roadmap F-items (future research): 14


Good — 412 pure proofs/lemmas in the formal files. Now let me check the crosswalk to see which roadmap clusters are covered vs. missing.


python -c "
import csv
with open('roadmap/crosswalk_203.csv', encoding='utf-8') as f:
    cw = list(csv.DictReader(f))
print(f'Crosswalk rows: {len(cw)}')
# Count by status
statuses = {}
for r in cw:
    s = r.get('status','?')
    statuses[s] = statuses.get(s, 0) + 1
print('By status:', statuses)
" 2>/dev/null || echo "crosswalk not found - checking path"
ls roadmap/

Check crosswalk status


Crosswalk rows: 203
By status: {'?': 203}
crosswalk_203.csv
cubie_theorem_roadmap_203.jsonl
master_theorem_table.csv


Check crosswalk columns


roadmap_id,roadmap_name,cluster,desired_status,actual_status,source_deliverable,coq_theorem_name,lean_theorem_name,proof_status,notes,next_action
1,Claim-boundary classification invariant,Claim discipline and terminology guardrails,abstract_passable_proof_obligation,OUT_OF_SCOPE,,,,N/A,"Cluster 0 rows are claim-boundary guardrails, not theorems.",Editorial review of claim classification.
2,Formal claim scope preservation,Claim discipline and terminology guardrails,abstract_passable_proof_obligation,OUT_OF_SCOPE,,,,N/A,"Cluster 0 rows are claim-boundary guardrails, not theorems.",Editorial review of claim classification.


python -c "
import csv
with open('roadmap/crosswalk_203.csv', encoding='utf-8') as f:
    rows = list(csv.DictReader(f))
statuses = {}
for r in rows:
    s = r.get('actual_status','')
    statuses[s] = statuses.get(s, 0) + 1
print('By actual_status:')
for k,v in sorted(statuses.items(), key=lambda x: -x[1]):
    print(f'  {k!r}: {v}')
"

Check actual crosswalk statuses


By actual_status:
  'DERIVED_CANDIDATE': 130
  'OUT_OF_SCOPE': 21
  'VERIFIED_EXACT': 15
  'FUTURE_OBLIGATION': 15
  'ENGINEERING_INVARIANT': 10
  'REWRITE_RULE': 10
  'EMPIRICAL_CLAIM': 2


python -c "
import csv

# Read roadmap
with open('C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/cubie_theorem_roadmap_full.csv', encoding='utf-8') as f:
    roadmap = list(csv.DictReader(f))

# Read master table
with open('roadmap/master_theorem_table.csv', encoding='utf-8') as f:
    master = list(csv.DictReader(f))

# Group master by cluster
master_clusters = {}
for r in master:
    c = r['cluster']
    master_clusters.setdefault(c, []).append(r)

# Show gap: what clusters in roadmap have NO coq/lean coverage
roadmap_clusters = {}
for r in roadmap:
    c = r['ClusterNo']
    roadmap_clusters.setdefault(c, {'name': r['Cluster'], 'items': []})
    if 'C' in r['Type']:
        roadmap_clusters[c]['items'].append(r['Item'])

# Our master table clusters
print('Master table clusters covered:')
for c, rows in sorted(master_clusters.items()):
    proofs = [r for r in rows if r['kind'] in ('Theorem','Lemma','Corollary')]
    print(f'  {c}: {len(rows)} decls ({len(proofs)} proofs)')
print()
print('Roadmap clusters with C-items not covered:')
covered_master = set(master_clusters.keys())
for cno, data in sorted(roadmap_clusters.items(), key=lambda x: float(x[0])):
    if data['name'] not in covered_master and len(data['items']) > 0:
        print(f'  Cluster {cno} ({data[\"name\"]}): {len(data[\"items\"])} items')
"

Find coverage gaps between roadmap and master table


Master table clusters covered:
  Cubie Bridge: 16 decls (4 proofs)
  Cubie Trust Compiler: 167 decls (113 proofs)
  Cubie-Omega Integration: 33 decls (24 proofs)
  CubieQ Addenda: 81 decls (33 proofs)
  CubieQ Geometric: 44 decls (30 proofs)
  CubieQ Non-Quantum: 54 decls (33 proofs)
  Ramen Corner Consensus: 219 decls (127 proofs)
  Runtime Trust Compiler: 40 decls (11 proofs)
  Semantic Calculus: 11 decls (5 proofs)
  Theorem Omega: 38 decls (27 proofs)
  ToR Admission Compiler: 11 decls (5 proofs)
  ToR Corner Spoofing: 2 decls (0 proofs)

Roadmap clusters with C-items not covered:
  Cluster 0 (Claim discipline and terminology guardrails): 1 items
  Cluster 1 (Cubie primitive geometry): 7 items
  Cluster 2 (Base geometric access): 6 items
  Cluster 3 (Recursive Cubie access and noise growth): 7 items
  Cluster 4 (Context, frame, lineage, and unified Golden Path): 3 items
  Cluster 5 (Seam strings, corners, and explainable denial): 9 items
  Cluster 6 (Surface spoofing and face promotion): 7 items
  Cluster 7 (Agentic recursion and delegated permissions): 19 items
  Cluster 8 (Request-to-Cubie construction and struct integrity): 13 items
  Cluster 9 (Two-corner runtime admission core): 3 items
  Cluster 10 (Identity, provenance, attestation, and policy seams): 7 items
  Cluster 11 (Policy compiler and bytecode VM): 4 items
  Cluster 12 (Lease, replay, host verifier, and epoch lifecycle): 15 items
  Cluster 13 (GPU goodput and waste predicates): 20 items
  Cluster 14 (Capacity accounting and TOCTOU protection): 4 items
  Cluster 15 (OpenVINO, cold path, and risk integers): 4 items
  Cluster 16 (HA, split-brain, and degraded availability): 7 items
  Cluster 17 (Regulatory, CAISI, and governance alignment): 8 items
  Cluster 18 (Conditional quantum and advanced research path): 14 items


cat "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/BUNDLE_INDEX.md" | head -100

Read BUNDLE_INDEX


# Cubie Non-Quantum v1.10 + Hardening v1.13 — Triple-Kernel Formal Submission

**Date:** April 27, 2026
**Patents:** US11956363B2, US12073439B2, US20240195628A1, Patent 18/005,497
**CNDA:** Intel CNDA Number 083697

This is the triple-kernel-validated submission package containing **76 formally verified theorems** across **8 Coq modules** and **2 Lean sub-packages**, with the user's three frameworks (CubieQ Geometric / Untitled.md, Quantum Contextual Consent / Math.md, Theorem Omega 8.0 v1.13 incremental) hardened on top of the existing 30-theorem base corpus.

## Verification Summary

| Module | Theorems | Coq | coqchk | Lean | Source |
|---|---|---|---|---|---|
| `CubieNonQuantum_v1_10` | 8 | PASS | PASS | PASS | base |
| `TheoremOmega6` | 1 | PASS | PASS | PASS | base |
| `CubieQApex` | 4 | PASS | PASS | PASS | base |
| `CubieQv14` | 8 | PASS | PASS | PASS | base |
| `OmegaSeven` | 9 | PASS | PASS | PASS | base |
| **`CubieQGeometric`** | **20** | **PASS** | **PASS** | **PASS** | **v1.13 hardening** |
| **`CubieQuantumConsent`** | **9** | **PASS** | **PASS** | **PASS** | **v1.13 hardening** |
| **`OmegaEight`** | **17** | **PASS** | **PASS** | **PASS** | **v1.13 hardening** |
| **TOTAL** | **76** | **8/8** | **8/8** | **8/8** | — |

All four `coqchk` no-cheats markers clean across every module: predicative `Set`, no type-in-type, no unsafe fixpoints, no positivity assumptions. Lean axiom audit reports zero `sorryAx`, zero `propext`, zero `Classical.choice`.

## What v1.13 Hardening Adds

The v1.13 hardening modules formalize the user's three integrated frameworks as kernel-verified Coq + Lean code, on top of the existing kernel-verified 30-theorem base:

**`CubieQGeometric`** — formalizes the Hierarchical Geometric Quantum Codes (HGQC) framework from Untitled.md. Includes Theorem 5 (Holographic Efficiency, with concrete bound `125 × 1259 < 157464 < 125 × 1260` proving the 0.08% density), Theorem 6 (Exponential Amplification with `19683 = 157 × 125 + 58` arithmetic witness), and Theorem 7 (Observer-Dependent RG with orthogonal fixed points). 20 new theorems, all kernel-verified.

**`CubieQuantumConsent`** — formalizes the Quantum Contextual Consent Information Percolation framework from Math.md. Includes T7 (non-commutative consent algebra `[A,B] ≠ [B,A]`), T6 (entanglement-enhanced threshold with concrete numeric witnesses `p_c = 25` at `f_ent = 100` and `p_c = 38` at `f_ent = 50`), T8 (Holevo bound `I(S;Access) ≤ S(ρ_consent)`), and T5 (measurement collapse idempotence). 9 new theorems, all kernel-verified.

**`OmegaEight`** — formalizes Theorem Omega 8.0 v1.13 incremental from the user's directorate disclosure. Includes Theorem 8.1 (Hierarchical Node Capacity `C_tree(N) = (54^N − 1)/53`), Theorem 8.2 (Hyper-Exponential State Space `R^C_tree(N)`), Theorem 8.3 (Holographic Projection Ambiguity), Theorem 8.4 (Adversarial Error Probability decay `(B(τ)/R)^N`), Theorem 8.5 (Entropy Margin Constraint), Theorem 8.6 (Joint Validity Matrix `J_uv = FaceMatch ∧ ColorMatch ∧ EdgeOK ∧ CornerOK ∧ HandoffOK`), and Theorem 8.7 (`Auth^v1.13` absolute bound). 17 new theorems, all kernel-verified.

## Reproduce The Build

```bash
cd formal
bash scripts/build_coq.sh         # compile all 8 .v files
bash scripts/coqchk_verify.sh     # independent kernel re-verification
bash scripts/build_lean.sh        # build both Lean sub-packages
bash scripts/emit_certificate.sh  # produce live-signed certificate
```

The certificate is written to `formal/output/v1.13_FormalCertificate_HARDENED_0427.txt` and the per-module audit logs are written to `formal/output/`.

Toolchain pin: Coq 8.18.0+dfsg-1build2 via apt, Lean 4.15.0 via elan.

## Files

```
cubie_final_submission/
├── README.md                                              (this file)
├── BUNDLE_INDEX.md                                        (file inventory)
├── formal/
│   ├── coq/
│   │   ├── _CoqProject
│   │   ├── CubieNonQuantum_v1_10.v
│   │   ├── TheoremOmega6.v
│   │   ├── CubieQApex.v
│   │   ├── CubieQv14.v
│   │   ├── OmegaSeven.v
│   │   ├── CubieQGeometric.v          [v1.13 hardening]
│   │   ├── CubieQuantumConsent.v      [v1.13 hardening]
│   │   └── OmegaEight.v               [v1.13 hardening]
│   ├── lean/
│   │   ├── cubie_nonquantum_v110/
│   │   │   └── CubieNonQuantum_v1_10.lean
│   │   └── centillion_omega7/
│   │       └── Centillion/
│   │           ├── TheoremOmega6.lean
│   │           ├── CubieQApex.lean
│   │           ├── CubieQv14.lean
│   │           ├── OmegaSeven.lean
│   │           ├── CubieQGeometric.lean      [v1.13 hardening]
│   │           ├── CubieQuantumConsent.lean  [v1.13 hardening]
│   │           └── OmegaEight.lean           [v1.13 hardening]
│   ├── scripts/
│   │   ├── build_coq.sh
│   │   ├── coqchk_verify.sh
│   │   ├── build_lean.sh
│   │   └── emit_certificate.sh
│   ├── references/
│   │   ├── SUBMISSION_MANIFEST.md
│   │   ├── AXIOM_AUDIT.md
│   │   ├── VerificationManifest.md
│   │   └── patent_alignment.md
│   └── output/
│       ├── v1.13_FormalCertificate_HARDENED_0427.txt
│       ├── coqchk_*.log (8 logs)
│       ├── lean_v110_build.log
│       └── lean_omega7_build.log
├── source_uploads/                    (user's three framework documents)
├── historical_buildspecs/             (BuildSpec v1.0–v1.4 + debate logs)
├── historical_packages/               (predecessor verified packages)
├── docs/master_table_v110/            (128-row predicate scaffold, 7 formats)
└── previous_submissions/              (verbatim predecessor zip)
```

## Patent Alignment


cat "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/SUBMISSION_MANIFEST.md" | head -80

Read submission manifest


cat "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/MASTER_TABLE_PART_01_ROWS_001_032.md" | head -60

Check part 1 of master table parts


# Cubie Non-Quantum Master Table v1.10 — COMPLETE UNTRUNCATED

This version is intentionally formatted as row-by-row sections instead of one giant Markdown pipe table to prevent truncation or column breaks from mathematical `|` symbols.

**Row count:** 128

## Row 001 —  001 — M1-01 — ALLM Cubie Ontology Primer

**Mathematical expression / statement**

```text
\operatorname{Parse}(x)\rightarrow\operatorname{ProjectToCubie}(x)
```

**LLM context**

Project information/actions into Cubie topology before reasoning over tokens, tables, or graphs.

**Plain-English human explanation**

First ask: what cube, face, nested level, state, and handoff does this belong to?

## Row 002 —  002 — Response 6+5 — Core Definition

**Mathematical expression / statement**

```text
\mathcal Q=(F,K,\Gamma,I,M,B,\mu,\chi,\Pi,g,d,\pi,J,h,\ell,\Sigma)
```

**LLM context**

Cubie is a recursive semantic object with geometry, state, access pattern, lineage, and handoff.

**Plain-English human explanation**

A Cubie is a cube-shaped data object with faces, colors, nested child cubes, visible state, hidden state, access rules, lineage, and handoff history.

## Row 003 —  003 — Response 6+5 — Axiom 0

**Mathematical expression / statement**

```text
\forall s\in M,\ \chi(s)\cong\mathcal Q
```

**LLM context**

Every oriented facelet contains another full Cubie.


Let me check what we might still be missing from the source folders:


ls "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/FILES FOR MATH/" 2>/dev/null

List FILES FOR MATH folder


Cubie_v1_11_MicDrop_Optimized_Package
Math (1).md
Untitled.md
V2.0 OMEGAfiles.zip
blue_shield_v9_cited_grouped.html
cubieq_omega_incremental_append.v
v1.10_CubieFinalSubmission_COMPLETE_0427.zip


ls "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/FILES FOR MATH/Cubie_v1_11_MicDrop_Optimized_Package/"

Check v1.11 package contents


Cubie_v1_11_MicDrop_Dashboard_Preview.png
Cubie_v1_11_MicDrop_Optimized_Master.csv
Cubie_v1_11_MicDrop_Optimized_Master.jsonl
Cubie_v1_11_MicDrop_Optimized_Master.xlsx
Cubie_v1_11_MicDrop_Optimized_README.md
MANIFEST_WITH_HASHES.txt
formal
~$Cubie_v1_11_MicDrop_Optimized_Master.xlsx


ls "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/FILES FOR MATH/Cubie_v1_11_MicDrop_Optimized_Package/formal/"

List formal files in v1.11 package


CubieNonQuantum_v1_10.lean
CubieNonQuantum_v1_10.v
cubieq_omega_incremental_next_addendum.v


ls "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/More math 180 files/" 2>/dev/null | head -30

Check More math 180 files


ATTESTATION.md
Blue_Shield_v1.0_Evidence_Memo.md
Certificate_Omega_v5_0.md
Cubie as a CPU-Side Runtime Trust Compiler.docx
CubieBridgeV1 40 VERIFICATION.pdf
CubieBridgeV1 40.lean
CubieBridgeV1 40.v
CubieBridgeV1_40.lean
CubieBridgeV1_40.v
CubieBridgeV1_40_VERIFICATION.txt
CubieBridgeV1_40_evidence.tar.gz
CubieOmegaBridgeV2 3 VERIFICATION.pdf
CubieOmegaBridgeV2 3.lean
CubieOmegaBridgeV2 3.v
CubieOmegaStage2V2 3 VERIFICATION.pdf
CubieOmegaStage2V2 3.lean
CubieOmegaStage2V2 3.v
CubieQ and the Cubie Object 2.pdf
CubieQ and the Cubie Object.pdf
CubieQd.pdf
CubieTrustCompilerV1_50.lean
CubieTrustCompilerV1_50.v
CubieTrustCompilerV1_50_VERIFICATION.txt
CubieTrustCompilerV1_50_evidence.tar.gz
CubieTrustCompilerV2 0 VERIFICATION.pdf
CubieTrustCompilerV2 0.lean
CubieTrustCompilerV2 0.v
CubieTrustCompilerV2_0.lean
CubieTrustCompilerV2_0.v
CubieTrustCompilerV2_0_VERIFICATION.txt


ls "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/More math 180 files/" | grep -E '\.(v|lean)$'

List all formal files in More math 180 files


CubieBridgeV1 40.lean
CubieBridgeV1 40.v
CubieBridgeV1_40.lean
CubieBridgeV1_40.v
CubieOmegaBridgeV2 3.lean
CubieOmegaBridgeV2 3.v
CubieOmegaStage2V2 3.lean
CubieOmegaStage2V2 3.v
CubieTrustCompilerV1_50.lean
CubieTrustCompilerV1_50.v
CubieTrustCompilerV2 0.lean
CubieTrustCompilerV2 0.v
CubieTrustCompilerV2_0.lean
CubieTrustCompilerV2_0.v
OAI _cubie_trust_compiler_theorems.v
OAI_Cubie_TrustCompiler_Theorems.lean
Plus Ramen v1 19.lean
Plus Ramen v1 19.v
Ramen v1 17 1.lean
Ramen v1 17 1.v
RamenCornerConsensus v1 19 addon.lean
RamenCornerConsensus v1 19 addon.v
RamenCornerConsensusV1 19 3.lean
RamenCornerConsensusV1191 (1).lean
RamenCornerConsensusV1191 (1).v
RamenCornerConsensusV1191.lean
RamenCornerConsensusV1191.v
RamenCornerConsensusV1192.lean
RamenCornerConsensusV1192.v
RamenCornerConsensus_v1_19_addon.lean
RamenCornerConsensus_v1_19_addon.v
Ramen_v1_17_1.lean
Ramen_v1_17_1.v
Ramen_v1_18.lean
Ramen_v1_18.v
Ramen_v1_19.lean
Ramen_v1_19.v
SemanticCalculus_v1_11.lean
SemanticCalculus_v1_11.v
TF-TheoremOmega (1).lean
TF-TheoremOmega.lean
TF-theoremOmega (1).v
TF-theoremOmega.v
TheoremOmega (1).lean
TheoremOmega (2).lean
TheoremOmega (3).lean
TheoremOmega.lean
TheoremOmega_v4_3.lean
TheoremOmega_v5_0 (1).lean
TheoremOmega_v5_0.lean
TheoremOmega_v6_0 2.lean
TheoremOmega_v6_0.lean
ToRAdmissionCompilerV1 30.lean
ToRAdmissionCompilerV1 30.v
ToRAdmissionCompilerV1_30.lean
ToRAdmissionCompilerV1_30.v
ToRCornerSpoofingV1_31.lean
ToRCornerSpoofingV1_31.v
cubieq_omega_incremental_next_addendum (1).v
cubieq_omega_incremental_next_addendum.v
theoremOmega (1).v
theoremOmega (2).v
theoremOmega v6 0.v
theoremOmega.v
theoremOmega_v4_3.v
theoremOmega_v5_0 (1).v
theoremOmega_v5_0.v
theoremOmega_v6_0 2.v
theoremOmega_v6_0.v


ls coq/ | sed 's/\.v$//' | sort > /tmp/repo_coq.txt
ls lean/ | sed 's/\.lean$//' | sort > /tmp/repo_lean.txt
echo "=== Repo Coq modules ===" && cat /tmp/repo_coq.txt
echo "=== Repo Lean modules ===" && cat /tmp/repo_lean.txt

List current repo modules


=== Repo Coq modules ===
CubieBridgeV1_40
CubieNonQuantum_v1_10
CubieOmegaBridgeV2_3
CubieOmegaStage2V2_3
CubieQApex
CubieQGeometric
CubieQuantumConsent
CubieQv14
CubieTrustCompilerV1_50
CubieTrustCompilerV2_0
CubieTrustCompilerV2_0_PerPredicate
OAI_cubie_trust_compiler_theorems
OmegaEight
OmegaSeven
RamenCornerConsensusV1191
RamenCornerConsensusV1192
RamenCornerConsensus_v1_19_addon
Ramen_v1_17_1
Ramen_v1_18
Ramen_v1_19
SemanticCalculus_v1_11
TheoremOmega4
TheoremOmega6
TheoremOmega_v4_3
TheoremOmega_v5_0
TheoremOmega_v6_0
ToRAdmissionCompilerV1_30
ToRCornerSpoofingV1_31
cubieq_omega_incremental_append
cubieq_omega_incremental_next_addendum
=== Repo Lean modules ===
CubieBridgeV1_40
CubieNonQuantum_v1_10
CubieOmegaBridgeV2_3
CubieOmegaStage2V2_3
CubieQApex
CubieQGeometric
CubieQuantumConsent
CubieQv14
CubieTrustCompilerV1_50
CubieTrustCompilerV2_0
CubieTrustCompilerV2_0_PerPredicate
OAI_Cubie_TrustCompiler_Theorems
OmegaEight
OmegaSeven
RamenCornerConsensusV1191
RamenCornerConsensusV1192
RamenCornerConsensusV1193
RamenCornerConsensus_v1_19_addon
Ramen_v1_17_1
Ramen_v1_18
Ramen_v1_19
SemanticCalculus_v1_11
TheoremOmega4
TheoremOmega6
TheoremOmega_v4_3
TheoremOmega_v5_0
TheoremOmega_v6_0
ToRAdmissionCompilerV1_30
ToRCornerSpoofingV1_31


# Check for files we're missing:
# 1. Plus Ramen v1 19.v/lean (could be RamenCornerConsensusV1193 Coq version)
# 2. TheoremOmega4 - do we have the Coq variant from math folder?
# 3. CubieOmegaBridgeV2_3 - check if there's a V2 3 (with space) variant

# Check Plus Ramen v1 19 (likely v1.19.3 chain)
python -c "
from pathlib import Path
txt = Path('C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/More math 180 files/Plus Ramen v1 19.v').read_text(encoding='utf-8', errors='replace')
print(txt[:300])
"

Check Plus Ramen v1 19 content


(* ============================================================================== *)
(* CENTILLION AI INC. -- RAMEN TRUST COMPILER (V1.19)                              *)
(*                                                                                *)
(* Adds to V1.18: Per-Flag Necessity (six th


# This is a duplicate of Ramen_v1_19.v based on content description
# Let's check what unique files might not be in repo

# Check TF-TheoremOmega
python -c "
from pathlib import Path
txt = Path('C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/More math 180 files/TF-TheoremOmega.lean').read_text(encoding='utf-8', errors='replace')
print(txt[:400])
"

Check TF-TheoremOmega content


-- Centillion AI Inc. Core Architecture
-- Theorem Omega 4.0: The Photonic Manifold
-- Formal Verification Target: Core Logic & Ashby's Bounding (Lean 4.15.0+ Remediated)
-- Dependencies: NONE (Base Init only)

universe u

-- ==========================================
-- PART 1: THE ACTION TENSOR
-- ==========================================
-- Defining the continuous space of an Agentic Payload
a


# TF-TheoremOmega is TheoremOmega4 variant — already have it
# Check the CubieTrustCompilerV2_0_PerPredicate — do we have its lean?
ls lean/ | grep -i perpredi

# Check "theorems_package" which had some files we already copied
ls "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/theorems_package/" 2>/dev/null

Check PerPredicate lean file and theorems_package


CubieTrustCompilerV2_0_PerPredicate.lean
ORDER.md
README.md
Theorems_All_2026-05-02.gdoc
Theorems_All_2026-05-02.txt
coq
docs
lean
scripts
v1.13_FormalCertificate_HARDENED_0427.txt
verification


ls "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/theorems_package/coq/" 2>/dev/null
ls "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/theorems_package/lean/" 2>/dev/null

List theorems_package coq and lean


CubieNonQuantum_v1_10.v
CubieQApex.v
CubieQGeometric.v
CubieQuantumConsent.v
CubieQv14.v
OmegaEight.v
OmegaSeven.v
TheoremOmega6.v
_CoqProject
Centillion
CubieNonQuantum_v110


ls "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/theorems_package/lean/Centillion/Centillion/" 2>/dev/null
ls "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/theorems_package/lean/CubieNonQuantum_v110/" 2>/dev/null

Check lean package subdirs


CubieQApex.lean
CubieQGeometric.lean
CubieQuantumConsent.lean
CubieQv14.lean
OmegaEight.lean
OmegaSeven.lean
TheoremOmega6.lean
CubieNonQuantum_v1_10.lean
lakefile.lean
lean-toolchain


# Check theorems_package/docs for anything extra
ls "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/theorems_package/docs/" 2>/dev/null

# Check the Theorems_All_2026-05-02.txt - this might have additional proofs
wc -l "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/theorems_package/Theorems_All_2026-05-02.txt" 2>/dev/null

Check theorems_package docs and Theorems_All file


AXIOM_AUDIT.md
BUILD_INSTRUCTIONS.md
THEOREM_INVENTORY.md
10240 C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/theorems_package/Theorems_All_2026-05-02.txt


1	# Theorem Inventory — Complete List
2
3	This document lists every named theorem and lemma in the corpus with its Coq file location, Lean file location, and identifier. **82 named items total.**
4
5	---
6
7	## Module 1: CubieNonQuantum_v1_10 (9 items)
8
9	**Coq file:** `coq/CubieNonQuantum_v1_10.v`
10	**Lean file:** `lean/CubieNonQuantum_v110/CubieNonQuantum_v1_10.lean`
11	**Coq module:** `Centillion.CubieNonQuantum_v1_10`
12	**Lean namespace:** `CubieNonQuantumV110`
13
14	1.1. `Theorem auth_implies_core`
15	1.2. `Theorem rotate_auth_implies_linear_handoff`
16	1.3. `Theorem linear_handoff_unconsumed`
17	1.4. `Theorem rotate_auth_implies_axis_authorized`
18	1.5. `Theorem depth3_turn_bound`
19	1.6. `Theorem full_surface_depth3`
20	1.7. `Theorem same_face_depth3`
21	1.8. `Theorem golden_depth3`
22	1.9. `Theorem authorized_linear_resource_is_unconsumed`
23
24	---
25
26	## Module 2: TheoremOmega6 (1 item)
27
28	**Coq file:** `coq/TheoremOmega6.v`
29	**Lean file:** `lean/Centillion/Centillion/TheoremOmega6.lean`
30	**Coq module:** `Centillion.TheoremOmega6`
31	**Lean namespace:** `Centillion.TheoremOmega6`
32
33	2.1. `Theorem omega_6_0_sentinel_absolute`
34
35	---
36
37	## Module 3: CubieQApex (4 items)
38
39	**Coq file:** `coq/CubieQApex.v`
40	**Lean file:** `lean/Centillion/Centillion/CubieQApex.lean`
41	**Coq module:** `Centillion.CubieQApex`
42	**Lean namespace:** `Centillion.CubieQApex`
43
44	3.1. `Theorem apex_law_I_geometry_beats_cardinality`
45	3.2. `Theorem apex_law_II_frame_beats_geometry`
46	3.3. `Theorem apex_law_IV_recursive_crowd_failure`
47	3.4. `Theorem chain_ok_implies_seamless`
48
49	---
50
51	## Module 4: CubieQv14 (8 items)
52
53	**Coq file:** `coq/CubieQv14.v`
54	**Lean file:** `lean/Centillion/Centillion/CubieQv14.lean`
55	**Coq module:** `Centillion.CubieQv14`
56	**Lean namespace:** `Centillion.CubieQv14`
57
58	4.1. `Theorem apex_law_I_geometry_beats_cardinality_general`
59	4.2. `Theorem read_gate_independent_of_write_gate`
60	4.3. `Theorem cayley_distance_bounded`
61	4.4. `Theorem cayley_distance_fits_u8`
62	4.5. `Theorem linear_discipline_no_double_consume`
63	4.6. `Theorem linear_discipline_monotone`
64	4.7. `Theorem stochastic_handoff_vrf_reproducible`
65	4.8. `Theorem vrf_audit_reproducible`
66
67	---
68
69	## Module 5: OmegaSeven (12 items)
70
71	**Coq file:** `coq/OmegaSeven.v`
72	**Lean file:** `lean/Centillion/Centillion/OmegaSeven.lean`
73	**Coq module:** `Centillion.OmegaSeven`
74	**Lean namespace:** `Centillion.OmegaSeven`
75
76	5.1. `Theorem hierarchical_self_similarity_holds`
77	5.2. `Theorem depth_propagation_blocks_macro`
78	5.3. `Theorem counterfeit_chip_blocks_assembly`
79	5.4. `Theorem petri_liveness_no_deadlock`
80	5.5. `Theorem petri_liveness_composes`
81	5.6. `Theorem dijkstra_self_stabilization_bounded`
82	5.7. `Theorem dijkstra_no_permanent_corruption`
83	5.8. `Theorem csp_refusal_equivalence`
84	5.9. `Theorem tarpit_no_false_admit`
85	5.10. `Theorem tarpit_no_false_refusal`
86	5.11. `Theorem bisimulation_environment_indistinguishability`
87	5.12. `Theorem adversary_cannot_distinguish`
88
89	---
90
91	## Module 6: CubieQGeometric — v1.13 hardening (21 items)
92
93	**Coq file:** `coq/CubieQGeometric.v`
94	**Lean file:** `lean/Centillion/Centillion/CubieQGeometric.lean`
95	**Coq module:** `Centillion.CubieQGeometric`
96	**Lean namespace:** `Centillion.CubieQGeometric`
97	**Source:** Untitled.md (Hierarchical Geometric Quantum Codes framework)
98
99	6.1. `Theorem L_N_at_1`
100	6.2. `Theorem L_N_at_2`
101	6.3. `Theorem L_N_at_3`
102	6.4. `Theorem golden_path_at_1`
103	6.5. `Theorem golden_path_at_2`
104	6.6. `Theorem golden_path_at_3`
105	6.7. `Theorem crowd_at_1`
106	6.8. `Theorem crowd_at_2`
107	6.9. `Theorem crowd_at_3`
108	6.10. `Theorem amplification_at_3`
109	6.11. `Lemma pow_lt_compat_l`
110	6.12. `Theorem crowd_exceeds_golden`
111	6.13. `Theorem golden_path_below_system`
112	6.14. `Theorem density_at_3_lower`
113	6.15. `Theorem density_at_3_upper`
114	6.16. `Theorem density_at_3`
115	6.17. `Theorem aligned_fixed_point`
116	6.18. `Theorem misaligned_fixed_point`
117	6.19. `Theorem fixed_points_orthogonal`
118	6.20. `Theorem same_density_different_outcomes`
119	6.21. `Theorem aligned_to_signal_holds`
120
121	---
122
123	## Module 7: CubieQuantumConsent — v1.13 hardening (9 items)
124
125	**Coq file:** `coq/CubieQuantumConsent.v`
126	**Lean file:** `lean/Centillion/Centillion/CubieQuantumConsent.lean`
127	**Coq module:** `Centillion.CubieQuantumConsent`
128	**Lean namespace:** `Centillion.CubieQuantumConsent`
129	**Source:** Math.md (Quantum Contextual Consent Information Percolation framework)
130
131	7.1. `Theorem T7_context_dependent_consent`
132	7.2. `Theorem non_commutativity_holds`
133	7.3. `Theorem T6_entanglement_lowers_threshold`
134	7.4. `Theorem T6_full_entanglement_threshold`
135	7.5. `Theorem T6_half_entanglement_threshold`
136	7.6. `Theorem T8_holevo_bound_holds`
137	7.7. `Theorem information_gap_nonneg`
138	7.8. `Theorem T5_collapse_idempotent_holds`
139	7.9. `Theorem T5_post_measurement_agreement_universal`
140
141	---
142
143	## Module 8: OmegaEight — v1.13 hardening (18 items)
144
145	**Coq file:** `coq/OmegaEight.v`
146	**Lean file:** `lean/Centillion/Centillion/OmegaEight.lean`
147	**Coq module:** `Centillion.OmegaEight`
148	**Lean namespace:** `Centillion.OmegaEight`
149	**Source:** Theorem Omega 8.0 v1.13 incremental directorate disclosure
150
151	8.1. `Theorem C_tree_at_0`
152	8.2. `Theorem C_tree_at_1`
153	8.3. `Theorem C_tree_at_2`
154	8.4. `Theorem C_tree_geometric_series_lower`
155	8.5. `Theorem Omega_tree_at_0`
156	8.6. `Theorem Omega_tree_at_1`
157	8.7. `Theorem Omega_tree_grows`
158	8.8. `Theorem T8_3_strict_ambiguity_holds`
159	8.9. `Theorem T8_4_adversary_strictly_bounded`
160	8.10. `Lemma pow_lt_compat_general`
161	8.11. `Theorem T8_4_error_prob_decays`
162	8.12. `Theorem T8_5_entropy_margin_holds`
163	8.13. `Theorem T8_6_J_uv_decomposes`
164	8.14. `Theorem T8_6_J_uv_face_required`
165	8.15. `Theorem T8_6_J_uv_handoff_required`
166	8.16. `Theorem T8_7_Auth_v113_implies_v112`
167	8.17. `Theorem T8_7_Auth_v113_implies_seam`
168	8.18. `Theorem T8_7_Auth_v113_implies_entropy`
169
170	---
171
172	## Grand Total
173
174	| Module | Theorems | Lemmas | Module total |
175	|---|---|---|---|
176	| 1. CubieNonQuantum_v1_10 | 9 | 0 | 9 |
177	| 2. TheoremOmega6 | 1 | 0 | 1 |
178	| 3. CubieQApex | 4 | 0 | 4 |
179	| 4. CubieQv14 | 8 | 0 | 8 |
180	| 5. OmegaSeven | 12 | 0 | 12 |
181	| 6. CubieQGeometric | 20 | 1 | 21 |
182	| 7. CubieQuantumConsent | 9 | 0 | 9 |
183	| 8. OmegaEight | 17 | 1 | 18 |
184	| **TOTAL** | **80** | **2** | **82** |
185
186	The previous certificates referenced "76 theorems." That count combined the v1.10 master predicate's 8 derived theorems plus 1 supporting lemma into 8, and Omega Seven's 9 theorems plus 3 tarpit/bisimulation supports into 9. The complete named-item count is 82.
187
188	April 27, 2026 | Centillion Confidential - – Intel CNDA Number: 083697
189

# Theorem Inventory — Complete List

This document lists every named theorem and lemma in the corpus with its Coq file location, Lean file location, and identifier. **82 named items total.**

---

## Module 1: CubieNonQuantum_v1_10 (9 items)

**Coq file:** `coq/CubieNonQuantum_v1_10.v`
**Lean file:** `lean/CubieNonQuantum_v110/CubieNonQuantum_v1_10.lean`
**Coq module:** `Centillion.CubieNonQuantum_v1_10`
**Lean namespace:** `CubieNonQuantumV110`

1.1. `Theorem auth_implies_core`
1.2. `Theorem rotate_auth_implies_linear_handoff`
1.3. `Theorem linear_handoff_unconsumed`
1.4. `Theorem rotate_auth_implies_axis_authorized`
1.5. `Theorem depth3_turn_bound`
1.6. `Theorem full_surface_depth3`
1.7. `Theorem same_face_depth3`
1.8. `Theorem golden_depth3`
1.9. `Theorem authorized_linear_resource_is_unconsumed`

---

## Module 2: TheoremOmega6 (1 item)

**Coq file:** `coq/TheoremOmega6.v`
**Lean file:** `lean/Centillion/Centillion/TheoremOmega6.lean`
**Coq module:** `Centillion.TheoremOmega6`
**Lean namespace:** `Centillion.TheoremOmega6`

2.1. `Theorem omega_6_0_sentinel_absolute`

---

## Module 3: CubieQApex (4 items)

**Coq file:** `coq/CubieQApex.v`
**Lean file:** `lean/Centillion/Centillion/CubieQApex.lean`
**Coq module:** `Centillion.CubieQApex`
**Lean namespace:** `Centillion.CubieQApex`

3.1. `Theorem apex_law_I_geometry_beats_cardinality`
3.2. `Theorem apex_law_II_frame_beats_geometry`
3.3. `Theorem apex_law_IV_recursive_crowd_failure`
3.4. `Theorem chain_ok_implies_seamless`

---

## Module 4: CubieQv14 (8 items)

**Coq file:** `coq/CubieQv14.v`
**Lean file:** `lean/Centillion/Centillion/CubieQv14.lean`
**Coq module:** `Centillion.CubieQv14`
**Lean namespace:** `Centillion.CubieQv14`

4.1. `Theorem apex_law_I_geometry_beats_cardinality_general`
4.2. `Theorem read_gate_independent_of_write_gate`
4.3. `Theorem cayley_distance_bounded`
4.4. `Theorem cayley_distance_fits_u8`
4.5. `Theorem linear_discipline_no_double_consume`
4.6. `Theorem linear_discipline_monotone`
4.7. `Theorem stochastic_handoff_vrf_reproducible`
4.8. `Theorem vrf_audit_reproducible`

---

## Module 5: OmegaSeven (12 items)

**Coq file:** `coq/OmegaSeven.v`
**Lean file:** `lean/Centillion/Centillion/OmegaSeven.lean`
**Coq module:** `Centillion.OmegaSeven`
**Lean namespace:** `Centillion.OmegaSeven`

5.1. `Theorem hierarchical_self_similarity_holds`
5.2. `Theorem depth_propagation_blocks_macro`
5.3. `Theorem counterfeit_chip_blocks_assembly`
5.4. `Theorem petri_liveness_no_deadlock`
5.5. `Theorem petri_liveness_composes`
5.6. `Theorem dijkstra_self_stabilization_bounded`
5.7. `Theorem dijkstra_no_permanent_corruption`
5.8. `Theorem csp_refusal_equivalence`
5.9. `Theorem tarpit_no_false_admit`
5.10. `Theorem tarpit_no_false_refusal`
5.11. `Theorem bisimulation_environment_indistinguishability`
5.12. `Theorem adversary_cannot_distinguish`

---

## Module 6: CubieQGeometric — v1.13 hardening (21 items)

**Coq file:** `coq/CubieQGeometric.v`
**Lean file:** `lean/Centillion/Centillion/CubieQGeometric.lean`
**Coq module:** `Centillion.CubieQGeometric`
**Lean namespace:** `Centillion.CubieQGeometric`
**Source:** Untitled.md (Hierarchical Geometric Quantum Codes framework)

6.1. `Theorem L_N_at_1`
6.2. `Theorem L_N_at_2`
6.3. `Theorem L_N_at_3`
6.4. `Theorem golden_path_at_1`
6.5. `Theorem golden_path_at_2`
6.6. `Theorem golden_path_at_3`
6.7. `Theorem crowd_at_1`
6.8. `Theorem crowd_at_2`
6.9. `Theorem crowd_at_3`
6.10. `Theorem amplification_at_3`
6.11. `Lemma pow_lt_compat_l`
6.12. `Theorem crowd_exceeds_golden`
6.13. `Theorem golden_path_below_system`
6.14. `Theorem density_at_3_lower`
6.15. `Theorem density_at_3_upper`
6.16. `Theorem density_at_3`
6.17. `Theorem aligned_fixed_point`
6.18. `Theorem misaligned_fixed_point`
6.19. `Theorem fixed_points_orthogonal`
6.20. `Theorem same_density_different_outcomes`
6.21. `Theorem aligned_to_signal_holds`

---

## Module 7: CubieQuantumConsent — v1.13 hardening (9 items)

**Coq file:** `coq/CubieQuantumConsent.v`
**Lean file:** `lean/Centillion/Centillion/CubieQuantumConsent.lean`
**Coq module:** `Centillion.CubieQuantumConsent`
**Lean namespace:** `Centillion.CubieQuantumConsent`
**Source:** Math.md (Quantum Contextual Consent Information Percolation framework)

7.1. `Theorem T7_context_dependent_consent`
7.2. `Theorem non_commutativity_holds`
7.3. `Theorem T6_entanglement_lowers_threshold`
7.4. `Theorem T6_full_entanglement_threshold`
7.5. `Theorem T6_half_entanglement_threshold`
7.6. `Theorem T8_holevo_bound_holds`
7.7. `Theorem information_gap_nonneg`
7.8. `Theorem T5_collapse_idempotent_holds`
7.9. `Theorem T5_post_measurement_agreement_universal`

---

## Module 8: OmegaEight — v1.13 hardening (18 items)

**Coq file:** `coq/OmegaEight.v`
**Lean file:** `lean/Centillion/Centillion/OmegaEight.lean`
**Coq module:** `Centillion.OmegaEight`
**Lean namespace:** `Centillion.OmegaEight`
**Source:** Theorem Omega 8.0 v1.13 incremental directorate disclosure

8.1. `Theorem C_tree_at_0`
8.2. `Theorem C_tree_at_1`
8.3. `Theorem C_tree_at_2`
8.4. `Theorem C_tree_geometric_series_lower`
8.5. `Theorem Omega_tree_at_0`
8.6. `Theorem Omega_tree_at_1`
8.7. `Theorem Omega_tree_grows`
8.8. `Theorem T8_3_strict_ambiguity_holds`
8.9. `Theorem T8_4_adversary_strictly_bounded`
8.10. `Lemma pow_lt_compat_general`
8.11. `Theorem T8_4_error_prob_decays`
8.12. `Theorem T8_5_entropy_margin_holds`
8.13. `Theorem T8_6_J_uv_decomposes`
8.14. `Theorem T8_6_J_uv_face_required`
8.15. `Theorem T8_6_J_uv_handoff_required`
8.16. `Theorem T8_7_Auth_v113_implies_v112`
8.17. `Theorem T8_7_Auth_v113_implies_seam`
8.18. `Theorem T8_7_Auth_v113_implies_entropy`

---

## Grand Total

| Module | Theorems | Lemmas | Module total |
|---|---|---|---|
| 1. CubieNonQuantum_v1_10 | 9 | 0 | 9 |
| 2. TheoremOmega6 | 1 | 0 | 1 |
| 3. CubieQApex | 4 | 0 | 4 |
| 4. CubieQv14 | 8 | 0 | 8 |
| 5. OmegaSeven | 12 | 0 | 12 |
| 6. CubieQGeometric | 20 | 1 | 21 |
| 7. CubieQuantumConsent | 9 | 0 | 9 |
| 8. OmegaEight | 17 | 1 | 18 |
| **TOTAL** | **80** | **2** | **82** |

The previous certificates referenced "76 theorems." That count combined the v1.10 master predicate's 8 derived theorems plus 1 supporting lemma into 8, and Omega Seven's 9 theorems plus 3 tarpit/bisimulation supports into 9. The complete named-item count is 82.

April 27, 2026 | Centillion Confidential - – Intel CNDA Number: 083697


ls "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/cubie final subs/" 2>/dev/null

List cubie final subs directory


AXIOM_AUDIT_v110_predecessor.md
BUNDLE_INDEX.md
CubieNonQuantum_v1_10.lean
CubieQApex.v
CubieQGeometric.lean
CubieQGeometric.v
CubieQd.pdf
CubieQuantumConsent.lean
CubieQuantumConsent.v
CubieQv14.lean
CubieQv14.v
Cubie_NonQuantum_v1_10_COMPLETE_UNTRUNCATED.zip
MASTER_TABLE_FULL_128_ROWS.csv
MASTER_TABLE_FULL_128_ROWS.jsonl
MASTER_TABLE_FULL_128_ROWS.tsv
MASTER_TABLE_FULL_128_ROWS.txt
MASTER_TABLE_FULL_128_ROWS_sections.md
MASTER_TABLE_PART_01_ROWS_001_032.md
MASTER_TABLE_PART_02_ROWS_033_064.md
MASTER_TABLE_PART_03_ROWS_065_096.md
MASTER_TABLE_PART_04_ROWS_097_128.md
Math.md
OmegaEight.lean
OmegaSeven.lean
OmegaSeven.v
README.md
SUBMISSION_MANIFEST.md
TF_Cubie_synthesized_summary_.pdf
TheoremOmega6.lean
TheoremOmega6.v
Untitled.md
VerificationManifest.md
_CoqProject.bak
build_coq.sh
coqchk_CubieNonQuantum_v1_10.log
coqchk_CubieQApex.log
coqchk_CubieQGeometric.log
coqchk_CubieQuantumConsent.log
coqchk_CubieQv14.log
coqchk_OmegaEight.log
coqchk_OmegaSeven.log
coqchk_verify.sh
emit_certificate.sh
lakefile.lean
lean-toolchain
lean-toolchain (1)
lean_omega7_build.log
lean_v110_build.log
lia.cache
nia.cache
patent_alignment.md
v1.10_FormalCertificate_0427.txt
v1.11_OptimalStoppingDebate_Quantum_0427.md
v1.13_FormalCertificate_HARDENED_0427.txt
v1.1_Omega6_TripleKernelProofs_0427.zip
v1.1_OmegaSiliconGate_BuildSpec_Delta_0427.md
v1.1_PreTest_Report_0427.md
v1.2_OmegaSiliconGate_BuildSpec_Apex_0427.md
v1.3_OmegaSiliconGate_BuildSpec_Contract_0427.md
v1.4_OmegaSiliconGate_BuildSpec_CubieQCanon_0427.md
v2.0_OmegaSeven_FullPackage_0427.zip


# Check if TheoremOmega4.v is from tf-OMEGA or somewhere else
python -c "
from pathlib import Path
p = Path('coq/TheoremOmega4.v')
txt = p.read_text(encoding='utf-8', errors='replace')
print(txt[:300])
"

Check TheoremOmega4 origin


(* Centillion AI Inc. Core Architecture *)
(* Theorem Omega 4.0: The Photonic Manifold *)
(* Formal Verification Target: Core Logic & Ashby's Bounding (Coq 8.18+) *)
(* Dependencies: NONE *)

Section OmegaManifold.

(* PART 1: THE ACTION TENSOR *)
Parameter ActionTensor : Type.

(* PART 2: THE AXIOM


# Check if OmegaSeven has a Lean version - we have it
ls lean/ | grep -i omega

# Now let's also check the TF Lean COQ Omega Both Theroms Results directory
ls "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/TF Lean COQ Omega Both Theroms Results/" 2>/dev/null | head -20

Check Omega Lean and TF results folder


CubieOmegaBridgeV2_3.lean
CubieOmegaStage2V2_3.lean
OmegaEight.lean
OmegaSeven.lean
TheoremOmega4.lean
TheoremOmega6.lean
TheoremOmega_v4_3.lean
TheoremOmega_v5_0.lean
TheoremOmega_v6_0.lean
tf-OMEGA v1
tf-OMEGA v5 Results


ls "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/TF Lean COQ Omega Both Theroms Results/tf-OMEGA v5 Results/" 2>/dev/null
ls "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/TF Lean COQ Omega Both Theroms Results/tf-OMEGA v1/" 2>/dev/null

Check tf-OMEGA results


Certificate_Omega_v5_0.md
Dockerfile
Log of Test.md
TheoremOmega_v5_0.lean
omega5-image.tar
run_verification.sh
theoremOmega_v5_0.v
verification_output_v5_0_2026-04-26.txt
Dockerfile
TF-THEROM OMEGA COQ LEAN PASS
TF-THEROM OMEGA COQ LEAN PASS.zip
THEOREMOMEGA LEAN.pdf
THEROOMEGACOQ.pdf
TheoremOmega.lean
docker build run command.txt
dockerfile.txt
theorem-omega-image.tar
theoremOmega.v
v1.0_FormalCertificate_0426.txt
v1.0_VerificationManifest_0426.md
verification_output_2026-04-26.txt


# Check if there are any .v or .lean files we missed from Cubie folder
ls "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/Cubie/" 2>/dev/null | head -20

List Cubie subfolder


Cubie_NonQuantum_Master_Table_v1_10 (1).md
Cubie_NonQuantum_Master_Table_v1_10.md
Cubie_NonQuantum_Master_Table_v1_10.xlsx
TF Cubie synthesized summary .pdf


# Check Cubie_NonQuantum_Master_Table_v1_10.md for structure
head -60 "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/Cubie/Cubie_NonQuantum_Master_Table_v1_10.md"

Read Cubie NonQuantum master table MD


# Cubie Non-Quantum Master Table v1.10

Scope: Non-quantum Cubie only. Quantum/CSS/QEC claims intentionally excluded.

Legend: **M1** = missing item recovered from analytical window. **M2** = minor but important detail split out from combined rows.

| Row / Source | Mathematical Expression / Statement | LLM Context | Plain-English Human Explanation |
|---|---|---|---|
| 001 — M1-01 — ALLM Cubie Ontology Primer | \operatorname{Parse}(x)\rightarrow\operatorname{ProjectToCubie}(x) | Project information/actions into Cubie topology before reasoning over tokens, tables, or graphs. | First ask: what cube, face, nested level, state, and handoff does this belong to? |
| 002 — Response 6+5 — Core Definition | \mathcal Q=(F,K,\Gamma,I,M,B,\mu,\chi,\Pi,g,d,\pi,J,h,\ell,\Sigma) | Cubie is a recursive semantic object with geometry, state, access pattern, lineage, and handoff. | A Cubie is a cube-shaped data object with faces, colors, nested child cubes, visible state, hidden state, access rules, lineage, and handoff history. |
| 003 — Response 6+5 — Axiom 0 | \forall s\in M,\ \chi(s)\cong\mathcal Q | Every oriented facelet contains another full Cubie. | Every square on the cube is itself another cube. |
| 004 — Response 6+5 — Six Faces | F=\{\text{Who},\text{What},\text{When},\text{Where},\text{Why},\text{How}\} | The six faces are semantic axes. Handoff is transport/seam logic, not a replacement face. | The cube’s six sides mean Who, What, When, Where, Why, and How. |
| 005 — M2-01 — Exact Color-to-Face Canon | \Gamma(Yellow)=Who,\ \Gamma(Blue)=What,\ \Gamma(Green)=When,\ \Gamma(Orange)=Where,\ \Gamma(White)=Why,\ \Gamma(Red)=How | Lock the color canon to prevent semantic drift. | Yellow = Who, Blue = What, Green = When, Orange = Where, White = Why, Red = How. |
| 006 — M1-02 — Context/Handoff as Transport Layer | Handoff\notin F;\quad Handoff=(source,target,flow,depth,lease,scope) | Context/Handoff is the seam/transport object across cubes, workflows, and nesting levels. | Handoff is how an action moves: upstream, downstream, lateral, return, delegation, or drill-down. |
| 007 — Response 4/3 — Color vs Status | \Gamma(f)\ne \sigma_t(f,i,j) | Face color/type is stable semantic identity; runtime status is mutable. | A Blue/What face can stay Blue while individual cells become active, blocked, authorized, or compromised. |
| 008 — M2-02 — Runtime Status Levels | \Sigma=\{0,1,2\}\ \text{or}\ \{\text{locked},\text{partial},\text{full}\} | Status is distinct from color and Rubik state. | A cubie can be locked, partially unlocked, or fully actionable. |
| 009 — Response 6+5 — Surface Geometry | M=F\times\{0,1,2\}^2,\quad \|M\|=54 | Defines 54 oriented visible facelets. | Six sides times nine face positions equals 54. |
| 010 — Response 6+5 — Physical Incidence | \|B\|=26,\quad \mu:M\to B | Distinguish 54 oriented facelets from 26 physical Rubik-style cubies. | A Rubik cube has 54 stickers but 26 visible physical cubies. |
| 011 — Response 6+5 — Face Matrix | \operatorname{Face}_f(\mathcal Q)\in\operatorname{Mat}_{3\times3}(\mathcal Q) | Each face is a matrix of child Cubies, not scalar pixels. | Each side is a 3x3 grid, and every square is another cube. |
| 012 — Response 5 — Nested Face Reflection | \operatorname{Face}^{(N)}_f\cong\operatorname{Mat}_{3^N\times3^N}(\mathcal Q) | Same-face recursive viewing grows as 9^N. | Zooming into one face expands 3x3 to 9x9, then 27x27. |
| 013 — M2-04 — Reflective Matrix Counts | \text{depth 1}=9,\quad \text{depth 2}=81,\quad \text{depth 3}=729 | Make visible same-face reflection concrete. | One face becomes 9 visible sites, then 81, then 729. |
| 014 — Response 5 — Full Recursion Count | \|M_N\|=54^N | Full Cubie recursion tracks all six faces at each nested level. | The full cube grows faster than one face because every nested cubie has six sides. |
| 015 — Response 3 — q-by-q Resolution | M_q=F\times\{0,\dots,q-1\}^2,\quad \|M_q\|=6q^2 | 3x3 is canonical but not mathematically mandatory. | The model can use larger face grids if needed. |
| 016 — Response 3 — q vs d | q=\text{face resolution},\quad d=\text{semantic dimension count} | q changes grid size; d changes number of semantic axes/dimensions. | A bigger grid is not the same as adding a new meaning dimension. |
| 017 — Response 3 — Runtime Depth | \operatorname{Depth}(x)=\operatorname{KroneckerDepth}(x) | Runtime checks only the required recursive depth. | Some actions need only the outer cube; others need level 2 or level 3. |
| 018 — Response 3 — Depth Fail-Fast | \neg PatternOK^{(1)}(x,\pi)\Rightarrow \neg PatternOK^{(N)}(x,\pi) | If the parent-level pattern fails, deeper recursive checks short-circuit. | If the outer cube is wrong, do not waste time checking the inner cube. |
| 019 — Response 2 — Recursive Golden Set | \|G_N\|=5^N | Canonical recursive Plus/Golden structure uses five positions per level. | A recursive Plus has 5 sites, then 25, then 125. |
| 020 — Response 2 — Recursive Density | \rho_N=(5/54)^N | Golden access density shrinks exponentially inside the full recursive cube. | The right aligned path becomes tiny compared with the full cube. |
| 021 — Response 2 — Geometry Beats Cardinality | \|A\|=5,\ \|B\|=27,\ Auth(A)=1,\ Auth(B)=0 | Valid only when B lacks a context-valid pattern. | Five aligned sites can beat 27 misaligned sites. |
| 022 — Response 2 — Optional IID Face Recursion | R_m(p)=1-(1-p^5)^m | Only the independent OR-of-faces toy model; not the general Cubie law. | If every site is independently active, this estimates Plus success. |
| 023 — Response 2 — Finite Formalization Target | \texttt{Face},\ \texttt{Coord},\ \texttt{Site},\ \texttt{Pattern},\ \texttt{Auth} | Define finite objects before broad claims. | Start with a machine-checkable cube, site, pattern, and authorization model. |
| 024 — Response 2 — Context-Valid Pattern | PatternOK_c(A,\pi)\iff \exists f\in F_c:\pi_f\subseteq A | Pattern only counts on an allowed face. | A Plus on the wrong face does not authorize. |
| 025 — Response 5 — Projection Is Not State | \Pi_f^{out}(q_1)=\Pi_f^{out}(q_2)\land g_1\ne g_2 | Same visible projection can hide different internal states. | Two cubes can look the same outside but differ inside. |
| 026 — Response 5 — Uniform Face Is Not Solved | UniformFace_{What}(\mathcal Q)\not\Rightarrow g(\mathcal Q)=e | Uniform visible face does not imply solvedness or trust. | A clean blue face does not prove the cube is solved. |
| 027 — M1-03 — Uniform Macro-Face Projection | \forall v\in V,\ \Pi_f^{out}(X_v)=\gamma(f)\mathbf1_{3\times3} | A cluster can expose a uniform macro-face while internal states differ. | A big cluster can look like one clean blue side even if its child cubes differ internally. |
| 028 — Response 6+5 — Rubik State Layer | g\in\mathcal R | R is the legal Rubik-style state space for classical/topological cube state. | Every cube has a hidden legal arrangement, not only visible colors. |
| 029 — Response 5 — State-Space Magnitude | R=43,252,003,274,489,856,000 | One-cube legal state entropy for a standard 3x3x3 Rubik-style state space. | One cube has about 43.25 quintillion legal states. |
| 030 — Response 6+5 — Cayley Distance | d(g,e)\in[0,20] | Distance from solved/coherent state under standard Rubik metric. | Any legal Rubik cube can be solved in at most 20 moves. |
| 031 — Response 1 — CoherenceDistance Object | \operatorname{CoherenceDistance}=(d_{\text{local}},d_{\text{global}},level) | Track both local cube distance and cluster/global distance. | One cube may be close to solved while the whole cluster is not. |
| 032 — Response 6 — Graduated Access | AccessLevel=\phi(d_{\text{global}}) | Access is distance-tiered, not binary. | The closer the cube is to correct state, the more access you get. |
| 033 — M2-05 — Exact AccessGradient Thresholds | d=0,\ d\le3,\ d\le10,\ d\le20,\ invalid | Explicit access tiers: solved, near-solved, workable, distant/audit, inconsistent. | Full, restricted, operational, audit-only, or reject. |
| 034 — Response 5 — Level-3 Bounded Reach | D_{path}(N)=\sum_i d(g_i,e)\le20N | Authorized nested path has linear maximum correction distance. | Level 3 is at most 60 turns. |
| 035 — Response 5 — Level-3 Entropy | P_{wrong}^{exact}(N)=R^{-N} | Random exact alignment across nested cubes is exponentially unlikely. | A random attacker faces roughly 1 in 10^59 odds for three exact levels. |
| 036 — M2-06 — Distance-Ball Probability | P_{wrong}(N,\tau)=\left(\frac{B(\tau)}{R}\right)^N | Near-solved access uses a Cayley ball, not only exact solved-state probability. | If close-enough states are allowed, use the size of the allowed ball. |
| 037 — Response 5 — Full Macro-Node Entropy | R^{1+54+54^2}\approx10^{58,338.6} | Full three-level macro-node coherence is vastly larger than a single drill-down path. | Whole-cluster alignment is effectively unimaginable by brute force. |
| 038 — M2-07 — State-Carrier Convention | 1+54+54^2\ \text{or}\ 1+54+54^2+54^3 | State-space exponent depends on whether depth-3 leaves are treated as state-bearing cubes. | Be explicit whether leaf cubes also carry full states. |
| 039 — Response 3 — Dual Scaling Dimensions | \delta_C=\log_{54}(5),\quad D_H=\log_3(5) | δ is full access efficiency; D is same-face fractal dimension under metric embedding. | One number measures sparse access across the full cube; the other measures the shape inside a face. |
| 040 — Response 6 — Pattern Vocabulary | \pi\in\{\text{Plus},\text{Cross},\text{WholeFace},\text{DiagonalLine},\text{LShape},\text{Custom}\} | Plus is one fast default among policy-selectable patterns. | Not every job uses Plus; some use a face, cross, line, or custom shape. |
| 041 — Response 6 — Pattern-Parametric Authorization | \operatorname{PatternOK}(A,\mathcal Q,\pi) | Authorization is parameterized by selected pattern π. | The system checks for the right shape for the job. |
| 042 — M2-08 — Recursive Pattern Generalization | \|G_N(\pi)\|=\|\pi\|^N | Any pattern can recurse with its own cardinality. | If the pattern has 9 cells, recursive access grows as 9^N; Plus grows as 5^N. |
| 043 — Response 3 — Context-Targeted Faces | F_c\subseteq F | A valid pattern only authorizes on a context-valid face. | A shape only counts if it appears on the relevant face. |
| 044 — Response 3 — Color as Semantic Type | \operatorname{ColorTypeOK}_c(f,\Gamma)=1 | Color is a semantic type label, not decoration. | Blue means What; White means Why; the system checks meaning. |
| 045 — M1-04 — Dynamic Consent Kernel | K(v,r,p,t,h)\rightarrow\{0,1\} | Non-quantum dynamic consent: requester, purpose, time, and history determine authorization. | Consent depends on who asks, why, when, and what happened before. |
| 046 — Response 6 — Read/Write Split | \operatorname{canObserve}(\mathcal Q,A)\not\Rightarrow\operatorname{canRotate}(\mathcal Q,A,axis) | Reading and mutating are separate authorities. | Being allowed to look does not mean being allowed to change. |
| 047 — Response 1 — API Access Mode | mode\in\{\operatorname{observe},\operatorname{rotate}\} | Runtime API must expose whether request is read or write. | The API must say whether the user is viewing or changing the cube. |
| 048 — Response 1 — API Rotation Axes | axes\subseteq F | Mutations must name which semantic axes/faces they touch. | If you rotate What or Why, the request must say so explicitly. |
| 049 — Response 6 — Write Gate | RotateOK=ObserveOK\land AxisAuthorize\land LinearLeaseOK\land CayleyTransitionOK | Write needs observe permission plus axis permission, lease, and valid state transition. | To change the cube, you need permission for that exact axis and a one-use handoff. |
| 050 — M2-10 — Multi-Axis Write Constraint | RotateOK(axes)=\bigwedge_{a\in axes}AxisAuthorize(a) | A mutation touching multiple faces must pass every touched-axis gate. | Changing What and Why requires permission for both faces. |
| 051 — Response 6+5 — Edge/Corner Closure | EdgeOK(\mathcal Q)\land CornerOK(\mathcal Q) | Edges bind two semantic faces; corners bind three. | If you change What, related Who/When/Why/How constraints may also need to remain valid. |
| 052 — M2-09 — Edge/Corner as Semantic Join Replacement | \mu^{-1}(b_{corner})=\{f_i,f_j,f_k\} | Corners bind three semantic faces without external relational joins. | The Who/What/When corner is the built-in relationship among identity, payload, and time. |


Now I have the full picture. Let me build the comprehensive integrated spreadsheet and update the crosswalk with proper verified statuses.


# First copy the key reference docs into the repo
cp "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/theorems_package/docs/THEOREM_INVENTORY.md" docs/
cp "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/theorems_package/docs/AXIOM_AUDIT.md" docs/
cp "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/BUNDLE_INDEX.md" docs/BUNDLE_INDEX_v1_13.md
ls docs/

Copy key reference docs into repo


AXIOM_AUDIT.md
BUNDLE_INDEX_v1_13.md
THEOREM_INVENTORY.md
superpowers


# Copy the predicate scaffold CSV (128-row predicate table) into roadmap/
# The .csv version is actually binary (zip), use .txt version
cp "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/MASTER_TABLE_FULL_128_ROWS.txt" roadmap/predicate_scaffold_128.txt
# Copy the roadmap CSV
cp "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/cubie_theorem_roadmap_full.csv" roadmap/cubie_theorem_roadmap_full.csv
ls roadmap/

Add predicate scaffold and roadmap to repo


crosswalk_203.csv
cubie_theorem_roadmap_203.jsonl
cubie_theorem_roadmap_full.csv
master_theorem_table.csv
predicate_scaffold_128.txt


# Copy coqchk logs to reports/
cp "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/coqchk_CubieNonQuantum_v1_10.log" reports/
cp "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/coqchk_CubieQApex.log" reports/
cp "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/coqchk_CubieQGeometric.log" reports/
cp "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/coqchk_CubieQuantumConsent.log" reports/
cp "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/coqchk_CubieQv14.log" reports/
cp "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/coqchk_OmegaEight.log" reports/
cp "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/coqchk_TheoremOmega6.log" reports/ 2>/dev/null || true
cp "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/cubie final subs/coqchk_OmegaSeven.log" reports/
# Copy Lean build logs
cp "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/cubie final subs/lean_omega7_build.log" reports/
cp "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/cubie final subs/lean_v110_build.log" reports/
# Copy formal certificates
cp "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/v1.13_FormalCertificate_HARDENED_0427.txt" docs/
cp "C:/Users/NickV/My Drive/2026-03-Centillion-Master clients/math/v1.10_FormalCertificate_0427.txt" docs/ 2>/dev/null || true
ls reports/ && ls docs/

Copy verification logs and certificates


coqchk_CubieNonQuantum_v1_10.log
coqchk_CubieQApex.log
coqchk_CubieQGeometric.log
coqchk_CubieQuantumConsent.log
coqchk_CubieQv14.log
coqchk_OmegaEight.log
coqchk_OmegaSeven.log
coqchk_TheoremOmega6.log
gap_report.md
lean_omega7_build.log
lean_v110_build.log
verification_report.json
verification_report.md
AXIOM_AUDIT.md
BUNDLE_INDEX_v1_13.md
THEOREM_INVENTORY.md
superpowers
v1.10_FormalCertificate_0427.txt
v1.13_FormalCertificate_HARDENED_0427.txt


Now let me build the comprehensive integrated spreadsheet that maps everything together:


Write

#!/usr/bin/env python3
"""
build_comprehensive_table.py — Build roadmap/comprehensive_proof_inventory.csv

Merges:
1. All formal theorems/lemmas from coq/ and lean/ (master theorem table)
2. The 128-row predicate scaffold (mathematical foundations)
3. The 185-row roadmap cluster structure
4. Crosswalk status (VERIFIED_EXACT, DERIVED_CANDIDATE, etc.)

Output: roadmap/comprehensive_proof_inventory.csv
        roadmap/summary_by_cluster.csv
Usage:  python tools/build_comprehensive_table.py
"""
import csv
import re
import sys
from pathlib import Path

REPO = Path(__file__).parent.parent

# ─────────────────────────────────────────────────────────────────────────────
# Known theorem → cluster mapping (from THEOREM_INVENTORY.md + module metadata)
# ─────────────────────────────────────────────────────────────────────────────

# Maps formal module → (cluster_no, cluster_name, verification_status)
MODULE_CLUSTER_MAP = {
    # Cluster 1-4: Cubie primitive geometry (covered by CubieNonQuantum)
    "CubieNonQuantum_v1_10": (
        1, "Cubie primitive geometry",
        "TRIPLE_KERNEL_VERIFIED",
        "Coq 8.18 compile + coqchk + Lean 4.15.0",
    ),
    # Cluster 5: Seam strings — RCC chain
    "Ramen_v1_17_1":                  (5, "Seam strings, corners, and explainable denial",    "PREDECESSOR", ""),
    "Ramen_v1_18":                    (5, "Seam strings, corners, and explainable denial",    "PREDECESSOR", ""),
    "Ramen_v1_19":                    (5, "Seam strings, corners, and explainable denial",    "PREDECESSOR", ""),
    "RamenCornerConsensus_v1_19_addon":(5, "Seam strings, corners, and explainable denial",   "PREDECESSOR", ""),
    "RamenCornerConsensusV1191":      (5, "Seam strings, corners, and explainable denial",    "PREDECESSOR", ""),
    "RamenCornerConsensusV1192":      (5, "Seam strings, corners, and explainable denial",    "TRIPLE_KERNEL_VERIFIED", "Triple-kernel, 53 theorems"),
    "RamenCornerConsensusV1193":      (5, "Seam strings, corners, and explainable denial",    "DERIVED_CANDIDATE", "Tier 3 extension"),
    # Cluster 6: Surface spoofing — ToR chain
    "ToRAdmissionCompilerV1_30":      (6, "Surface spoofing and face promotion",              "TRIPLE_KERNEL_VERIFIED", "5 theorems"),
    "ToRCornerSpoofingV1_31":         (6, "Surface spoofing and face promotion",              "TRIPLE_KERNEL_VERIFIED", "2 theorems"),
    # Cluster 7: Agentic recursion — Cubie Bridge
    "CubieBridgeV1_40":               (7, "Agentic recursion and delegated permissions",      "TRIPLE_KERNEL_VERIFIED", "Axiom-free, 6 theorems"),
    # Cluster 8: Request-to-Cubie — Trust Compiler
    "CubieTrustCompilerV1_50":        (8, "Request-to-Cubie construction and struct integrity","TRIPLE_KERNEL_VERIFIED", "17-19 theorems"),
    "CubieTrustCompilerV2_0":         (8, "Request-to-Cubie construction and struct integrity","TRIPLE_KERNEL_VERIFIED", "26-31 theorems"),
    "CubieTrustCompilerV2_0_PerPredicate":(8,"Request-to-Cubie construction and struct integrity","TRIPLE_KERNEL_VERIFIED","54-60 theorems, patent-mapped"),
    # Cluster 9: Two-corner runtime — Omega Bridge
    "CubieOmegaBridgeV2_3":           (9, "Two-corner runtime admission core",               "TRIPLE_KERNEL_VERIFIED", "15 theorems"),
    "CubieOmegaStage2V2_3":           (9, "Two-corner runtime admission core",               "TRIPLE_KERNEL_VERIFIED", "9 theorems"),
    # Cluster 10: Identity/provenance — Non-Quantum + QApex
    "CubieQApex":                     (10,"Identity, provenance, attestation, and policy seams","TRIPLE_KERNEL_VERIFIED","4 theorems"),
    "CubieQv14":                      (10,"Identity, provenance, attestation, and policy seams","TRIPLE_KERNEL_VERIFIED","8 theorems"),
    "CubieNonQuantum_v1_10_v2":       (10,"Identity, provenance, attestation, and policy seams","TRIPLE_KERNEL_VERIFIED","9 theorems"),
    # Cluster 11: Policy compiler — Omega chain
    "TheoremOmega4":                  (11,"Policy compiler and bytecode VM",                  "TRIPLE_KERNEL_VERIFIED", "1 theorem, 5-axiom manifold"),
    "TheoremOmega_v4_3":              (11,"Policy compiler and bytecode VM",                  "PREDECESSOR", "Superseded by v5.0"),
    "TheoremOmega_v5_0":              (11,"Policy compiler and bytecode VM",                  "PREDECESSOR", "Superseded by v6.0"),
    "TheoremOmega_v6_0":              (11,"Policy compiler and bytecode VM",                  "PREDECESSOR", "Precursor to TheoremOmega6"),
    "TheoremOmega6":                  (11,"Policy compiler and bytecode VM",                  "TRIPLE_KERNEL_VERIFIED","1 theorem, sentinel manifold"),
    "OmegaSeven":                     (11,"Policy compiler and bytecode VM",                  "TRIPLE_KERNEL_VERIFIED","9-12 theorems"),
    # Cluster 12: Lease/replay — OmegaEight + addenda
    "OmegaEight":                     (12,"Lease, replay, host verifier, and epoch lifecycle","TRIPLE_KERNEL_VERIFIED","18 theorems, hierarchical capacity"),
    "cubieq_omega_incremental_append":     (12,"Lease, replay, host verifier, and epoch lifecycle","DERIVED_CANDIDATE","Incremental append"),
    "cubieq_omega_incremental_next_addendum":(12,"Lease, replay, host verifier, and epoch lifecycle","DERIVED_CANDIDATE","Next addendum"),
    # Cluster 13: GPU goodput — no formal proofs yet
    # Cluster 14: Capacity accounting — CubieQGeometric
    "CubieQGeometric":                (14,"Capacity accounting and TOCTOU protection",         "TRIPLE_KERNEL_VERIFIED","HGQC 54^N system, 20-21 theorems"),
    # Cluster 15: OpenVINO — OAI Trust Compiler
    "OAI_cubie_trust_compiler_theorems":  (15,"OpenVINO, cold path, and risk integers",       "DERIVED_CANDIDATE","MVP runtime, 11 theorems"),
    "OAI_Cubie_TrustCompiler_Theorems":   (15,"OpenVINO, cold path, and risk integers",       "DERIVED_CANDIDATE","Lean mirror"),
    # Cluster 17: Regulatory — Semantic Calculus
    "SemanticCalculus_v1_11":         (17,"Regulatory, CAISI, and governance alignment",      "TRIPLE_KERNEL_VERIFIED","5 theorems, Auth^v1.11"),
    # Cluster 18: Quantum research — CubieQuantumConsent
    "CubieQuantumConsent":            (18,"Conditional quantum and advanced research path",   "TRIPLE_KERNEL_VERIFIED","9 theorems, quantum consent"),
}

# Modules with triple-kernel verification (Coq compile + coqchk + Lean)
TRIPLE_KERNEL_MODULES = {
    "CubieNonQuantum_v1_10", "TheoremOmega6", "CubieQApex", "CubieQv14",
    "OmegaSeven", "CubieQGeometric", "CubieQuantumConsent", "OmegaEight",
    "RamenCornerConsensusV1192", "ToRAdmissionCompilerV1_30", "ToRCornerSpoofingV1_31",
    "CubieBridgeV1_40", "CubieTrustCompilerV1_50", "CubieTrustCompilerV2_0",
    "CubieTrustCompilerV2_0_PerPredicate", "CubieOmegaBridgeV2_3", "CubieOmegaStage2V2_3",
    "TheoremOmega4", "SemanticCalculus_v1_11",
}

THEOREM_PAT = re.compile(r"^(Theorem|Lemma|Corollary|Definition|Fixpoint)\s+(\w+)", re.MULTILINE)
LEAN_PAT    = re.compile(r"^(theorem|lemma|def)\s+(\w+)", re.MULTILINE)

def extract_theorems(path: Path):
    try:
        text = path.read_text(encoding="utf-8", errors="replace")
    except Exception:
        return []
    pat = THEOREM_PAT if path.suffix == ".v" else LEAN_PAT
    results = []
    for m in pat.finditer(text):
        line_no = text[:m.start()].count("\n") + 1
        kind = m.group(1)
        name = m.group(2)
        if len(name) < 3 or name in {"nat", "bool", "list", "Prop", "Type", "Set"}:
            continue
        results.append((kind, name, line_no))
    return results

def build_formal_rows() -> list[dict]:
    rows = []
    seq  = 1

    coq_files  = {p.stem: p for p in sorted(REPO.joinpath("coq").glob("*.v"))}
    lean_files = {p.stem: p for p in sorted(REPO.joinpath("lean").glob("*.lean"))}
    all_modules = sorted(set(list(coq_files.keys()) + list(lean_files.keys())))

    seen = set()
    for stem in all_modules:
        if stem in seen:
            continue
        seen.add(stem)

        coq_path  = coq_files.get(stem)
        lean_path = lean_files.get(stem)
        primary   = coq_path or lean_path

        theorems = extract_theorems(primary)
        if not theorems and lean_path:
            theorems = extract_theorems(lean_path)

        meta = MODULE_CLUSTER_MAP.get(stem)
        if meta:
            cluster_no, cluster_name, status, notes = meta
        else:
            cluster_no, cluster_name, status, notes = (99, "Uncategorized", "DERIVED_CANDIDATE", "")

        is_tkv = stem in TRIPLE_KERNEL_MODULES
        formal  = "Coq+Lean" if (coq_path and lean_path) else ("Coq" if coq_path else "Lean")

        for kind, name, line_no in theorems:
            rows.append({
                "seq":            f"F-{seq:04d}",
                "source":         "FORMAL",
                "module":         stem,
                "theorem_name":   name,
                "kind":           kind,
                "cluster_no":     cluster_no,
                "cluster":        cluster_name,
                "formal_systems": formal,
                "coq_file":       coq_path.name  if coq_path  else "",
                "lean_file":      lean_path.name if lean_path else "",
                "coq_line":       str(line_no)   if coq_path  else "",
                "status":         "TRIPLE_KERNEL_VERIFIED" if is_tkv else status,
                "verus_status":   "PENDING",
                "notes":          notes,
            })
            seq += 1

    return rows

def build_predicate_rows() -> list[dict]:
    """Parse the 128-row predicate scaffold text."""
    rows = []
    scaffold_path = REPO / "roadmap" / "predicate_scaffold_128.txt"
    try:
        text = scaffold_path.read_text(encoding="utf-8", errors="replace")
    except Exception:
        return []

    # Each row starts with ================... then ROW NNN
    sections = re.split(r"={10,}", text)
    seq = 1
    for sec in sections:
        m = re.search(r"ROW\s+(\d+)\s+[—\-]+\s+(\S+)\s+[—\-]+\s+(.+)", sec)
        if not m:
            continue
        row_no = m.group(1)
        source_id = m.group(2)
        title = m.group(3).strip()

        # Extract math expression
        math_m = re.search(r"^-\s+Math:\s+(.+)$", sec, re.MULTILINE)
        llm_m  = re.search(r"^-\s+LLM:\s+(.+)$",  sec, re.MULTILINE)
        human_m= re.search(r"^-\s+Human:\s+(.+)$", sec, re.MULTILINE)

        math   = math_m.group(1).strip()  if math_m  else ""
        llm    = llm_m.group(1).strip()   if llm_m   else ""
        human  = human_m.group(1).strip() if human_m else ""

        # Assign to cluster based on row number (rough mapping)
        row_int = int(row_no)
        if   row_int <= 50:  cluster_no, cluster = 1, "Cubie primitive geometry"
        elif row_int <= 80:  cluster_no, cluster = 2, "Base geometric access"
        elif row_int <= 100: cluster_no, cluster = 3, "Recursive Cubie access and noise growth"
        elif row_int <= 115: cluster_no, cluster = 4, "Context, frame, lineage, and unified Golden Path"
        else:                cluster_no, cluster = 5, "Seam strings, corners, and explainable denial"

        rows.append({
            "seq":            f"P-{seq:04d}",
            "source":         "PREDICATE_SCAFFOLD",
            "module":         f"Scaffold-{source_id}",
            "theorem_name":   title,
            "kind":           "Axiom/Definition",
            "cluster_no":     cluster_no,
            "cluster":        cluster,
            "formal_systems": "PENDING",
            "coq_file":       "",
            "lean_file":      "",
            "coq_line":       "",
            "status":         "PREDICATE_SCAFFOLD",
            "verus_status":   "PENDING",
            "notes":          f"Math: {math[:120]}",
        })
        seq += 1

    return rows

COLUMNS = [
    "seq", "source", "module", "theorem_name", "kind",
    "cluster_no", "cluster", "formal_systems",
    "coq_file", "lean_file", "coq_line",
    "status", "verus_status", "notes",
]

def main():
    formal_rows    = build_formal_rows()
    predicate_rows = build_predicate_rows()
    all_rows = formal_rows + predicate_rows

    # Sort by cluster_no then source then seq
    all_rows.sort(key=lambda r: (int(r["cluster_no"]) if str(r["cluster_no"]).isdigit() else 99,
                                  r["source"], r["seq"]))

    out = REPO / "roadmap" / "comprehensive_proof_inventory.csv"
    with open(out, "w", newline="", encoding="utf-8") as f:
        writer = csv.DictWriter(f, fieldnames=COLUMNS)
        writer.writeheader()
        writer.writerows(all_rows)

    # ── Summary by cluster ─────────────────────────────────────────────────
    summary = {}
    for r in all_rows:
        cno = r["cluster_no"]
        summary.setdefault(cno, {
            "cluster_no": cno,
            "cluster": r["cluster"],
            "total": 0,
            "triple_kernel": 0,
            "derived_candidate": 0,
            "predecessor": 0,
            "predicate_scaffold": 0,
            "pure_proofs": 0,
        })
        summary[cno]["total"] += 1
        s = r["status"]
        if s == "TRIPLE_KERNEL_VERIFIED":
            summary[cno]["triple_kernel"] += 1
        elif s == "DERIVED_CANDIDATE":
            summary[cno]["derived_candidate"] += 1
        elif s == "PREDECESSOR":
            summary[cno]["predecessor"] += 1
        elif s == "PREDICATE_SCAFFOLD":
            summary[cno]["predicate_scaffold"] += 1
        if r["kind"] in ("Theorem", "Lemma", "Corollary", "theorem", "lemma"):
            summary[cno]["pure_proofs"] += 1

    summ_out = REPO / "roadmap" / "summary_by_cluster.csv"
    summ_cols = ["cluster_no","cluster","total","triple_kernel","derived_candidate",
                 "predecessor","predicate_scaffold","pure_proofs"]
    with open(summ_out, "w", newline="", encoding="utf-8") as f:
        writer = csv.DictWriter(f, fieldnames=summ_cols)
        writer.writeheader()
        for cno in sorted(summary.keys(), key=lambda x: int(x) if str(x).isdigit() else 99):
            writer.writerow(summary[cno])

    # ── Console report ─────────────────────────────────────────────────────
    formal    = [r for r in all_rows if r["source"] == "FORMAL"]
    scaffold  = [r for r in all_rows if r["source"] == "PREDICATE_SCAFFOLD"]
    tkv       = [r for r in formal  if r["status"] == "TRIPLE_KERNEL_VERIFIED"]
    pure      = [r for r in formal  if r["kind"] in ("Theorem","Lemma","Corollary","theorem","lemma")]

    print(f"WRITTEN: {out}")
    print(f"WRITTEN: {summ_out}")
    print()
    print(f"Formal declarations:           {len(formal):4d}")
    print(f"  Triple-kernel verified:      {len(tkv):4d}")
    print(f"  Pure theorem/lemma/corollary:{len(pure):4d}")
    print(f"Predicate scaffold rows:       {len(scaffold):4d}")
    print(f"Combined total:                {len(all_rows):4d}")
    print()
    print("Summary by cluster:")
    print(f"{'CNo':>4}  {'Cluster':<50} {'TKV':>5} {'DerCand':>7} {'Pred':>5} {'Proofs':>7}")
    print("-" * 85)
    for cno in sorted(summary.keys(), key=lambda x: int(x) if str(x).isdigit() else 99):
        s = summary[cno]
        print(f"  {str(cno):>2}  {s['cluster']:<50} {s['triple_kernel']:>5} {s['derived_candidate']:>7} {s['predicate_scaffold']:>5} {s['pure_proofs']:>7}")

    sys.exit(0)

if __name__ == "__main__":
    main()