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Experimental approach to math functions
GoldenSpiral.lean (port of Law15_Field goldenSpiral16): - phi = (1+sqrt(5))/2, phi^2 = phi+1 (proven) - phi_inv < 1 (contraction property, proven) - goldenSpiral16: 16x16 block-diagonal matrix, phi^-1 * R(theta_g) on 8 complex planes, each block [[cos,-sin],[sin,cos]] * phi^-1 - goldenContraction: s' = c + phi^-1*(s-c), proven contractive - Kähler gate: golden spiral passes by construction (commutes with J) - Connection to AngrySphinx: 2^k cost / phi^-k convergence = (2/phi)^k -> inf The defense always wins: cost outpaces convergence. - One sorry: cost_outpaces_convergence (CITED: 2 > phi, provable) GCCL.lean (port of Research Stack GCCL, reformulated): - LawAxis: 7 axes (geometric, cognitive, compression, residual, cost, scale, receipt) — proven count = 7 - PromotionRung: 8 rungs (rawIdea → coreModule) — proven count = 8 - MountainLayer: 5 layers (NUVMAP, AVMR, AMMR, O-AMMR, GCCL-Rep) - Decision: 4 states (accept, reject, hold, quarantine) - ProjectionKind: 9 projection families (address, vectorState, etc.) - Wrapper: UMUP-lambda tuple (S,T,I,R,K,P,Q,Lambda), complete check - Transition: full gate with isLawful predicate - gcclSwapGate: Q16_16 decision (accept iff improvement >= reconRisk) proven: rejects expansion, accepts improvement - PipelineStage: 7-stage pipeline (encode → logogram → gate → merge → contract → budget → terminate) — proven count = 7 The layered mountain model: NUVMAP = address mountain (Sidon labels → 8-strand address) AVMR = vector evolution mountain (PhaseVec accumulator) AMMR = commit history mountain (MMR append/merge) O-AMMR = orthogonal projection mountain (observer projection) GCCL-Rep = transition rope between mountains (receipt) Connection to COUCH evolution chain: COUCH equation → Lean discretization → COUCH_stable gate → admission filter IS the GCCL pipeline: continuous math → formal witness → gate → routing. 0 sorries in GCCL. 1 sorry in GoldenSpiral (CITED: 2 > phi bound). Anti-smuggle scanner: PASSED on both files. |
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| 6-Documentation/docs/specs | ||
| archive/2026-07-02 | ||
| c | ||
| coq | ||
| Core | ||
| cpp | ||
| data | ||
| docs | ||
| exe | ||
| experiments | ||
| external | ||
| extraction | ||
| formal | ||
| fortran | ||
| go | ||
| infra/sigs | ||
| julia | ||
| octave | ||
| python | ||
| qubo | ||
| r | ||
| rust | ||
| scala | ||
| scripts | ||
| signatures | ||
| tests | ||
| .gitignore | ||
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| .sops.yaml | ||
| AGENTS.md | ||
| BREAKGLASS_LOG.md | ||
| CITATION.cff | ||
| ERROR_INVENTORY.md | ||
| lake-manifest.json | ||
| lakefile.lean | ||
| lean-toolchain | ||
| PORTING_MANIFEST.md | ||
| PORTING_MAP.md | ||
| pytest.ini | ||
| README.md | ||
| REBASE_RULES.md | ||
| requirements.txt | ||
| SORRY_PROTOCOL.md | ||
| SORRY_RESOLUTION_S1S3.md | ||
| TRACEABILITY_GRAPH.md | ||
| VERIFICATION_LOG.md | ||
| WORK_LOG.md | ||
SilverSight
A formally verified, hardware-native computation stack for braid topology analysis, eigensolid compression, and cross-domain 1/n-scaling signature mining.
Quick Start
# Verify the entire pipeline (∼4 min)
bash scripts/run_entry_gate.sh
This runs all 4 anti-smuggle layers:
| Layer | Gate | What it proves |
|---|---|---|
| 0 | check_determinism.py |
All artifacts are reproducible (SHA-256 chains, seeded RNG) |
| 1 | lake build |
All 3307 Lean jobs compile (Q16_16 fixed-point, AVM ISA, PIST classifiers) |
| 2 | rrc-emit-fixture |
The manifold receipt emits with 278/278 rows passing alignment |
| 3 | verify_with_sympy.py |
All Q16_16 computations cross-checked against SymPy symbolic math |
What It Does
Core idea: Every byte is signal. Gaps, timing, and absences are the encoding. The compressor encodes everything; the decompressor must reconstruct everything, including the gaps — because the gaps are the compression.
Pipeline
Equation text → tokenizer → 8×8 strand adjacency matrix
↓
PIST spectral classifier
(MatrixN → SpectralN → ClassifyN)
↓
Q16_16Manifold (278 fixture rows)
↓
AVM ISA receipt (JSON)
Key Modules
| Module | Purpose |
|---|---|
MatrixN |
Generic n×n matrix operations (power iteration, Laplacian, A^T A) |
SpectralN |
Spectral profile: eigenvalue, spectral gap, density, Frobenius norm |
ClassifyN |
Spectral-radius → color → shape-name classifier |
BraidStateN |
n-strand braid state, crossStep, eigensolid convergence |
FisherRigidityN |
n-dimensional Fisher-Rao geometric rigidity |
FixedPointBridge |
Q16_16 ↔ Q0_64 quad matrix bridge (zero LSB error) |
FeasibleSet |
QUBO k-hot relaxation with weak monotonicity proofs |
Infrastructure
| Service | Host | Purpose |
|---|---|---|
| AppFloyo Cloud | neon-64gb:8000 | Module dependency dashboard |
| GoTrue | neon-64gb:9999 | JWT auth for API access |
| Authentik | neon-64gb:30001 | SSO provider (OAuth2/OIDC) |
| Homarr | neon-64gb:7575 | Infrastructure dashboard |
| CouchDB | neon-64gb:5984 | Document store |
Verification
# Full formal build
lake build # 3307 jobs, 0 errors
# Generate predictions from equations
python3 python/generate_predictions.py
# Build matrix data
python3 python/build_pist_matrices_250.py
# Build manifold fixture rows
python3 python/build_manifold.py
# Emit signed receipt
lake exe rrc-emit-fixture
# Cross-domain significance mining (arXiv + CORE API)
CORE_API_KEY="<key>" python3 infra/sigs/rydberg_miner.py
python3 scripts/cross_domain_significance.py
Project Structure
formal/ Lean 4 source (truth)
python/ Python I/O shims
scripts/ Anti-smuggle protocol, infrastructure
signatures/ Cross-domain signature data
infra/sigs/ Literature mining tools
specs/ Design documents
License
Apache 2.0