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Experimental approach to math functions
Two unsolved geometric problems as a combined octagon test: 1. Moving Sofa (Moser 1966): max-area shape navigating L-corridor. Unsolved. Best: Gerver 2.2195. Upper: 2.8284. Reformulated as: corridor graph + admissible subsets = coloring. 2. Hadwiger-Nelson (1950): chromatic number of the plane. Unsolved. Known: 5 ≤ χ(ℝ²) ≤ 7. de Grey (2018): 5-chromatic graph. Already has spectral structure: Hoffman bound χ ≥ λ_max + 1. The connection: both are geometric constraint satisfaction. - Sofa: which shapes satisfy the corridor constraint? - HN: which colorings satisfy the unit-distance constraint? - Reformulation: sofa = corridor coloring, HN = plane coloring. Pipeline connection: COUCH gate in GCCL.lean already references this. 'Apartment constraint' = sofa-in-corridor. FYC gate = rejects impossible traversal = rejects shapes that can't make the turn. Experiment: 1. Discretize corridor → graph → adjacency matrix → spectrum 2. Test known sofa shapes (Gerver, Hammersley) for spectral distinguishability 3. Build de Grey's 5-chromatic graph → compute Hoffman bound 4. Is the bound tight (λ_max+1=5)? Or loose? Priority: BETTER than 3-SAT because the sofa is unsolved (spectral shortcut = real result) and HN already has spectral structure (measure how tight). Different problem class (geometric optimization) from previous tests (combinatorial, number-theoretic, structural). Effort: 6-12 hours Python+numpy, no GPU needed. |
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| PORTING_MANIFEST.md | ||
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| README.md | ||
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| SORRY_PROTOCOL.md | ||
| SORRY_RESOLUTION_S1S3.md | ||
| TRACEABILITY_GRAPH.md | ||
| VERIFICATION_LOG.md | ||
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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