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Experimental approach to math functions
Capstone document connecting the session's conceptual framework to all measured findings. One-sentence statement: 'Computation in the space of invariants, rather than in any specific representation.' The matter→light move: nonlinear constraints (matter) → spectral decomposition (light) → invariant extraction (truth). The observerless observer = invariant geometry: computation defined without privileging any representation. Results extracted by choosing invariants that survive ALL representations. The Φ-metric defines the geometry of observability. Three 'endian' regimes = three projections of the same invariant geometry: - Big-endian: global invariants (QR/eigenvalues) - Little-endian: local rules (KV cache/PPM) - Water/block: continuous dynamics (golden spiral/SLOS) Key limitation: symmetry group balance. - Too much symmetry → no computation (cospectral graphs) - Too little symmetry → no compression (text at 3.088 b/B) Conservation law = invariant preservation: total invariant information ≥ K(data) Every session measurement maps to invariant language: - Octagon (4/4) = Φ-metric converts nonlinear → spectral invariant - Conservation (8 branches) = invariant preservation bound - CRT (O(1)) = coprime invariant reconstruction - p-adic = prime invariant decomposition - Cospectral failure = same invariants, different objects - Etesami-Haemers = invariant embedding at O(n²) - GW SNR = signal invariant, noise representation-dependent - Reaction primes = prime factorization = invariant decomposition Pipeline = invariant extraction engine: DNA (matter) → matrix (operator) → spectrum (light) → invariants (truth) |
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| extraction | ||
| formal | ||
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| AGENTS.md | ||
| BREAKGLASS_LOG.md | ||
| CITATION.cff | ||
| ERROR_INVENTORY.md | ||
| lake-manifest.json | ||
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| 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