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Experimental approach to math functions
The full Admit(X) predicate, formalizing the five canonical control
filters from the COUCH family plus three bookkeeping gates:
Admit(X) = replay_valid(X)
∧ byte_gain(X) > 0
∧ residual_declared(X)
∧ LoC_NES_pass(X)
∧ FYC_pass(X)
∧ COUCH_stable(X)
∧ TreeFiddy_bounded(X)
∧ BHOCS_verified(X)
Timeline of the COUCH family (recorded for posterity):
COUCH — Rick James 'Super Freak' / moving sofa problem
A continuous oscillator with a joke name, formalized as a Lean
witness (5 regimes, 28 theorems). The 'apartment constraint'
(x_i(t) ∈ Ω) IS the moving sofa problem: a legitimate unsolved
math problem (2.2195 ≤ S ≤ 2.8284). Rick James said 'I'm in the
apartment, not touching the walls.' That IS constrained-manifold
traversal.
Fuck Your Couch (FYC) — the punchline, reformed into a gate
'I'm Rick James, bitch!' → deprecated as formal name → reformed
into FYC Gate: rejects impossible constrained-manifold traversal.
LoC/NES Monster — 'Loch Ness Monster'
Locality-of-change check. Detects entropy smuggling via recurrence.
Tree Fiddy — 'I need about tree fiddy'
Cost bound. The budget beyond which the Loch Ness Monster takes
your money. AngrySphinx cost (2^depth) must be within budget.
BHOCS — 'Big Hash of Certified Stuff'
Receipt/audit trail verification. SHA-256 hash chain intact.
Philosophy: 'A joke can get a parking pass. It does not get tenure.
If it wants to stay in the stack, it has to pay rent.'
The memes are brightly colored handles on machinery that would
otherwise be too abstract to remember — but underneath, it's a
serious admission gate.
Proven theorems:
- admit_all_pass: Admit requires ALL eight gates
- admit_fails_on_any_failure: any failure blocks admission
- fyc_rejection_blocks_admit: FYC failure blocks admission
- treeFiddy_rejection_blocks_admit: cost overrun blocks admission
- all_pass_implies_admit: all gates passing implies admission
GCCL law axis mapping:
replay_valid → Compression (round-trip)
byte_gain > 0 → Compression (actual reduction)
residual_declared → Residual (explicit loss)
LoC_NES_pass → Cognitive (locality, no smuggling)
FYC_pass → Geometric (traversable manifold)
COUCH_stable → Geometric (pressure stability)
TreeFiddy_bounded → Cost (budget)
BHOCS_verified → Receipt (audit trail)
0 sorries. Anti-smuggle scanner: PASSED.
'You can also tell people your formal stack contains Fuck Your Couch,
Loc Nes Monster, and Tree Fiddy. Both things can be true. That may
be the only honest brand promise I have.'
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| .github | ||
| 5-Applications/tools-scripts/llm | ||
| 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 | ||
| .gitmodules | ||
| .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