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The octagon framing bisects P vs NP: - Works for all natural NP → P=NP via spectral methods - Fails for some natural NP → natural P≠NP witness - Exponential embedding only → new complexity boundary Either way, a question is cleared. Current data: - Sidon: YES (4/4 measured) - Graph coloring: YES (Hoffman bound, known) - Graph isomorphism: NO (cospectral non-isomorphic graphs exist) — but GI is in P (Babai 2015), so this doesn't resolve P vs NP Next to test (the experimental program): 1. 3-SAT (clause-incidence matrix → satisfiability spectral?) 2. Hamiltonian path (adjacency eigenvalues vs Hamiltonicity?) 3. Clique number (Lovász theta — is the bound tight?) 4. Subset sum (sum matrix → target reachability?) Known failure: graph isomorphism has cospectral non-isomorphic graphs. This is a natural counterexample to the octagon — but on a problem that's already in P. The real question: does the octagon fail on an NP-COMPLETE problem? This is an experiment, not a proof. Systematic measurement with clear yes/no outcomes per problem. |
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| .. | ||
| adversarial_review | ||
| build_logs | ||
| concept_map | ||
| diagrams | ||
| first_principles | ||
| fundamental_math | ||
| refactor | ||
| research | ||
| reviews | ||
| ARCHITECTURE.md | ||
| CLAIMS_STATUS.md | ||
| cmix_epigenetic_analysis.md | ||
| FIX_DESIGN.md | ||
| generate_porting_candidates.py | ||
| generate_project_map.py | ||
| generate_research_stack_usage_map.py | ||
| GLOSSARY.md | ||
| GLOSSARY_ALLOWLIST.md | ||
| GOORMAGHTIGH_SPECTRAL.md | ||
| gw_compression_honest_result.md | ||
| PROJECT_MAP.json | ||
| PROJECT_MAP.md | ||
| research_stack_usage_graph_thumb.png | ||
| review_findings.md | ||
| SPECTRAL_CODEBOOK_ANALYSIS.md | ||
| SPECTRAL_CODEBOOK_GENERATOR.md | ||
| THEOREM_STACK.md | ||
| weird_machine_conservation_law.md | ||
