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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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| .. | ||
| braid_group_action.md | ||
| CAPABILITY_GRID_MAPPING.md | ||
| COLLECTIVE_INTELLIGENCE_OPTIMIZATION.md | ||
| COMPRESSION_HONEST_FINDINGS.md | ||
| FIXEDPOINT_BRIDGE_DESIGN.md | ||
| iteration_dag.md | ||
| iteration_regime.md | ||
| OCTAGON_PRINCIPLE.md | ||
| sidon_preservation_creation.md | ||
| unified_crt_torus_dag.md | ||