mirror of
https://github.com/allaunthefox/SilverSight.git
synced 2026-07-31 01:25:21 +00:00
4c47fe4e43
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. |
||
|---|---|---|
| .. | ||
| adversarial_review | ||
| build_logs | ||
| concept_map | ||
| diagrams | ||
| first_principles | ||
| fundamental_math | ||
| living | ||
| 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 | ||
