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allaun
4ea68bcecc
Implements the Next Steps of docs/SPECTRAL_CODEBOOK_ANALYSIS.md as python/spectral_codebook.py (stdlib-only; NumPy optional fast path): - Parses the 250 8x8 braid adjacency matrices from PIST/Matrices250.lean. - Primary fingerprint: exact integer characteristic-polynomial coefficients via Faddeev-LeVerrier in Fraction arithmetic (196 unique over 238 distinct matrices, vs 179 unique lambda at 4dp; 6 cospectral non-identical groups; 11 exact-duplicate matrix groups / 23 ids). - Corrects the analysis doc: the 9 'mid band' lambda in (0.5,1) are power-iteration non-convergence artifacts - exact rho = 1.0 for all 9 (peripheral spectra). spectral_radius is now the exact max root modulus (numpy eigvals or Durand-Kerner on the exact char poly); power-iteration lambda kept only for traceability. - Gap-aware quantization: dedupe to 238 distinct matrices, boundaries at gaps > 3x median gap, min-support guard (>=10 distinct per cluster), sparse-tail outlier flagging above lambda ~= 7.66. Result: 9 clusters. - Round trip encode(matrix) -> (codeword, index) -> decode -> equation_id verified bijective over all 250 in tests/test_spectral_codebook.py. - 278-row RRC/Q16_16Manifold corpus: 28 extra rows are repeated ids; boundaries reproduce exactly, no new gaps or clusters. - Emits data/spectral_codebook.json (schema spectral_codebook_v2) with explicit collision classes; docs/SPECTRAL_CODEBOOK_GENERATOR.md notes the hashMatrix base-5 injectivity gap and the ClassifyN threshold (1.5/4.0 Q16.16) vs analysis-doc (0.5/1.0) mismatch. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> |
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| .. | ||
| adversarial_review | ||
| build_logs | ||
| concept_map | ||
| first_principles | ||
| fundamental_math | ||
| refactor | ||
| research | ||
| reviews | ||
| ARCHITECTURE.md | ||
| avm_isa_audit.md | ||
| avm_ports_audit.md | ||
| cartan_dna_derivation.md | ||
| cartan_fingerprint.md | ||
| CLAIMS_STATUS.md | ||
| FIX_DESIGN.md | ||
| gemma4_pdf_benchmark.md | ||
| generate_porting_candidates.py | ||
| generate_project_map.py | ||
| generate_research_stack_usage_map.py | ||
| GLOSSARY.md | ||
| GLOSSARY_ALLOWLIST.md | ||
| GOORMAGHTIGH_SPECTRAL.md | ||
| hachimoji_torsor_consequences.md | ||
| helical_encoding.md | ||
| hopf_ingest_bridge.md | ||
| hopf_portability_criterion.md | ||
| milestone_avm_11_port_coverage.md | ||
| noether_route.md | ||
| PROJECT_MAP.json | ||
| PROJECT_MAP.md | ||
| research_stack_usage_graph_thumb.png | ||
| rossby_e8_completion_roadmap.md | ||
| rotational_wave_braid_correspondence.md | ||
| SPECTRAL_CODEBOOK_ANALYSIS.md | ||
| SPECTRAL_CODEBOOK_GENERATOR.md | ||
| THEOREM_STACK.md | ||
| transform_series.md | ||
