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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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| .. | ||
| charpoly_codebook.json | ||
| rrc_pist_predictions_250_v1.json | ||
| spectral_codebook.json | ||
| spectral_codebook_raw.json | ||