allaunthefox
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f44a36e2fa
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docs: correct spectral codebook analysis per independent review
Corrections:
- Mid-band was power-iteration artifact (all 20 peripheral matrices have exact rho=1.0)
- 190 unique lambda → 180 unique rho (exact) + 192 unique char polynomials
- 7.57 bits was a count → 1.257 bits Shannon band entropy
- 7-cluster table fabricated → 3 active bands (null/peripheral/bulk)
- 12 duplicate matrices in 250-row corpus (238 distinct)
Preserved:
- Density-rho correlation 0.9806 (confirmed exact)
- Top spectral gap 4.88 at rho=[11.68, 16.56] (confirmed exact)
- Cartan gap 17/1792 as principled distinguishability floor
- F function orthogonal to Cartan structure
- Characteristic polynomial > spectral radius as codebook key
Known bugs documented:
- Power iteration non-convergence (22 matrices, >1e-3 error)
- Phinary packing not injective (float accumulation)
- Torus winding saturates at n>=65536 (Q16.16 clamp)
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2026-07-01 21:03:50 +00:00 |
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allaunthefox
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7d59ad5739
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docs: spectral codebook analysis of 250-equation corpus
Key findings:
- 190 distinguishable spectral states (7.57 bits/equation)
- Density-Lambda correlation: 0.9807 (near-perfect)
- Largest spectral gap: 4.88 at lambda=[11.68, 16.56]
- 7 natural clusters from gap-aware boundary detection
- Mid band (9 matrices, lambda=[0.67, 0.95]) is compression sweet spot
Raw data: data/spectral_codebook_raw.json (250 entries)
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2026-07-01 20:17:46 +00:00 |
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