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STEP 1 — integer spiral-index packing (EXACT): pack_spiral_index/ unpack_spiral_index with corpus-wide base=2·max|c|+1 and offset-encoded digits, recorded in the codebook JSON header; round-trip verified over all 250 matrices. Fixes the sign bug in integration_sprint.py's integer path (unoffset signed packing collapsed (-1,1) with (1,0) in base 2). STEP 2 — f(n) layout (DECORATIVE): per-entry radius_sq + angle_frac, computed in decimal arithmetic (indices reach ~1e44 >> 2^52); verified against VERIFICATION_LOG V007 f(20121); min angular separation ≈4.64e-6 of a turn reported. STEP 3 — Cartan Δ-floor (--cartan-floor): Δ=17/1792 exact (CartanConnection.lean:70) as Fisher-distance resolution floor on Δ₇; 13 sub-Δ pairs merge 196 fingerprints into 187 Δ-resolution codewords vs 9 gap-rule clusters; emitted alongside, not replacing, the 3×-median rule. Caveat asserted in tests: the |c|/Σ|c| simplex projection is lossy (one corpus pair at Fisher distance 0) — similarity, not identity. STEP 4 — torus-winding saturation fix: TorusWinding gains a_exact/b_exact (plain ℤ, no Q16.16 clamp); torus_to_spiral_index prefers them, making the round trip lossless (regression-tested at n=1e9). BraidEigensolid.lean needs the same widening — noted, Lean untouched. Also corrects charpoly_codebook.py's stale docstring counts (192/180 → 196/182, cross-checked against the exact Faddeev–LeVerrier fingerprints: identical on all 250 matrices). Tests: 43 passed (19 new). 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 | ||