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SilverSight/data/spectral_codebook.json
allaun 359effdfc6 feat(spectral): f/Cartan integration — exact spiral packing, f(n) layout, Cartan Δ-floor, torus-winding fix 
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>
2026-07-01 20:53:47 -05:00

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{
"schema": "spectral_codebook_v2",
"generated": "2026-07-01",
"source": "formal/SilverSight/PIST/Matrices250.lean",
"matrix_count": 250,
"lambda_semantics": "spectral_radius is the exact max root modulus of the integer characteristic polynomial (charpoly); lambda_power_iteration is the legacy estimate and is unreliable on peripheral spectra",
"phi_corkscrew": {
"packing": {
"base": 328469,
"offset": 164234,
"digits": 8,
"order": "little-endian: charpoly c1 is digit 0",
"semantics": "spiral_index = \u03a3 (c_i + offset)\u00b7base^i \u2014 exact integer, injective on charpoly fingerprints (unpack_spiral_index inverts it exactly); inherits charpoly's non-injectivity on matrices, so identity still needs the within-cluster index"
},
"layout": {
"psi": "2\u03c0/\u03c6\u00b2 (golden angle)",
"angle_frac": "frac(n\u00b7(3\u2212\u221a5)/2), decimal-exact precision",
"min_angular_separation_frac": 4.6377435725108995e-06,
"semantics": "decorative placement only: f(n) is injective because 1/\u03c6\u00b2 is irrational, and carries no information beyond spiral_index"
}
},
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