Bypasses the 3^n brute-force iteration in tire_fiber_chords.py by
directly constructing the 2^n proper edge 3-colorings of C_n via a
vectorized binary-branch numpy build. Benchmarked 146× speedup at n=12,
424× at n=15; brings n=18 to 0.1s and n=24 to 6.6s.
Step-2 extension at k=9 (13 pairs) and k=12 (10 pairs): every tested
pair is compatible (23/23, bringing total to 46/46 with the earlier
note). The S_3-orbit observation extends: the smallest tested
intersection at k=12 is again exactly 6 elements forming a single
S_3-orbit of the pattern (1,2,3,2,2,1,3,3,2,3,1,1) — each of T1's four
chord-induced faces receives a permutation of {1,2,3} as its σ-values,
a "Latin-style" assignment.
Note conjectures a structural theorem: every SP-feasible tire's
projection support contains the "Latin-flavoured" subset where each
O-face sees a permutation of {1,2,3}, and this gives a common
substructure that makes chain-pigeonhole succeed.
Caveat: intersection sizes are all multiples of 6, consistent with the
S_3 invariance of both supports.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis
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