For pairs (T1, T2) sharing a cycle γ, intersect T1's D-projection
(inner-spoke pattern from outer tire) with T2's U-projection
(outer-spoke pattern from inner tire) on γ. Compatibility = nonempty
intersection.
Result: 23/23 tested pairs are compatible, spanning k ∈ {3,4,5,6},
both SR/SP models, and a range of chord configurations on each side.
Notable: small intersections have clean S_3-orbit structure. Worst
tested case (k=6, antipodal-chord T1 vs unchorded SR T2) has
intersection of size 6 — exactly the 3! rainbow patterns (a,b,c,b,c,a).
This suggests structural rather than accidental overlap, and points to
a theorem worth proving.
Caveats: 23 cases at k≤6 isn't a proof; longer chains (step 3) require
more than pairwise overlap.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis
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