Step 1 of birkhoff_heesch_reducibility action items. Brute-force
enumerates N(T'_{f'}; σ) for G_n = C_n + n pendants at 3 colors,
n=3..12. Two empirical findings: (1) fiber sizes are always 1 or 2
(constant σ on even n gives size 2; everything else gives size 1);
(2) projecting C onto k evenly-spread positions covers {1,2,3}^k iff
n ≥ 2k. The second implies that for a tire with |B_out| ≥ |B_in|,
every ring coloring on the inner boundary is realisable — so the
chain-pigeonhole intersection step is trivially nonempty whenever the
shared cycle is not locally the longest. Includes script, raw JSON,
text dump, and 4-page data note.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis
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