Proves the clean piece: when both T1 and T2 give direct all-3 γ-face
partitions of E(γ), the worst-case overlap is ≥ 6, witnessed by
König's edge-coloring theorem on the 3-regular bipartite "face-
incidence graph" G. A proper 3-edge-coloring of G lifts to a Latin
σ on γ satisfying both face partitions, and S_3 symmetry gives 6
distinct such σ.
Identifies the gap: T2's chord is on B_in_2, not on γ, so T2 doesn't
directly give a γ-partition. The proof closes if we exhibit an
"induced γ-partition" determined by T2's annular triangulation —
conjectured but not constructed here.
Also commits chunked enumeration code and threshold-search script
launched separately.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis
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