didericis c5f81842c7 Run Heawood pigeonhole between nested connected tire clusters ...

Add the two-sided cluster decomposition proposition: a vertex's full
Heawood face-sum splits as exactly one child-cluster contribution plus
one parent-cluster contribution (the at-most-two-clusters bound makes the
pairing binary and complete). Explain why this fails per-tire -- a vertex
on many same-depth tires has only a fragment of its face-star in any one
tire -- and recast the chain-pigeonhole and 4CT conjectures to nested
clusters with a cluster restriction relation.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

2026-06-17 01:10:30 -04:00

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