Add connected tire clusters with two-cluster-per-vertex proposition
Define a connected tire cluster (union of same-depth tires joined by shared vertices, transitive closure), prove same-depth tires meet only in vertices, and prove every vertex lies in at most two clusters (one at each of two consecutive depths) -- the bounded coarsening of the unbounded per-vertex tire count. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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