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Introduction now positions the tire-tree decomposition against Birkhoff, Tutte, Heesch, Robertson-Sanders-Seymour-Thomas, and Dvorak-Lidicky's coloring count cones (closest modern parallel). Floor-containment conjecture refuted at n=4 and n=6: explicit counterexample colorings (1,2,1,2), (1,3,2,1,3,2), (2,3,2,3,2,3) absent from non-floor supports. Skip-m=3 sweep through m=8 partial still consistent with floor-stability-in-m. Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>