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"A minimal four-colorable counterexample" reads as "a minimal counterexample that is itself 4-colorable", which contradicts the section's standing hypothesis $\chi(G_0) \geq 5$. The section's content is the structure of the flip neighborhood (and the colored flip classes of its members) under that hypothesis, so name it that. Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>