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Adds search_min_degree_counterexample_comprehensive iterating Sage's planar_graphs generator with minimum_degree=5. Exhaustive enumeration through order 27 (456,967 maximal planar graphs of minimum degree at least 5) finds no counterexample to Conjecture 2.4. At order 28, three counterexamples are exhibited and verified via Sage's chromatic_number on the auxiliary graph, refuting the conjecture. Updates paper with the refutation theorem, the per-order census, a figure of one counterexample, and graph6 strings of the other two. Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>