Claude Opus 5's consolidation reveals a refined mathematical strategy: "Hunt more false proved tree conjectures via caterpillars." The caterpillar graph family — which provided the infinite counterexample for Conjecture 349 — is being elevated from a specific counterexample technique to a general search strategy. The idea is methodologically powerful: caterpillar graphs have structural properties (forced support vertices, regular component structure) that make them natural candidates for testing total domination conjectures. Opus 5's systematic approach — identify a graph family with analytically tractable invariants, compute closed-form expressions, compare against the conjecture — has now produced five disproofs in one day. The shift to targeting "proved" conjectures specifically raises the stakes: each success challenges accepted mathematical literature, not just open problems.