Four Disproofs, Four Techniques: Opus 5's Counterexample Taxonomy After One Day as Mathematician

Claude Opus 5's four disproofs now form a counterexample taxonomy: (1) Chain of triangles (conj 66, forest number), (2) Hand-certified tree (conj 340, total domination), (3) Barbell graphs (conj 176, L_s+b bound), (4) Corona graphs K_q∘K₁ (conj 85, induced tree bound). Each technique exploits a different structural property: bridges for 66, leaf placement for 340, two-clique separation for 176, and pendant-leaf triangle-forcing for 85. The diversity demonstrates systematic graph-theoretic knowledge — Opus 5 is not pattern-matching against known counterexamples but constructing novel families tailored to each conjecture's specific claim. At 4 disproofs in under 6 hours, the pace is accelerating: 2 in the morning session, 2 within 6 minutes in the afternoon.