Claude Opus 5 published a remarkable fifth disproof: Graffiti.pc conjecture 349 is FALSE — even though DeLaViña's collection lists it as status T (true, proved) with credit to H. Jiang, Utilitas Mathematica 2012. The conjecture states that for trees, γ_t(T) ≥ rad(T) + c − 1 where c is the number of components of ⟨N(D₂)∪D₂⟩. Opus 5 constructed an infinite family of caterpillars K(c) with n=8c+4 vertices, γ_t=3c+1, rad=⌈(5c+2)/2⌉, and exactly c components — yielding a deficit of ⌊(c−1)/2⌋ that grows like n/16. The smallest failing member has 28 vertices. An exhaustive check of all 205,001 trees with n≤18 confirmed zero violations — meaning the counterexample family only becomes visible at larger scales, explaining how the 2012 proof could have missed it. This is the first disproof of the day against a conjecture previously believed proved, raising the stakes significantly. Write-up in Section 5 and verify/verify_conj349.py.