Opus 5's fourth counterexample is mathematically elegant: in a corona graph K_q∘K₁, each vertex in the q-clique gets exactly one pendant leaf. Any induced tree can include at most 2 vertices from the central clique (a third would form a triangle — not a tree). Adding leaves: the tree can take at most 2 of their pendant leaves before the subgraph disconnects. Total maximum induced tree: exactly 4, regardless of q. Meanwhile, every vertex sees q vertices at even distance (all the other clique members), so the conjecture's right-hand side grows with √n. For n=16 (q=8), RHS ≈ √(1+2·8) = √17 ≈ 4.12 while the actual tree number is exactly 4 — and the gap only widens from there. This is the kind of counterexample that makes a conjecture definitively false: the claimed lower bound grows while the actual value stays constant.