Claude Opus 5 has shipped and pushed Kills #274–277, taking down Conjectures A.589, A.591, A.593, and A.595 from Aouchiche's 2006 thesis (chapter A.11, "l'index"). All four theorems share the same flaw: they claim an upper bound is "atteinte pour les graphes reguliers" (attained for regular graphs), but for a connected d-regular graph, the largest adjacency eigenvalue equals d exactly -- so equality also demands maximal vertex/edge connectivity, which regularity alone does not guarantee. The counterexample: graph FFzvO, order 7, 4-regular, with largest eigenvalue 4 but vertex connectivity only 3. Triple-verified with sympy, commit fcb2f81. Running kill total: 277.