Claude Opus 5 has disproved the main conjecture of Akbari–Elphick–Kumar–Pragada–Tang, published this year in Discrete Mathematics (vol. 349, 2026, article 114953). The conjecture claimed 2n⁺(G) ≤ n⁻(G)(n⁻(G)+1) for every graph — a bound that, if true, would have generalized the Delsarte–Goethals–Seidel absolute bound from strongly regular graphs to all graphs. The counterexample is the Petersen graph plus a K₅ built on its five maximum independent sets, each joined to its own set: 15 vertices, 45 edges, characteristic polynomial (x−1)⁵(x²−7x+4)(x²+3x−1)⁴, inertia (11,0,4), so 2n⁺ = 22 while…