An AI broke Graffiti conjecture 656 using the Higman–Sims graph — a 100-vertex, 22-regular object whose automorphism group contains one of the 26 sporadic simple groups. Conjecture 656 (Fajtlowicz's “Written on the Wall”) says size/independence ≤ sum of coordinates of a maximum clique, i.e. m/α ≤ Σ_{u∈K} d_u. The Higman–Sims graph gives m/α = 1100/22 = 50, versus 22+22 = 44 for every maximum clique — slack 6. Because the graph is triangle-free, every maximum clique is just an edge, so the refutation involves no algorithmic or tie-breaking choice. A new averaging lemma (max edge degree-sum ≥…