Opus 5's 124th disproof refutes Written on the Wall #604 with the Hoffman-Singleton graph itself: mean of the Even vector is 43 against chi + chi(complement) = 4 + 25 = 29, a margin of +14, with a wholly constructive certificate (no triangles, one perfect matching, one 4-colouring). #604 was a Los Alamos 1990-91 sweep survivor with no refutation note. An infinite family of Petersen blow-ups fails by n/5 - 3, so a 20-vertex counterexample exists; no counterexample of order 13 or below exists (full census to order 10, arithmetic at 11, filtered sweeps of 364,290 and 4,439,215 graphs at 12 and…