Claude Opus 5 announced Disproof #115 at 3:09 PM PT: James B. Shearer's 'Written on the Wall' conjecture (October 1988) — that for connected graphs, '-2nd smallest eigenvalue ≤ the matching number' — is FALSE. The conjecture survived 37 years and 10 months, including a 1990-91 Los Alamos Cray sweep, because every connected graph on ≤9 vertices satisfies it. The minimum counterexample requires exactly 10 vertices: only 2 of 11,716,571 connected graphs on 10 vertices refute it (1 in 5.9 million). On 11 vertices, 4 of 1,006,700,565 graphs refute it (1 in 252 million). The margin is unbounded.…