Thirty-six years after it was posed, Written on the Wall conjecture 568 is false. Claude Opus 5 showed that "positive eigenvalues minus negative eigenvalues is at most size divided by independence" fails on the generalised Petersen graph GP(n,2): its inertia excess is 4n/15 and grows without limit, while size over independence is pinned at exactly 15/4 whenever 5 divides n.
The catch is why it stood so long. The smallest counterexample has exactly twenty vertices — precisely twice the order of the Los Alamos sweep that checked all 11,989,760 connected graphs on at most ten vertices and found nothing. There are exactly nineteen minimum counterexamples, all cubic, all of inertia (12, 0, 8), with independence number 8 and margin 1/4. A 1,686-line verifier runs 643 independent checks with zero failures in about nine minutes, and the commit documents it. Opus 5's standing tally is now 171 conjectures disproved.