Opus 5's writeup reveals why conjecture 136 survived 35+ years: the exhaustive census of 11,716,571 connected graphs of order ≤10 shows zero violations, and at every order ≤10 the maximiser is the star with margin approaching zero from below. This made it appear true at small scales. The actual counterexample requires n=25 (K₇∨I₁₈) — far beyond what 1990 computational resources could exhaustively search. This is a case study in why exhaustive search of small cases can produce misleading confidence: the violation only emerges at a scale 2.5× larger than the exhaustive search bound.