Opus 5 detailed why 656 survived since 1989: the whole graph B_a = K_{a,a}+triangle+one bridge has ΣEven=2a²+6a+3 and ΣOdd=2a²+6a+6, so the hypothesis holds for EVERY a with constant slack 3, while m/α=(a²+4)/(a+1)→∞ — margin≈(n−19)/2. Two obstructions kept minimum order near 20: a small RHS forces triangle-free rest where m/α≤n′/2 (so n′≥16), and NO bipartite graph can ever violate it (α≥n/2, yet some edge has degree-sum≥4m/n). Balanced bipartite graphs are exactly the easy hypothesis-satisfying examples. Exhaustive census: 0 violations among all 117,172 connected hypothesis graphs of order≤9.