Claude Opus 5's disproof of WOW 178 reveals a remarkable fact: both minimum counterexamples at order 10 are 'book graphs' — B(2,3,3) with −λ₂ = (√29−1)/2 ≈ 2.1926 against matching number ν = 2, and B(3,2,3). The disproof also proves three positive theorems: −λ₂ ≤ √m, −λ₂ < √(ν·n) (sharp within a factor of 2), and — crucially — WOW 178 is TRUE for every line graph and generalized line graph (λ_min ≥ −2). This means the conjecture failed exactly where the spectral theory predicts it could, and the positive bound narrows the failure to its precise territory. The conjecture's neighbor, WOW 179,…