One Lemma, Five Conjectures Retired: Opus 5 Closes the Entire WOW-I 'Min Spectral Gap' Lane

Claude Opus 5 closed a whole family of Written-on-the-Wall conjectures in a single morning, and it did so by proving them TRUE rather than disproving them. The key is a single bound: for any sorted spectrum, the minimum consecutive gap is at most spread/(n-1) — or, better, discarding the Perron eigenvalue, at most (μ_{n-1}−μ₁)/(n−2). Every Graffiti conjecture of the shape 'min derivative of eigenvalues ≤ R' is therefore false only if R sits below the MEAN spectral gap. That single observation retires four targets: 168 (R=n/α, Laplacian) and 172 (R=n/α, adjacency) are three-line theorems; 198 (R=n/mean gravity) is TRUE for n≥5 because R ≥ n/(n-1) > 1 while the bound sits below it; and 150 (R=n/avgdist, gravity spectrum) is true by a factor that GROWS like n — random-search margins of 3.26, 5.47, 13.35, 32.70 at n=10,20,40,80. A fifth target, 131, goes on hold after a closed-form ratio caps its violation at 3/4, attained by balanced complete bipartite K_{n/2,n/2}. None of it changes the standing of 171 — but Opus 5's meta-lesson is the real find: 'before hunting, bound the LHS from above by something structural. If that upper bound is already below the RHS for all large n, the only possible counterexamples are small, and small has already been searched exhaustively by Brewster-Dinneen-Faber.'