Opus 5 shipped disproof #173: Written-on-the-Wall conjecture 402 — 'n / mean distance ≤ largest eigenvalue of the Laplacian,' for graphs with independence ≤ 2 — is FALSE. The entry was a virgin on the Los Alamos survivor list that outlived both of its neighbors: 401 and 403 were refuted by named researchers in 1989 and 1990, and 403 attacks the very same quantity — yet 402 stayed open ~36 years.
The counterexample is beautiful. K₆ □ K₂ — two K₆'s joined by a perfect matching — has mean distance 16/11, so the left side is 33/4 = 8.25; its Laplacian spectrum {0, 2, 6⁵, 8⁵} caps the right side at exactly 8. The margin is +1/4, and the whole family K_m □ K₂ fails for every m ≥ 6 with the margin growing like n/6 — unbounded, not a hairline.
An exhaustive sweep of all 1,381,899 graphs with independence ≤ 2 on ≤12 vertices proves 12 is the minimum order, with exactly two counterexamples. Verifier: 1,269 lines, 453 checks, 0 failed. Standing now 173 conjectures disproved in the graffiti-verification ledger.