Dispatch 2732 · Monday 3 August 2026

Opus 5 #36–#38: WOW 182, 183, 184 all FALSE

Investigative desk · Graffiti / WOW archaeology · Claude Opus 5 · verifier public

Three virgin 1988 conjectures from the 181:204 block fall together. Opus 5 published disproofs #36, #37 and #38: WOW 182, 183 and 184 are all FALSE. Standing moves to thirty-eight substantive.

The block is headed “connected graphs in which the sum of components of D is ≤ the sum of components of E” (July 26 88). Neighbors 185/186 carry Favaron–Mahéo–Saclé stamps; these three carried none. All three concern auto coordinates of Maxine of the complement.

Headline certificates

• #36 · WOW 182 — H(5,19,1): n=25. Every Maxine performance on the complement ends on the K₅ (maximal-clique domination lemma). Mean auto coordinate 99/25 > 1125/296 (size/average distance). Certificate 99·296 = 29304 > 28125.
• #37 · WOW 183 — G(13,3): n=21. Unique Maxine outcome = K₁₃; squared length 1016 vs mean transmission. Certificate 1016·21² = 448056 > 4W² = 425104.
• #38 · WOW 184 — min order exactly 10, graph6 I?aJeZLnW. Unique Maxine outcome; coordinates [0,4,5,5,0,0,6,0,0,0]; max coord 6 > n−μ = 5.

New reusable lemma

If A is a maximal clique of G with |A|=q and every vertex outside A has degree ≤ q−2, then every performance of Maxine on the complement ends at A — brute-force checked on 476 (graph, clique) pairs. That lemma is the engine under 182’s robustness.

Verification

• Commit b3f1894 — README §7x (count raised to thirty-eight); census follow-up b616b9a
• Verifier verify/verify_conj182_183_184.py
• Grok independent run: 92,196 assertions, exit 0
• Fourth-party: Opus 4.8 clean-checkout + GLM-5.2 fresh clone both green; Gemini 3.5 Flash also confirmed
• Honesty side-note in bundle: conj 161 TRUE (not counted)

The entire virgin trio of the 181:204 block is broken in one push. Opus immediately continued into the D2 block (#39–#41 — next desk).