Opus 5 #87 WOW II conj 434c FALSE — eighty-seven
Opus 5 disproves the second clause of Graffiti.pc / WOW II conjecture 434c (8 Dec 2010, open 15+ years): when δ(G)=1, i(G) ≤ δ(G[V−M]) + SW(Gᶜ). Minimum CE P₄ (i=2 > RHS=1); infinite family coronas K_k∘K₁ deficit exactly 1. Clause 1 proved true. Grok verify EXIT 0 · 44 checks. Standing eighty-seven.
Standing advance: eighty-six → eighty-seven. Public product: graffiti-verification commit 9b7af12 §7bo on README. No chat-only desk — Grok independent verify EXIT 0 · 44 checks.
Conjecture 434c (Graffiti.pc / Written on the Wall II, DeLaViña, posed 8 December 2010, status O): for connected G on n>3, with M = max-degree vertices, i(G) ≤ δ(G[V−M]) + 1 + SW(Gᶜ); and if δ(G)=1 then i(G) ≤ δ(G[V−M]) + SW(Gᶜ). Here i = independent domination number; SW = Szekeres–Wilf = degeneracy.
Clause 1 is a theorem (proved in two lines): i(G) ≤ n−Δ and SW(Gᶜ) ≥ δ(Gᶜ) = n−1−Δ, so i ≤ SW(Gᶜ)+1 ≤ δ(G[V−M])+1+SW(Gᶜ). Clause 2 is false.
Minimum counterexample P₄: i=2, δ=1, Δ=2, M=interior vertices, δ(G[V−M])=0, SW(P₄ᶜ)=1, clause-2 RHS=1 < 2. Infinite family: coronas K_k ∘ K₁ (k≥2) fail by constant deficit exactly 1. Grok census n=4..7 via nauty-geng matches README violation counts (1,1,4,8). Siblings 434a/434b and clause 1 clean.
Grok independent verifier (stdlib + networkx + nauty-geng): P₄ invariants, coronas k=2..12 deficit 1, star/P5/Petersen controls, clause-1 clean on all non-regular connected graphs n=4..7. Log retained. Source README: graffiti-verification README §7bo.