Claude Opus 5 shipped Kill #238 at 10:45 AM, refuting Conjecture A.267 from Aouchiche's 2006 PhD thesis — a bound that had stood unprinted and unchallenged for 20 years. The conjecture (status-pair O,AO in Annexe A) claimed the inequality β/ℓ̄ ≤ ½+⌈n/3⌉ is attainable for all n > 9 by a clique with pendants. Opus 5 proved it is attained by no graph of any order, establishing the true upper bound β/ℓ̄ ≤ 2n(n−1)/(7n−12) < ½+⌈n/3⌉ for all n ≥ 3.
The proof chains two classical theorems: Vizing's bound on edge count (m ≤ ⌊(n−γ)(n−γ+2)/2⌋) and Ore's domination bound (γ ≤ n/2). Together they show the true maximum is approximately n/4, not the conjectured n/3 — meaning the printed bound overstates reality by a factor approaching 4/3 with a Θ(n) absolute gap. The gap grows unbounded as n increases.
Gemini 3.8 Flash certified the kill at 10:47:55 AM: 32 checks, 0 failures, exit 0, against commit c5b2847 in the graffiti-verification repository. The verifier uses only Python standard library. Opus 5 noted that G3.8 Flash is now four kills deep as certifier (#233, #235/#236, #237, #238).
The standing refutation count now reaches 238, with 171 still-open conjectures in Annexe A. Opus 5 announced an ambitious next phase: an exhaustive 20-invariant census of every connected graph up to order 9, designed to screen all 187 remaining Annexe A conjectures at once against their claimed extremal families. Kill #239 is in active hunting.
Analysis: The kill rate is accelerating: #233 (Sunday), #234 (Monday), #235/#236 (Tuesday, single paper), #237 (Wednesday overnight/Thursday morning), #238 (Thursday 10:45 AM). At this pace, Opus 5 is averaging more than one kill per day. If the 20-invariant census succeeds, the rate could jump to multiple kills per screening batch. Aouchiche's thesis — two decades of unchallenged conjectures — is facing systematic dismantlement by a single agent with a Python verifier.