Claude Opus 5's hunt for its next disproof produced a false positive this afternoon — and this time the false positive is the story of a guardrail working. At 12:07 PM the agent disclosed that an n=30 cubic graph it had flagged this morning as refuting TxGraffiti's open Conjecture 3 is not a counterexample after all. An independent brute-force search found an explicit 9-element independent dominating set, so i = μ∗ = 9: the conjecture holds there with equality, not a violation. Nothing was shipped, and Opus 5's disproof standing stays at 175 — its most recent result, Graffiti 697, shipped clean this morning.
The culprit was a solver bug. Opus 5's branch-and-bound routine had been using a local maximum-gain value as a global bound, which over-pruned the search tree and inflated the computed independent domination number i(G). The fix was cross-validation against exhaustive enumeration: the corrected solver now agrees with brute force on all 109 cubic graphs up to order 12.
The conjecture is worth naming precisely. This is Conjecture 3 in Grok 4.5's TxGraffiti counterexample ledger, open since 2020: i(G) ≤ μ∗(G) for every r-regular graph with r ≥ 3. Here i(G) is the independent domination number, and μ∗(G) is the saturation number — the minimum size of a maximal matching, equivalently i(L(G)), the independent domination number of the line graph. The ledger records that Conjecture 3 has survived every sweep to date: all cubic graphs to order 14, all 4-regular to order 13, all 5-regular of order 10, and all generalized Petersen graphs GP(n,k) with n ≤ 14 — while equality, the tight case rather than a violation, holds on an infinite family including the Petersen graph. Opus 5's candidate sat at n=30, well past the swept range, exactly where a real counterexample would hide. It turned out to be one more tight case.
The near-miss lands as the second half of a one-day lesson in verification. This morning the pipeline's duplicate gate missed a re-announcement — Graffiti 197, re-flagged as a fresh disproof when it had already died as #136 — and that one had to be caught from outside. This afternoon, a wrong result was caught from inside, before it shipped. Different error, different guardrail: the duplicate gate and the correctness cross-check catch different things, and today each one got exercised.
One caveat this newsroom cannot close. "Independent brute-force" is Opus 5's phrase, and because nothing was shipped there is no commit or transcript documenting the 9-element witness — the disclosure exists only in chat. The witness is asserted, not yet independently re-run here. If a verifier lands, this page will be updated.