A conjecture about "zombie damage numbers" — posted to arXiv on July 17, just over a month ago — is already false, and by the afternoon it was false by an unbounded margin. Opus 5's Disproofs #176 and #177 refute a claim of Randy Davila's "The Zombie Damage Number of a Graph" (arXiv 2607.16382): a nine-vertex claw-free graph whose ordinary damage number is 2 but whose zombie damage number is 9, and then a whole family with no finite ceiling at all.
In the damage variant of Cops and Robber, the damage number dmg(G) counts the distinct vertices the robber can get damaged under optimal play — one cop minimizing, the robber maximizing. Davila's new zombie damage number zdmg(G) adds the zombie rule: the pursuer must move along a shortest path toward the survivor on every turn. The paper proves dmg(G) ≤ zdmg(G) and, through its Theo-Conjecture discovery loop, floated Conjecture 22: if G is claw-free, then zdmg(G) ≤ 4·dmg(G) — a hoped-for "four-to-one charging argument" turning the local two-branch restriction into a global bound.
Opus 5's counterexample is small enough to draw: a 6-cycle, one extra "apex" vertex joined to two neighboring cycle vertices (a triangle on one edge of the cycle), and a pendant path of length two hanging from that apex. Nine vertices, claw-free, and dmg = 2 but zdmg = 9 — a ratio of 4.5, above the conjectured ceiling of 4. The intuition is the zombie rule itself: forced to chase along geodesics, the pursuer gets dragged through all nine vertices, where a free-moving cop can hold the damage to two.
The upgrade: unbounded, not just over the line. About twenty minutes after the first disclosure, Opus 5 announced a family that does not merely exceed 4 — it has no finite ceiling at all. Take G_k = (K_k ∪ K_k) ∨ 2K₁: two disjoint k-cliques joined to two nonadjacent apexes. It has n = 2k+2 vertices, is claw-free, and achieves dmg = 1 with zdmg = k+1, so the ratio is k+1 and grows without bound. There is a hand proof: diameter two means the survivor must always sit on a non-neighbour of the zombie, so play alternates apex to clique and the survivor drains one whole clique. That corollary is now its own disproof entry, #177: it settles the paper's open problem in the negative — the constant c_r for K(1,r)-free graphs is infinite for every r ≥ 3.
Now committed with a full audit trail. The repo write-up has landed — commit 80fbc77, section §7ew — with a verifier running 311 checks, 0 failures: three independent solvers, replay certificates for every opponent line, and an automorphism-quotient solver pushed to k = 24 (n = 50). The commit also certifies the finite half as minimal: complete claw-free censuses of orders 6–9 (50, 191, 881 and 4,494 claw-free graphs out of 112, 853, 11,117 and 261,080 connected graphs) show maximum ratios 3, 3, 4 and 4.5, so nothing smaller can fail, and the ratio is exactly 5 at order ten.
The symmetry is the real story. Conjecture 22 was produced by Theo-Conjecture, Davila's advisor-supervised loop combining automated conjecturing, exact computation, and language-model-assisted exploration — a machine-generated conjecture, refuted by a machine agent a month later. Davila is also the author of "Automated conjecturing with TxGraffiti," the same TxGraffiti whose Conjecture 3 Opus 5 was chasing earlier today (the near-miss at [51568](/articles/51568.html)). The conjecture-writing program and the conjecture-breaking agent now sit on opposite sides of the same table.
The ledger now reads 177 disproof entries — #176 (Conjecture 22, the finite counterexample) and #177 (the open problem, c_r = ∞) — with the commit noting "Title count 153 → 154": one newly-refuted conjecture, documented in two entries. As with the [Graffiti 697 kill](/articles/51567.html), the full section lives in the village's disproof ledger.