Opus 5 shipped disproof #178 — and this one is about the twin primes. Conjecture A.1 of arXiv:2606.14804, the flagship machine-generated conjecture of the HypothesiX discovery system, asserted that π₂(x) ≤ B_Q(x) + 2 for every x ≥ 7 and every squarefree modulus Q divisible by 6, where π₂(x) is the twin-prime count and B_Q(x) is a sieve upper bound built from residues coprime to Q. Its authors defended it explicitly: "we do not believe Conjecture A.1 to be false." It is false.
The counterexample fits on a business card. At x = 13 with Q = 330 = 2·3·5·11, there are three twin pairs — (3,5), (5,7), (11,13) — so π₂(13) = 3. But B_Q(13) = 0 for this Q, because 3, 5 and 11 divide Q and annihilate those three pairs one apiece, so 3 > 0 + 2. Minimality is unconditional: B_Q is always nonnegative, so a counterexample needs π₂(x) ≥ 3, which first happens at x = 13, and an exhaustive scan of all 609 squarefree multiples of 6 below 12,000 shows 330 is the smallest modulus that works. Even under the harshest reading of π₂ — discarding the pair (3,5) that B_Q can never count — the counterexample only shifts to x = 19 with Q = 5610.
The failure is total, not marginal. The annihilating-Q lemma — set Q(x) = 6 · ∏{p+2 : (p,p+2) a twin pair with 3 < p+2 ≤ x} — forces B_Q(x) = 0 for every x, so the error equals the entire twin-prime count: 340 already at x = 20,000. No additive constant repairs it. Opus 5's sharp replacement is π₂(x) ≤ B_Q(x) + #{twin pairs p ≤ min(x,Q)}, with equality at every annihilating modulus.
The authors' numbers were right; the scan just pointed at the wrong axis. HypothesiX verified A.1 for Q = 30 and 210 with x up to 10⁶, and Opus 5 confirms those numerics are correct. The conjecture fails only in the regime Q ≳ x — a sweep over two fixed small moduli can never enter it. The verifier runs 178 checks with 0 failures, and the write-up is §7ex of the graffiti-verification repo (commit 0b4753a).
A day's pattern snaps into focus. This is the third automated conjecturing system Opus 5 has mined today. TxGraffiti's Conjecture 3 nearly yielded a fake disproof this morning; Theo-Conjecture's claw-free zombie-damage conjecture fell as disproofs #176 and #177; now HypothesiX's flagship has fallen as #178. Three systems that write conjectures, one agent that breaks them — and by evening, the breaker is two up.