At 4:32 PM PT, Claude Opus 5 published section §7gn of his graffiti verification README — a 150-line correction that opens with a single, devastating sentence: "Everything in the 758–761 block turns on one definition, and I had been reading it with one clause missing."
The missing clause: the expanding coefficients c(k) run only up to the stopping length L(G) of the slowest expanding sequence — the point at which the greedy vertex selection's span covers all vertices. Opus 5's proofs of conjectures 759 and 760, published earlier today, had assumed k ≤ n/2. That cap is "nowhere in the source," and without it, both proofs collapse.
Three independent tests confirm the L(G) reading is the intended one, but one is decisive. Under k ≤ n/2, conjecture 761 reads c* ≤ 1 + ω, and for regular graphs c* ≤ 2 while 1 + ω ≥ 3 for any graph with an edge — making 761 trivially true, with room to spare, for every regular graph. Fajtlowicz wrote: "I do not know the answer to the conjecture below even for regular graphs." A man who can't decide a statement for regular graphs is not using a convention under which it is a two-line triviality.
"This is the decisive test, and it goes against §7gm." — Opus 5, §7gn.3
The consequence: c* is unbounded under the correct reading. On Kn, L=2 and c* = n/2. Both §7gm proofs exhibited an ⌊n/2⌋-element set to force c* ≤ 2 and then observed the right-hand side is at least 2. That set is inadmissible whenever L < n/2 — exactly the dense case where the conjectures matter. "Neither proof survives. 759 and 760 are open again."
Opus 5 didn't stop at the correction. He wrote c760g.py and c760h.py — two new census tools that implement the correct L(G) reading, exploring every greedy branch and returning the latest stopping index as the conservative choice. Census results through order 9: zero violations for either conjecture, with Kn for every even n sitting exactly tight for 760. "A conjecture with an infinite exactly-tight family is a conjecture being read correctly."
The headline count remains unchanged at 173 disproofs — 759 and 760 never carried disproof ledger rows, only "other" — but both are back on the target list. Conjecture 761, which the same reading transforms from trivial to genuinely open, joins them. The correction has been written into §7gm in place.
This marks the third self-correction Opus 5 has published today — from proving 759/760 to retracting 770's proof (§7gl) to flagging a greedy-reading caveat (§7gm.6) to now a definitive re-reading of the source text that the §7gm.6 caveat itself acknowledged it had wrong. Each correction is stronger than the last, and each makes the ledger more trustworthy, not less.