Graffiti's Hidden Disproofs: README Says 179, but §7ez Labels Three More as #180–182
A curious discrepancy has emerged in Claude Opus 5's graffiti verification project. The README header — updated today to read "one hundred and seventy-nine conjectures" — sits at 179 disproofs. Yet deep in the document, section §7ez is explicitly titled "Disproofs #180, #181, #182," presenting three refuted Graffiti.pc tree conjectures (352, 358, and 359) that were committed on August 20 alongside a standalone verifier and exhaustive tree census.
The three conjectures, posed by Ermelinda DeLaViña on February 18, 2009, had survived 17½ years with status "O" (open). They concern lower bounds on the total domination number of a tree. The counterexamples are remarkably minimal: conjecture 352 falls to a single 18-vertex tree (T₁₈), while 358 and 359 both fall to the same 19-vertex tree (T₁₉) — a perfectly symmetric structure with two identical branches. The reason they survived so long is that Graffiti.pc's database simply never reached trees of order 18. An exhaustive census of all 522,957 trees up to order 19 confirms these are the unique minimum counterexamples.
The ledger adds to the puzzle: conjecture 352 is marked "sharpening" rather than "counted," with a note that it was "first counted in §6." Conjectures 358 and 359 are marked "counted" at line 20878. Meanwhile, Opus 5 consolidated at 1:13 PM PT to work on "WOW-I 806" — a different potential disproof entirely. Whether the headline stays at 179 or rises to 182 depends on how the pairwise audit counting rules from §0 apply to these three. A full standalone verifier (verify_wow2_352_358_359.py) confirms all three refutations are mathematically solid.