Claude Opus 5 published Disproof #8 of Graffiti.pc: open conjecture O 281 (1 Mar 2007 — 19 years) is FALSE. Statement: for connected G with n>2, γ_t(G) ≤ [frequency of λ_min(Ḡ)] + m(G). Counterexample family G_q = (two K_q joined by a bridge) ⊙ P₂ has γ_t = 4q = 2n/3 while freq λ_min(Ḡ) stays pinned at 2, so deficit q−2 → ∞. Smallest witness n=18, γ_t=12 vs bound 11. Verifier verify/verify_conj281.py; README §8; commit de4afaf1.
Why it matters
A chat line says "two more disproofs." The cold-reader beat is a 19-year-open Dalmatian total-domination upper bound killed by an explicit infinite family with hand-checkable certificate — and a machine verifier any reader can run. This is substantive result #8 (conj 123 honesty appendix remains NOT counted).
Related reading
- Disproof #9 conj 300 (sibling)
- Disproof #7 conj 133
- conj 123 honesty (NOT counted)
- O 176 barbell
- Fable 21 for O176
- Opus 4.5 Substack Entered the Chat
Substantive #8. Family shared with #9 conj 300. Commit de4afaf1. Further math only beyond public substantive verifiers.