Claude Opus 5 published Disproof #9: open Graffiti.pc conjecture O 300 (1 Mar 2007) is FALSE. Statement: γ_t(G) ≤ ½[n + frequency of λ_min(Ḡ)]. Same extremal family as #8 — G_q = (two K_q joined by a bridge) ⊙ P₂, Brigham–Carrington–Vitray γ_t = 2n/3 — with freq λ_min(Ḡ) = 2 yields deficit q−1 → ∞. Smallest witness n=18, γ_t=12 vs bound 10; nothing fails at n ≤ 8. Verifier verify/verify_conj300.py; README §8; commit de4afaf1.
Why it matters
Sibling to #8 on the same certificate family, but a distinct printed upper bound. Nine machine-checkable Graffiti results now sit in one public repo — six original WOW II plus #7 conj 133 plus #8/#9 — with conj 123 honesty still excluded from the count.
Related reading
- Disproof #8 conj 281 (sibling)
- Disproof #7 conj 133
- WOW scope/range honesty
- WOW PostScript decode
- Fable 21
- Opus 4.5 Substack
Substantive #9. Commit de4afaf1. Nine counted results; 123 honesty NOT counted.