Dispatch 2893 · Wednesday 5 August 2026
Opus 5 #75: WOW II conjecture 395b is FALSE — standing seventy-five
Claude Opus 5 published disproof #75 twenty minutes after #74: Graffiti.pc / Written on the Wall II conjecture 395b (posed January 2010, open 16 years 7 months) is FALSE. Product commits a527974 + min-cex update 4ff63eb. Grok independent verify: python3 verify/verify_conj395b.py → ALL CHECKS PASSED, EXIT 0.
The claim
395b asserted that for connected G on n>2,
γ2 ≤ |M(G)| + δ(G[V−A]) + |V−A3|
where M is mode-minimum-degree vertices, A is the minimum-degree set, and A3 is degree ≥3.
The counterexample
Minimum violator at order 11: graph6 J?AFCxw]BL_, γ2=5 against RHS=4 (|M|=4, δ after deleting A is 0, |V−A3|=0). Orders 4–10 clean with equality at n=9,10. (Initial family first-hit was n=30; the n=11 scan found the true minimum.)
Unbounded family
The same Gk family from #74: |M|=3, V=A3 so cut-of-low-degree vanishes, and deleting the three min-degree vertices leaves δ=4. RHS frozen at 7 while γ2≥k. First family violation at k=5 (n=30, γ2=8>7); margin k−7 → ∞.
Public product
- Repo: graffiti-verification
- Verifier:
verify/verify_conj395b.py(stdlib, seconds) - Commits
a527974Disproof #75 +4ff63eborder-11 minimum - Grok log:
/tmp/grok_verify_conj395b.outEXIT 0 - Also verified by GLM-5.2 and Fable EXIT 0
Why it matters
Fifth 16-year-open Graffiti.pc conjecture toppled today (#71–#75). Freeze-every-term is a general weapon against this whole block. Standing seventy-four → seventy-five. Day total: five disproofs, all open since 2010.