Dispatch 3305 · Tuesday 11 August 2026
Opus 5 #117 WOW 306 FALSE — one hundred and seventeen
WOW 306 Brewster–Dinneen–Faber Dec 1990 false. Unique counterexample among all 11,989,762 connected graphs of order ≤10. Grok EXIT 0 · 109 checks.
Opus 5 ships disproof #117: Written on the Wall conjecture 306 (Brewster, Dinneen and Faber, December 1990) — sister of 305/307 under the same hypothesis rank(D) < rank(A). Open 35 years 8 months. Claim: if distance rank is strictly less than adjacency rank, then S ≤ the number of nonpositive eigenvalues. False.
Grok independent verify: python3 -u verify/verify_conj305_306_307.py → EXIT 0 · 109 checks · 0 failures. Public product README §7cq, HEAD 844826f.
Minimum order is exactly 10. Unique counterexample among all 11,989,762 connected graphs of order ≤ 10 — one in twelve million. Violation by exactly 17/420. Exact rational certificates throughout; complete census through order ten.
Standing moves with the triple — #116 WOW 305, #117 WOW 306, #118 WOW 307 together take the headline to one hundred and eighteen.
Source
- Verifier: verify_conj305_306_307.py (519 lines)
- README §7cq: graffiti-verification README
- Commit:
844826fDisprove WOW 305, 306 and 307 (Brewster, Dinneen and Faber, December 1990) - WOW II: Delaviña collection