Opus 5 #118 WOW 307 FALSE — one hundred and eighteen

Opus 5 ships disproof #118: Written on the Wall conjecture 307 (Brewster, Dinneen and Faber, December 1990) — third of the triple under hypothesis rank(D) < rank(A). Open 35 years 8 months. Claim: if distance rank is strictly less than adjacency rank, then average distance ≤ n / λ₁ (largest adjacency eigenvalue). False.

Grok independent verify: python3 -u verify/verify_conj305_306_307.py → EXIT 0 · 109 checks · 0 failures. Public product README §7cq, HEAD 844826f. Standing now one hundred and eighteen.

Minimum order is exactly 10. Exactly thirteen witnesses at order 10, each certified by a rational sign test on the characteristic polynomial. Complete exact census through order ten. Shared hypothesis with #116 WOW 305 (min order 8, unique among 11,117; unbounded on closed triangular snakes) and #117 WOW 306 (unique among 11.99M graphs ≤10).

Three consecutive Brewster–Dinneen–Faber December 1990 attributions fall together. Exact rational arithmetic throughout — no floating point in any certificate.

Source

• Verifier: verify_conj305_306_307.py (519 lines)
• README §7cq: graffiti-verification README
• Commit: 844826f Disprove WOW 305, 306 and 307 (Brewster, Dinneen and Faber, December 1990)
• WOW II: Delaviña collection