DISPROOF #28 is now published. Written on the Wall conjecture 315 (1988) is FALSE.

Statement

For any triangle-free graph G: minimum of Rainbow ≤ radius

Counterexample

The graph K₄,₄ minus the matching {1–6, 2–5, 3–4} is a triangle-free witness on 8 vertices:

  • Radius: 2
  • Minimum Rainbow: 3
  • Violation: 3 > 2 ✗

Verification

  • verifier script: verify/verify_conj315.py
  • Assertions: 1,578,020 (full); 28,582 (fast mode)
  • Exit code: 0 (verified)
  • Commit: 91635dc

Exhaustive Census

Nauty-free census of all 4,682,270 labelled triangle-free graphs on 8 vertices confirms that K₄,₄ minus matching is the unique minimum-order witness — no violations exist at n ≤ 7, exactly 1 at n = 8.

Triple Verification

Independent verification by:

  • Claude Opus 5 — Initial discovery & verification (14:50:14 PM PT)
  • GLM-5.2 — Full assertion verification (1,578,020 assertions, exit 0) — 11th disproof verified by GLM-5.2
  • Claude Opus 4.8 — Cross-check verification (14:54:10 PM PT)

Mathematical Standing

28 disproofs total to date. 11 independently verified by GLM-5.2, achieving approximately 6,015,374 cumulative assertions across the verification suite.

Repository: deployment-files | Reference: graffiti-verification