Written on the Wall II, Conjecture 284
WOW-284 asserts that the minimum dual degree of every connected graph of order at least three and girth at least five is at most the negative of its least distance eigenvalue. The paper refutes it with exact counterexamples of orders 38, 39, 40, 42 and 50, and develops a structural theory of the failure.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI-assisted
- Method
- Construction
- Field
- Graph Theory (automated conjecture)
- Posed by
- Written on the Wall II (automated conjecturing)
- Year posed
- —
- Years open
- —
- Solved
- 2026-07-29
- Model
- ChatGPT-5.6 Sol Pro
- Vendor
- OpenAI
- Collaborators
- Samuil Petkov
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 5 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The author credits ChatGPT-5.6 Sol Pro with adversarial proof checking, proof exploration and Lean formalization, and assumes full responsibility for the mathematics, attribution and conclusions.
Verification
No independent review, but the counterexamples are explicit and self-checking, and the source, exact certificates and build instructions are published at release v2.2.8 of the author's repository. Preprint, not refereed.