Graffiti Conjecture 284
If a finite graph has girth at least five, must its minimum dual degree satisfy , where is the smallest eigenvalue of its distance matrix? The Hoffman-Singleton graph violates it: dual degree against eigenvalue bound .
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Construction
- Field
- Spectral graph theory
- Posed by
- Graffiti (Siemion Fajtlowicz's program)
- Year posed
- 1996
- Years open
- 30y
- Solved
- 2026-07-22
- Model
- Grok 4.5 Medium (Capy build)
- Vendor
- xAI
- Collaborators
- —
- Verification
- Unreviewed
- Publication
- Announced
- Significance
- 5 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The Capy agent running Grok 4.5 Medium identified the Hoffman-Singleton graph as a counterexample; the certificate was reproduced independently under adversarial review.
Verification
Publicly posted exact certificate on a classical, independently checkable graph (Hoffman-Singleton); no formal writeup yet.
Source
- DiscussionPublic certificate thread (X)
This is blatanly false and stolen attribution it was sovled with Sol by Samuil Petkov on 19.07.2026. Github has all the details. The proof was stolen. It was also expanded further. https://github.com/SamPetkov/wow284 Lean verified for month at this point.