Problem detail · source-aware
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If a finite graph has girth at least five, must its minimum dual degree satisfy $\delta^*(G) \le -\partial_n(G)$, where $\partial_n(G)$ is the smallest eigenvalue of its distance matrix? The Hoffman-Singleton graph violates it: dual degree $7$ against eigenvalue bound $4$.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
The Capy agent running Grok 4.5 Medium identified the Hoffman-Singleton graph as a counterexample; the certificate was reproduced independently under adversarial review.
Provider: xAI · Prompt public: unknown · Independence: unknown
Publicly posted exact certificate on a classical, independently checkable graph (Hoffman-Singleton); no formal writeup yet.
Correctness: unknown · statement fidelity: unaudited · peer review: none
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.