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The interchange graph $G(R,S)$ has the $(0,1)$-matrices with row sums $R$ and column sums $S$ as vertices, adjacent when they differ by a single $2\times 2$ interchange. Brualdi asked whether $G(R,S)$ is always Hamiltonian. It satisfies more: it is maximally Hamiltonian, Hamilton-laceable when bipartite and Hamilton-connected when not.
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The declaration says the computational search and verification programs and the Lean 4 formalization were developed with AI-assisted tools under author direction, and that no AI system is an author. The structural induction carrying the proof is the authors'.
Provider: Anthropic / OpenAI · Prompt public: unknown · Independence: unknown
The paper reports a Lean 4 formalization alongside computational search and verification programs. We have not compiled it. arXiv preprint, not yet peer-reviewed.
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: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.