{
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  "problem_id": "vibemathed:brualdi-interchange-graph-hamiltonicity",
  "title": "Brualdi's Question on Hamiltonicity of Interchange Graphs",
  "canonical_statement": "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.",
  "plain_summary": "VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
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      "title": "arXiv:2607.13165 - Interchange graphs of (0,1)-matrices are maximally Hamiltonian",
      "summary": "VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
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      "attempted_at": "2026-07-14T00:00:00.000Z",
      "human_collaborators": [
        "Jeffrey S. Baggett",
        "Huiya Yan"
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      "outcome": "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'.",
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      "verifier": "VibeMathed (source-reported label)",
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    {
      "label": "VibeMathed: Brualdi's Question on Hamiltonicity of Interchange Graphs",
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  "uncertainties": [
    "VibeMath has not independently verified the mathematical claim.",
    "AI-attempt independence and training-data exposure are unknown unless explicitly documented.",
    "VibeMath has not independently audited the mathematical statement, proof, or novelty claim."
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  "generated_at": "2026-09-13T16:28:40.178Z"
}