{
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  "source": "vibemath",
  "problem_id": "vibemathed:boots-royle-cao-vince-conjecture",
  "title": "Boots-Royle/Cao-Vince Conjecture on Planar Spectral Radius",
  "canonical_statement": "Boots and Royle, and independently Cao and Vince, conjectured that the join of an edge with a path on $n-2$ vertices is the unique planar graph of maximum adjacency spectral radius for every $n \\ge 9$. Tait and Tobin proved it for sufficiently large $n$ in 2017; the conjecture now holds for all $n \\ge 9$.",
  "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.",
  "current_status": "resolved",
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      "occurred_at": "2026-07-21T00:00:00.000Z",
      "title": "arXiv:2607.19268 - A complete solution to the Boots-Royle/Cao-Vince conjecture",
      "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": "2026-07-21T00:00:00.000Z",
      "human_collaborators": [
        "Lele Liu",
        "Bo Ning",
        "Yi Wang"
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      "prompt_public": null,
      "outcome": "The declaration credits the model with generating the code that searched for extremal planar graphs, and with assisting in several computations and symbolic derivations, alongside language polishing.",
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      "sources": [
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        {
          "label": "VibeMathed: Boots-Royle/Cao-Vince Conjecture on Planar Spectral Radius",
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      "sources": [
        {
          "label": "VibeMathed: Boots-Royle/Cao-Vince Conjecture on Planar Spectral Radius",
          "url": "https://vibemathed.com/problem/boots-royle-cao-vince-conjecture",
          "kind": "source-assertion",
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      "label": "arXiv:2607.19268 - A complete solution to the Boots-Royle/Cao-Vince conjecture",
      "url": "https://arxiv.org/abs/2607.19268",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Boots-Royle/Cao-Vince Conjecture on Planar Spectral Radius",
      "url": "https://vibemathed.com/problem/boots-royle-cao-vince-conjecture",
      "kind": "source-assertion",
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      "generated_at": "2026-09-13T16:28:40.178Z"
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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"
}