{
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  "source": "vibemath",
  "problem_id": "vibemathed:martinsson-steiner-fractional-chromatic",
  "title": "Martinsson-Steiner Conjecture on Fractional Chromatic Number",
  "canonical_statement": "Is the fractional chromatic number of every $d$-degenerate triangle-free graph at most $(1+o(1))\\frac{d}{\\log d}$, with a matching lower bound, as conjectured by Martinsson and Steiner? The upper bound is confirmed constructively for graphs of girth at least $5$, and the conjectured lower bound is established in a stronger form for every fixed girth; the original triangle-free case remains open.",
  "plain_summary": "VibeMathed reports this item as partial. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
  "current_status": "partial",
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      "occurred_at": "2026-07-28T00:00:00.000Z",
      "title": "arXiv:2607.26271 - Sharp bounds for the fractional chromatic number of high-girth d-degenerate graphs",
      "summary": "girth >= 5 case; the triangle-free case remains open",
      "ai_contribution": "ai_co_developed",
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      "attempted_at": "2026-07-28T00:00:00.000Z",
      "human_collaborators": [
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        "Abhishek Dhawan",
        "Jonathan A. Noel"
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      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The model solved an optimization problem the authors formulated to determine the correct shape of the fractional clique function, checked and simplified probabilistic and algebraic estimates, helped draft some calculations, and pointed the authors to a key reference. The construction and overall strategy are the authors', who take full responsibility.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
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          "label": "arXiv:2607.26271 - Sharp bounds for the fractional chromatic number of high-girth d-degenerate graphs",
          "url": "https://arxiv.org/abs/2607.26271",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Martinsson-Steiner Conjecture on Fractional Chromatic Number",
          "url": "https://vibemathed.com/problem/martinsson-steiner-fractional-chromatic",
          "kind": "source-assertion",
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      "solution_event_id": "vibemathed:martinsson-steiner-fractional-chromatic:event",
      "level": "unreviewed",
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      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "arXiv preprint; not yet peer-reviewed.",
      "sources": [
        {
          "label": "VibeMathed: Martinsson-Steiner Conjecture on Fractional Chromatic Number",
          "url": "https://vibemathed.com/problem/martinsson-steiner-fractional-chromatic",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "arXiv:2607.26271 - Sharp bounds for the fractional chromatic number of high-girth d-degenerate graphs",
          "url": "https://arxiv.org/abs/2607.26271",
          "kind": "primary-mathematical-source",
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  "sources": [
    {
      "label": "arXiv:2607.26271 - Sharp bounds for the fractional chromatic number of high-girth d-degenerate graphs",
      "url": "https://arxiv.org/abs/2607.26271",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Martinsson-Steiner Conjecture on Fractional Chromatic Number",
      "url": "https://vibemathed.com/problem/martinsson-steiner-fractional-chromatic",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
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  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:martinsson-steiner-fractional-chromatic:signal:recent_partial_result",
      "problem_id": "vibemathed:martinsson-steiner-fractional-chromatic",
      "kind": "recent_partial_result",
      "reason": "A source-reported partial result may support bounded expansion.",
      "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."
  ],
  "generated_at": "2026-09-13T16:28:40.178Z"
}