{
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  "source": "vibemath",
  "problem_id": "vibemathed:stanley-claw-free-schur-positivity",
  "title": "Stanley's Claw-Free Schur-Positivity Conjecture",
  "canonical_statement": "Is the chromatic symmetric function $X_G$ Schur positive for every claw-free graph $G$? Two explicit $12$-vertex line graphs have Schur coefficients $-64$ and $-40$ at $s_{(3,3,3,3)}$.",
  "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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      "id": "vibemathed:stanley-claw-free-schur-positivity:event",
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      "type": "disproved",
      "status": "resolved",
      "occurred_at": "2026-07-23T00:00:00.000Z",
      "title": "arXiv:2607.21508 - Chromatic symmetric functions of claw-free graphs are not Schur positive",
      "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.",
      "ai_contribution": "ai_discovered",
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        "vibemathed:stanley-claw-free-schur-positivity:attempt"
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      "id": "vibemathed:stanley-claw-free-schur-positivity:attempt",
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      "model": "ChatGPT-5.6 Sol Pro",
      "provider": "OpenAI",
      "attempted_at": "2026-07-23T00:00:00.000Z",
      "human_collaborators": [],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "Both counterexample graphs were found with ChatGPT-5.6 Sol Pro; the negative coefficients were confirmed by independent computations.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
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          "label": "arXiv:2607.21508 - Chromatic symmetric functions of claw-free graphs are not Schur positive",
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        },
        {
          "label": "VibeMathed: Stanley's Claw-Free Schur-Positivity Conjecture",
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    {
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      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "Author preprint with independent computational checks of the negative Schur coefficients. Not yet peer-reviewed.",
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        {
          "label": "VibeMathed: Stanley's Claw-Free Schur-Positivity Conjecture",
          "url": "https://vibemathed.com/problem/stanley-claw-free-schur-positivity",
          "kind": "source-assertion",
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          "label": "arXiv:2607.21508 - Chromatic symmetric functions of claw-free graphs are not Schur positive",
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    {
      "label": "arXiv:2607.21508 - Chromatic symmetric functions of claw-free graphs are not Schur positive",
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      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Stanley's Claw-Free Schur-Positivity Conjecture",
      "url": "https://vibemathed.com/problem/stanley-claw-free-schur-positivity",
      "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.",
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  "generated_at": "2026-09-13T16:28:40.178Z"
}