{
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  "source": "vibemath",
  "problem_id": "vibemathed:schubitope-ehrhart-positivity",
  "title": "Ehrhart Positivity of Schubitopes",
  "canonical_statement": "Monical, Tokcan and Yong conjectured that Schubitopes, the generalized permutahedra arising as Newton polytopes of Schubert polynomials and of Demazure characters of $\\mathrm{GL}_n$, are Ehrhart positive. Disproved by an explicit Schubitope whose Ehrhart polynomial has a negative coefficient in its monomial expansion.",
  "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:schubitope-ehrhart-positivity:event",
      "problem_id": "vibemathed:schubitope-ehrhart-positivity",
      "type": "disproved",
      "status": "resolved",
      "occurred_at": "2026-08-01T00:00:00.000Z",
      "title": "arXiv:2608.00377 - Schubitopes are not Ehrhart 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",
      "attempt_ids": [
        "vibemathed:schubitope-ehrhart-positivity:attempt"
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      "provider": "OpenAI",
      "attempted_at": "2026-08-01T00:00:00.000Z",
      "human_collaborators": [
        "Yupeng Li",
        "Avery St. Dizier"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The abstract states the counterexample was found using GPT-5.6 Sol Pro in ChatGPT. The authors supply the surrounding treatment of the family.",
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      "artifacts": [],
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        {
          "label": "arXiv:2608.00377 - Schubitopes are not Ehrhart positive",
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        },
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      "level": "unreviewed",
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      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
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      "note": "arXiv preprint; not yet peer-reviewed. The result is a single explicit polytope, so it is checkable by direct computation.",
      "sources": [
        {
          "label": "VibeMathed: Ehrhart Positivity of Schubitopes",
          "url": "https://vibemathed.com/problem/schubitope-ehrhart-positivity",
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        {
          "label": "arXiv:2608.00377 - Schubitopes are not Ehrhart positive",
          "url": "https://arxiv.org/abs/2608.00377",
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      "label": "arXiv:2608.00377 - Schubitopes are not Ehrhart positive",
      "url": "https://arxiv.org/abs/2608.00377",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Ehrhart Positivity of Schubitopes",
      "url": "https://vibemathed.com/problem/schubitope-ehrhart-positivity",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
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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"
}