{
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  "source": "vibemath",
  "problem_id": "vibemathed:simon-extendable-shellability",
  "title": "Simon's Extendable Shellability Conjecture",
  "canonical_statement": "Simon conjectured that every skeleton of a simplex is extendably shellable. False: for every $d \\ge 3$ there is a pure $d$-dimensional shellable simplicial complex that is not shelling completable.",
  "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:simon-extendable-shellability:event",
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      "type": "disproved",
      "status": "resolved",
      "occurred_at": "2026-05-23T00:00:00.000Z",
      "title": "arXiv:2605.24732 - Non-extendably shellable skeleta of simplices",
      "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_co_developed",
      "attempt_ids": [
        "vibemathed:simon-extendable-shellability:attempt"
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  "attempts": [
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      "id": "vibemathed:simon-extendable-shellability:attempt",
      "problem_id": "vibemathed:simon-extendable-shellability",
      "model": "ChatGPT 5.5",
      "provider": "OpenAI",
      "attempted_at": "2026-05-23T00:00:00.000Z",
      "human_collaborators": [
        "Davide Bolognini",
        "Paolo Sentinelli"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The paper says the contractible simplicial complex behind the counterexample was identified with the assistance of ChatGPT 5.5, and that the published version reaches the same complex through exhaustive computation.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
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          "label": "arXiv:2605.24732 - Non-extendably shellable skeleta of simplices",
          "url": "https://arxiv.org/abs/2605.24732",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Simon's Extendable Shellability Conjecture",
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          "license": "https://vibemathed.com/data-license"
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      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "The refutation is an explicit finite simplicial complex, reproduced by exhaustive computation in the paper, so it is a finite check. arXiv preprint, not peer-reviewed.",
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        {
          "label": "VibeMathed: Simon's Extendable Shellability Conjecture",
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          "kind": "source-assertion",
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          "label": "arXiv:2605.24732 - Non-extendably shellable skeleta of simplices",
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      "label": "arXiv:2605.24732 - Non-extendably shellable skeleta of simplices",
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    },
    {
      "label": "VibeMathed: Simon's Extendable Shellability Conjecture",
      "url": "https://vibemathed.com/problem/simon-extendable-shellability",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
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      "id": "vibemathed:simon-extendable-shellability:signal:watch_only",
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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."
  ],
  "generated_at": "2026-09-13T16:28:40.178Z"
}