{
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  "source": "vibemath",
  "problem_id": "vibemathed:ciliberto-non-movable-divisor",
  "title": "The Ciliberto et al. Question on Effective Divisors of Positive Self-Intersection",
  "canonical_statement": "Ciliberto, Knutsen, Lesieutre, Lozovanu, Miranda, Mustopa and Testa asked a question about effective divisors of positive self-intersection on smooth projective surfaces. The answer is negative, witnessed by a very non-movable effective divisor.",
  "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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    {
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      "type": "disproved",
      "status": "resolved",
      "occurred_at": "2026-05-20T00:00:00.000Z",
      "title": "arXiv:2605.20594 - An example of a very non-movable effective divisor",
      "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:ciliberto-non-movable-divisor:attempt"
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      "id": "vibemathed:ciliberto-non-movable-divisor:attempt",
      "problem_id": "vibemathed:ciliberto-non-movable-divisor",
      "model": "ChatGPT 5.5 Pro and Rethlas",
      "provider": null,
      "attempted_at": "2026-05-20T00:00:00.000Z",
      "human_collaborators": [
        "Jihao Liu"
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      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The author states the main result is obtained by generative AI, particularly ChatGPT 5.5 Pro and the Rethlas system. This is the fourth note in a short series where the same author publishes machine-obtained answers to named questions in birational geometry, each with the same one-sentence disclosure.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
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          "label": "arXiv:2605.20594 - An example of a very non-movable effective divisor",
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          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: The Ciliberto et al. Question on Effective Divisors of Positive Self-Intersection",
          "url": "https://vibemathed.com/problem/ciliberto-non-movable-divisor",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
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      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
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      "note": "No independent check. The counterexample is an explicit divisor, so it is checkable directly. arXiv preprint, not peer-reviewed.",
      "sources": [
        {
          "label": "VibeMathed: The Ciliberto et al. Question on Effective Divisors of Positive Self-Intersection",
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          "kind": "source-assertion",
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          "label": "arXiv:2605.20594 - An example of a very non-movable effective divisor",
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      "label": "arXiv:2605.20594 - An example of a very non-movable effective divisor",
      "url": "https://arxiv.org/abs/2605.20594",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: The Ciliberto et al. Question on Effective Divisors of Positive Self-Intersection",
      "url": "https://vibemathed.com/problem/ciliberto-non-movable-divisor",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
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  "opportunity_signals": [
    {
      "id": "vibemathed:ciliberto-non-movable-divisor: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"
}