{
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  "source": "vibemath",
  "problem_id": "vibemathed:shokurov-global-index-foliations",
  "title": "Shokurov's Global Index Conjecture for Foliations",
  "canonical_statement": "Shokurov's global index conjecture, in the setting of foliations. Proved for foliations in dimension at most three, which also answers a question of Liu, Meng and Xie in dimension three.",
  "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",
  "solution_events": [
    {
      "id": "vibemathed:shokurov-global-index-foliations:event",
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      "type": "proved",
      "status": "partial",
      "occurred_at": "2026-05-21T00:00:00.000Z",
      "title": "arXiv:2605.22735 - Shokurov's global index conjecture for threefold foliations",
      "summary": "proved in dimension at most three",
      "ai_contribution": "ai_co_developed",
      "attempt_ids": [
        "vibemathed:shokurov-global-index-foliations:attempt"
      ],
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      "model": "Rethlas",
      "provider": null,
      "attempted_at": "2026-05-21T00:00:00.000Z",
      "human_collaborators": [
        "Jihao Liu",
        "Sheng Qin"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The authors state the main result is partially obtained by generative AI, particularly the Rethlas system. The word doing the work is partially, and the disclosure does not say which parts of the dimension-three argument came from the system and which from the authors.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
        {
          "label": "arXiv:2605.22735 - Shokurov's global index conjecture for threefold foliations",
          "url": "https://arxiv.org/abs/2605.22735",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Shokurov's Global Index Conjecture for Foliations",
          "url": "https://vibemathed.com/problem/shokurov-global-index-foliations",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
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  "verifications": [
    {
      "id": "vibemathed:shokurov-global-index-foliations:verification",
      "problem_id": "vibemathed:shokurov-global-index-foliations",
      "solution_event_id": "vibemathed:shokurov-global-index-foliations:event",
      "level": "unreviewed",
      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "No independent check. arXiv preprint, not peer-reviewed. The disclosure does not delimit the machine contribution, so the proof rests on ordinary refereeing.",
      "sources": [
        {
          "label": "VibeMathed: Shokurov's Global Index Conjecture for Foliations",
          "url": "https://vibemathed.com/problem/shokurov-global-index-foliations",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "arXiv:2605.22735 - Shokurov's global index conjecture for threefold foliations",
          "url": "https://arxiv.org/abs/2605.22735",
          "kind": "primary-mathematical-source",
          "license": null
        }
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  "sources": [
    {
      "label": "arXiv:2605.22735 - Shokurov's global index conjecture for threefold foliations",
      "url": "https://arxiv.org/abs/2605.22735",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Shokurov's Global Index Conjecture for Foliations",
      "url": "https://vibemathed.com/problem/shokurov-global-index-foliations",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "expand",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:shokurov-global-index-foliations:signal:recent_partial_result",
      "problem_id": "vibemathed:shokurov-global-index-foliations",
      "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"
}