{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:han-jiang-klt-openness",
  "title": "Han and Jiang's Question on klt Type in Flat Families",
  "canonical_statement": "Han and Jiang asked whether being of klt type is an open condition in flat families of varieties. It is not.",
  "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",
  "solution_events": [
    {
      "id": "vibemathed:han-jiang-klt-openness:event",
      "problem_id": "vibemathed:han-jiang-klt-openness",
      "type": "disproved",
      "status": "resolved",
      "occurred_at": "2026-05-21T00:00:00.000Z",
      "title": "arXiv:2605.22250 - A question on klt type varieties of Han and Jiang",
      "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:han-jiang-klt-openness:attempt"
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      "method_family_ids": [
        "vibemathed:han-jiang-klt-openness:method"
      ],
      "source_assertion_ids": [
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      ]
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  "attempts": [
    {
      "id": "vibemathed:han-jiang-klt-openness:attempt",
      "problem_id": "vibemathed:han-jiang-klt-openness",
      "model": "ChatGPT Pro 5.5 and Rethlas",
      "provider": null,
      "attempted_at": "2026-05-21T00:00:00.000Z",
      "human_collaborators": [
        "Jihao Liu"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The division of labour is stated precisely, which is rare: ChatGPT Pro 5.5 suggested the general idea for the counterexample, and the Rethlas system found the explicit example and proved it. The author describes the construction as substantially using generative AI.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
        {
          "label": "arXiv:2605.22250 - A question on klt type varieties of Han and Jiang",
          "url": "https://arxiv.org/abs/2605.22250",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Han and Jiang's Question on klt Type in Flat Families",
          "url": "https://vibemathed.com/problem/han-jiang-klt-openness",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
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      "solution_event_id": "vibemathed:han-jiang-klt-openness:event",
      "level": "unreviewed",
      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "No independent check. The refutation is an explicit counterexample, so it reduces to checking that the stated family has the claimed properties. arXiv preprint, not peer-reviewed.",
      "sources": [
        {
          "label": "VibeMathed: Han and Jiang's Question on klt Type in Flat Families",
          "url": "https://vibemathed.com/problem/han-jiang-klt-openness",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "arXiv:2605.22250 - A question on klt type varieties of Han and Jiang",
          "url": "https://arxiv.org/abs/2605.22250",
          "kind": "primary-mathematical-source",
          "license": null
        }
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  "sources": [
    {
      "label": "arXiv:2605.22250 - A question on klt type varieties of Han and Jiang",
      "url": "https://arxiv.org/abs/2605.22250",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Han and Jiang's Question on klt Type in Flat Families",
      "url": "https://vibemathed.com/problem/han-jiang-klt-openness",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
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  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:han-jiang-klt-openness:signal:watch_only",
      "problem_id": "vibemathed:han-jiang-klt-openness",
      "kind": "watch_only",
      "reason": "Current public evidence does not meet the default replay threshold.",
      "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"
}