{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:kirby-4-37-irreducible-projective-plane",
  "title": "The Kinoshita Conjecture and Kirby Problem 4.37",
  "canonical_statement": "Kinoshita conjectured that every embedded projective plane in $S^4$ is reducible. False: an irreducible embedded projective plane exists in $S^4$. The construction also answers both parts of Problem 4.37 of the Kirby problem list.",
  "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": [
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      "id": "vibemathed:kirby-4-37-irreducible-projective-plane:event",
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      "type": "disproved",
      "status": "resolved",
      "occurred_at": "2026-05-13T00:00:00.000Z",
      "title": "arXiv:2605.12921 - An irreducible real projective plane in the 4-sphere",
      "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_assisted",
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        "vibemathed:kirby-4-37-irreducible-projective-plane:attempt"
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      "problem_id": "vibemathed:kirby-4-37-irreducible-projective-plane",
      "model": "ChatGPT, Cursor and Gemini",
      "provider": null,
      "attempted_at": "2026-05-13T00:00:00.000Z",
      "human_collaborators": [
        "Mark Hughes",
        "Seungwon Kim",
        "Maggie Miller",
        "Gheehyun Nahm"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "Deliberately bounded, and the authors draw the boundary themselves: they acknowledge using ChatGPT, Cursor and Gemini during initial exploration and computation, and state that all final computations were performed and verified by the authors without the use of AI. So the models were exploratory instruments and none of the standing mathematics rests on them.",
      "failed_routes": [],
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      "sources": [
        {
          "label": "arXiv:2605.12921 - An irreducible real projective plane in the 4-sphere",
          "url": "https://arxiv.org/abs/2605.12921",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: The Kinoshita Conjecture and Kirby Problem 4.37",
          "url": "https://vibemathed.com/problem/kirby-4-37-irreducible-projective-plane",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
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      "cost_usd": null,
      "independence": "unknown"
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      "solution_event_id": "vibemathed:kirby-4-37-irreducible-projective-plane:event",
      "level": "unreviewed",
      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "The authors state they performed and verified all final computations themselves without AI. The result is an explicit construction plus a $\\pi_1$ computation, so it is checkable by hand. arXiv preprint, not peer-reviewed.",
      "sources": [
        {
          "label": "VibeMathed: The Kinoshita Conjecture and Kirby Problem 4.37",
          "url": "https://vibemathed.com/problem/kirby-4-37-irreducible-projective-plane",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
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          "label": "arXiv:2605.12921 - An irreducible real projective plane in the 4-sphere",
          "url": "https://arxiv.org/abs/2605.12921",
          "kind": "primary-mathematical-source",
          "license": null
        }
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  "sources": [
    {
      "label": "arXiv:2605.12921 - An irreducible real projective plane in the 4-sphere",
      "url": "https://arxiv.org/abs/2605.12921",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: The Kinoshita Conjecture and Kirby Problem 4.37",
      "url": "https://vibemathed.com/problem/kirby-4-37-irreducible-projective-plane",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
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  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:kirby-4-37-irreducible-projective-plane:signal:watch_only",
      "problem_id": "vibemathed:kirby-4-37-irreducible-projective-plane",
      "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"
}