{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:quartic-hessian-conjecture-dimension-four",
  "title": "The Quartic Hessian Conjecture in Dimension Four",
  "canonical_statement": "The Hessian conjecture is open exactly in dimension four. The source reports a proof for every quartic polynomial in dimension four, a proper slice of the full open problem.",
  "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",
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      "type": "proved",
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      "occurred_at": "2026-08-14T00:00:00.000Z",
      "title": "The Quartic Hessian Conjecture in Dimension Four",
      "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.",
      "ai_contribution": "ai_assisted",
      "attempt_ids": [
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      "provider": "OpenAI, Anthropic, DeepSeek",
      "attempted_at": "2026-08-14T00:00:00.000Z",
      "human_collaborators": [
        "Zixiang Ni"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The source credits AI systems with exploring candidate arguments, adversarial review, algebraic checking, and editorial assistance.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
        {
          "label": "The Quartic Hessian Conjecture in Dimension Four",
          "url": "https://arxiv.org/abs/2608.14217",
          "kind": "primary-mathematical-source",
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        },
        {
          "label": "VibeMathed: The Quartic Hessian Conjecture in Dimension Four",
          "url": "https://vibemathed.com/problem/quartic-hessian-conjecture-dimension-four",
          "kind": "source-assertion",
          "license": "CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/)"
        }
      ],
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      "independence": "unknown"
    }
  ],
  "verifications": [
    {
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      "solution_event_id": "vibemathed:quartic-hessian-conjecture-dimension-four:event",
      "level": "unreviewed",
      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "VibeMathed reports a days-old sole-author preprint and no independent review.",
      "sources": [
        {
          "label": "VibeMathed: The Quartic Hessian Conjecture in Dimension Four",
          "url": "https://vibemathed.com/problem/quartic-hessian-conjecture-dimension-four",
          "kind": "source-assertion",
          "license": "CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/)"
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          "label": "The Quartic Hessian Conjecture in Dimension Four",
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          "kind": "primary-mathematical-source",
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  "sources": [
    {
      "label": "The Quartic Hessian Conjecture in Dimension Four",
      "url": "https://arxiv.org/abs/2608.14217",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: The Quartic Hessian Conjecture in Dimension Four",
      "url": "https://vibemathed.com/problem/quartic-hessian-conjecture-dimension-four",
      "kind": "source-assertion",
      "license": "CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/)"
    }
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  "recommended_mode": "expand",
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  "opportunity_signals": [
    {
      "id": "vibemathed:quartic-hessian-conjecture-dimension-four:signal:recent_partial_result",
      "problem_id": "vibemathed:quartic-hessian-conjecture-dimension-four",
      "kind": "recent_partial_result",
      "reason": "A source-reported partial result may support bounded expansion.",
      "generated_at": "2026-08-17T15:54:39.560Z"
    }
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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."
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  "generated_at": "2026-08-17T15:54:39.560Z"
}