{
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  "source": "vibemath",
  "problem_id": "vibemathed:quartic-syk-spectral-edge",
  "title": "Spectral Edge of the Quartic SYK Model",
  "canonical_statement": "Determine the leading asymptotic of the largest eigenvalue of the $N$-Majorana quartic SYK Hamiltonian as $N \\to \\infty$. The preprint proves $\\lambda_1/\\sqrt{N} \\to 4\\int_0^\\infty g_0(t)^4\\,dt \\approx 0.32504$ almost surely, via the limiting free energy at every fixed positive temperature.",
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  "current_status": "candidate",
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      "occurred_at": "2026-07-22T00:00:00.000Z",
      "title": "arXiv:2607.18998 - The spectral edge of the quartic SYK model",
      "summary": "VibeMathed reports this item as candidate. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
      "ai_contribution": "ai_co_developed",
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      "provider": "OpenAI",
      "attempted_at": "2026-07-22T00:00:00.000Z",
      "human_collaborators": [
        "Yukun He"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "Developed with GPT-5.6; the finite-bath interpolation reduces the quartic SYK pressure to a local cavity-kernel identity.",
      "failed_routes": [],
      "artifacts": [],
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          "label": "arXiv:2607.18998 - The spectral edge of the quartic SYK model",
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          "label": "VibeMathed: Spectral Edge of the Quartic SYK Model",
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    },
    {
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      "kind": "source-assertion",
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      "generated_at": "2026-09-13T16:28:40.178Z"
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    "The source status is candidate and must not be represented as solved.",
    "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."
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  "generated_at": "2026-09-13T16:28:40.178Z"
}