{
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  "source": "vibemath",
  "problem_id": "vibemathed:finite-field-restriction-paraboloid",
  "title": "The Finite Field Restriction Problem for the Paraboloid",
  "canonical_statement": "For the three-dimensional paraboloid $P_3$ over a prime field in which $-1$ is not a square, the Fourier extension operator maps $L^2$ to $L^r$ for $r > 176/51 = 3.45098\\ldots$, improving the exponent by combining a bilinear approach with point-line incidence bounds.",
  "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:finite-field-restriction-paraboloid:event",
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      "type": "proved",
      "status": "partial",
      "occurred_at": "2026-06-22T00:00:00.000Z",
      "title": "arXiv:2606.22882 - A bilinear approach to the finite field restriction problem, II",
      "summary": "a record exponent; the conjectured range is not yet reached",
      "ai_contribution": "ai_assisted",
      "attempt_ids": [
        "vibemathed:finite-field-restriction-paraboloid:attempt"
      ],
      "method_family_ids": [
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      "model": "ChatGPT",
      "provider": "OpenAI",
      "attempted_at": "2026-06-22T00:00:00.000Z",
      "human_collaborators": [
        "Mark Lewko"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The author states he used ChatGPT to help organize the argument and to identify the cutoffs used to optimize the estimates. Choosing those cutoffs is what fixes the exponent, so the contribution touches the result rather than only the write-up.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
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          "label": "arXiv:2606.22882 - A bilinear approach to the finite field restriction problem, II",
          "url": "https://arxiv.org/abs/2606.22882",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: The Finite Field Restriction Problem for the Paraboloid",
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      "independence": "unknown"
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      "id": "vibemathed:finite-field-restriction-paraboloid:verification",
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      "solution_event_id": "vibemathed:finite-field-restriction-paraboloid:event",
      "level": "unreviewed",
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      "statement_fidelity": "unaudited",
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      "verifier": "VibeMathed (source-reported label)",
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      "note": "Single-author arXiv preprint; not yet peer-reviewed.",
      "sources": [
        {
          "label": "VibeMathed: The Finite Field Restriction Problem for the Paraboloid",
          "url": "https://vibemathed.com/problem/finite-field-restriction-paraboloid",
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          "label": "arXiv:2606.22882 - A bilinear approach to the finite field restriction problem, II",
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          "kind": "primary-mathematical-source",
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  "sources": [
    {
      "label": "arXiv:2606.22882 - A bilinear approach to the finite field restriction problem, II",
      "url": "https://arxiv.org/abs/2606.22882",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: The Finite Field Restriction Problem for the Paraboloid",
      "url": "https://vibemathed.com/problem/finite-field-restriction-paraboloid",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
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  "recommended_mode": "expand",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:finite-field-restriction-paraboloid:signal:recent_partial_result",
      "problem_id": "vibemathed:finite-field-restriction-paraboloid",
      "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"
}