{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R792",
  "content_hash": null,
  "slug": "tmpc-attempt-literature-audit",
  "type": "attempt",
  "title": "The literature search found nearby sharp and moment-constrained inequalities",
  "summary": "Classical sharp Poincare theory and Gaussian moment improvements supply context; the exact two-moment Dirichlet constant was not found.",
  "relevance": "For The sharp Dirichlet Poincare constant with two moment constraints, record tmpc-attempt-literature-audit (“The literature search found nearby sharp and moment-constrained inequalities”) documents a concrete method, search boundary, or failed route. The record states: Classical sharp Poincare theory and Gaussian moment improvements supply context; the exact two-moment Dirichlet constant was not found.",
  "relevance_source": "recorded",
  "body": "Kuznetsov and Nazarov survey sharp Poincare, Steklov, and related constants, including the classical interval inequalities with endpoint conditions. Xu, Liu, and Lu treat sharp Wirtinger constants on \\([0,1]\\) for endpoint interpolation conditions and reduce the \\(L^2\\) constant to an eigenvalue problem for an integral operator. Bartier, Blanchet, Dolbeault, and Escobedo prove an improved Gaussian Poincare inequality under orthogonality to low-degree Hermite polynomials; they explicitly interpret those conditions as moment conditions.\n\nFocused searches combined `Poincare`, `Wirtinger`, `Dirichlet`, `moment constraints`, `orthogonality to polynomials`, and the two characteristic equations in this record. They found no primary source stating this exact pair of integral constraints, the factorization into \\(E\\) and \\(O\\), or the certified value above. The novelty claim remains unverified.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.1186/s13660-019-2121-8",
      "locator": "Guiqiao Xu, Zehong Liu, and Wanting Lu, A kind of sharp Wirtinger inequality, Journal of Inequalities and Applications 2019:166, abstract and L2 eigenvalue discussion; Nikolay Kuznetsov and Alexander Nazarov, Mathematika 61 (2015), 328-344, DOI 10.1112/S0025579314000229; Jean-Philippe Bartier, Adrien Blanchet, Jean Dolbeault, and Miguel Escobedo, Applied Mathematics Letters 24 (2011), 76-81, Proposition 1, DOI 10.1016/j.aml.2010.08.020"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1186/s13660-019-2121-8",
    "locator": "Guiqiao Xu, Zehong Liu, and Wanting Lu, A kind of sharp Wirtinger inequality, Journal of Inequalities and Applications 2019:166, abstract and L2 eigenvalue discussion; Nikolay Kuznetsov and Alexander Nazarov, Mathematika 61 (2015), 328-344, DOI 10.1112/S0025579314000229; Jean-Philippe Bartier, Adrien Blanchet, Jean Dolbeault, and Miguel Escobedo, Applied Mathematics Letters 24 (2011), 76-81, Proposition 1, DOI 10.1016/j.aml.2010.08.020"
  },
  "relations": [
    {
      "slug": "R794",
      "title": "Parity reduction gives the sharp eigenvalue equation",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "two-moment-poincare-constant",
      "title": "two moment poincare constant",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}