{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1138",
  "content_hash": null,
  "slug": "random-littlewood-irreducibility-limit-claim-status-20260731",
  "type": "claim",
  "title": "Current status and unresolved remainder",
  "summary": "UNKNOWN as of 2026-07-31. The MathOverflow thread has no accepted proof of the limit. Bary-Soroker, Koukoulopoulos, and Kozma prove the limit along special degree sequences under stated hypotheses and obtain an unconditional limsup result, while the full all-degree limit remains described as conjectural in the checked literature. Prove that for every \\(\\eta>0\\) there is \\(N_0\\) such that \\(\\Pr(f_n\\text{ is irreducible over }\\mathbb Q)>1-\\eta\\) for every \\(n\\ge N_0\\).",
  "relevance": "For random littlewood irreducibility limit, pins the dated research frontier: UNKNOWN as of 2026-07-31. The MathOverflow thread has no accepted proof of the limit. Bary-Soroker, Koukoulopoulos, and Kozma prove the limit along special degree sequences under stated hypotheses and obtain an unconditional limsup result, while the full all-degree limit remains described as.",
  "relevance_source": "recorded",
  "body": "UNKNOWN as of 2026-07-31. The MathOverflow thread has no accepted proof of the limit. Bary-Soroker, Koukoulopoulos, and Kozma prove the limit along special degree sequences under stated hypotheses and obtain an unconditional limsup result, while the full all-degree limit remains described as conjectural in the checked literature.\n\nA complete resolution must satisfy this condition: Prove that for every \\(\\eta>0\\) there is \\(N_0\\) such that \\(\\Pr(f_n\\text{ is irreducible over }\\mathbb Q)>1-\\eta\\) for every \\(n\\ge N_0\\).",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://mathoverflow.net/questions/7969/irreducible-polynomials-with-constrained-coefficients",
      "locator": "See dataset.references[0] for the exact external source and locator."
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://mathoverflow.net/questions/7969/irreducible-polynomials-with-constrained-coefficients",
    "locator": "See dataset.references[0] for the exact external source and locator."
  },
  "models": [],
  "relations": [
    {
      "slug": "R1137",
      "title": "Resolve the stated acceptance condition",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "random-littlewood-irreducibility-limit",
      "title": "random littlewood irreducibility limit",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}