{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1629",
  "content_hash": null,
  "slug": "lehmers-mahler-measure-problem-status-packet-quality-20260801",
  "type": "claim",
  "title": "Dated status and exact unresolved remainder",
  "summary": "Unresolved in this packet after the dated source check. Strongest checked result: Dobrowolski gives a degree-dependent lower bound above 1 for noncyclotomic algebraic integers, while the gap shrinks with degree. Lehmer's degree-10 example remains the smallest known Mahler measure above 1. Exact unresolved remainder: Prove a constant c>1 such that every noncyclotomic monic integer polynomial P satisfies M(P)>=c, or disprove such a uniform gap.",
  "relevance": "For Lehmer's Mahler measure problem, this successor gives readable dated status prose and the exact remaining research boundary.",
  "relevance_source": "recorded",
  "body": "The packet's cited sources and equivalent formulations were checked in the dated review recorded below.\n\nStrongest checked result: Dobrowolski gives a degree-dependent lower bound above 1 for noncyclotomic algebraic integers, while the gap shrinks with degree. Lehmer's degree-10 example remains the smallest known Mahler measure above 1.\n\nExact unresolved remainder: Prove a constant c>1 such that every noncyclotomic monic integer polynomial P satisfies M(P)>=c, or disprove such a uniform gap.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://www.mathnet.ru/eng/mmj150",
      "locator": "Discussion of Lehmer's problem in the Mahler-measure section"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://www.mathnet.ru/eng/mmj150",
    "locator": "Discussion of Lehmer's problem in the Mahler-measure section"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R1094",
      "title": "Current status and unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing",
      "metadata": {
        "reason": "Replaces unreadable status prose with the dated review from 2026-08-01."
      }
    },
    {
      "slug": "lehmers-mahler-measure-problem",
      "title": "lehmers mahler measure problem",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}