{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1524",
  "content_hash": null,
  "slug": "exponential-square-free-group-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: The sole answer proposes a consequence of Schanuel's conjecture. Comments identify gaps in how reduced words enter the argument and ask whether Ax-Schanuel yields an unconditional proof; the thread contains no settled unconditional resolution. Exact unresolved remainder: Prove that every nonempty freely reduced word in f^{+/-1} and g^{+/-1} differs from the identity at some x>0, or exhibit a nonempty freely reduced word that is the identity on all x>0. A conditional proof must state its hypothesis explicitly and does not settle the unconditional target.",
  "relevance": "For A free group generated by exponential and squaring maps, 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: The sole answer proposes a consequence of Schanuel's conjecture. Comments identify gaps in how reduced words enter the argument and ask whether Ax-Schanuel yields an unconditional proof; the thread contains no settled unconditional resolution.\n\nExact unresolved remainder: Prove that every nonempty freely reduced word in f^{+/-1} and g^{+/-1} differs from the identity at some x>0, or exhibit a nonempty freely reduced word that is the identity on all x>0. A conditional proof must state its hypothesis explicitly and does not settle the unconditional target.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://doi.org/10.1080/00927872.2010.489918",
      "locator": "abstract and results on algebraic roots of exponential polynomials under Schanuel's conjecture"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1080/00927872.2010.489918",
    "locator": "abstract and results on algebraic roots of exponential polynomials under Schanuel's conjecture"
  },
  "relations": [
    {
      "slug": "R1301",
      "title": "Current checked status and unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing"
    },
    {
      "slug": "exponential-square-free-group",
      "title": "exponential square free group",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}