{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1300",
  "content_hash": null,
  "slug": "exponential-square-free-group-next-route-20260801",
  "type": "attempt",
  "title": "Complete the stated acceptance conditions",
  "summary": "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": "Gives the next worker a direct completion target while separating partial progress from a full answer.",
  "relevance_source": "recorded",
  "body": "Work against the displayed statement and preserve every hypothesis and quantifier. 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. Any computation must retain a replayable witness and a matching exclusion or completeness certificate.",
  "status": "open_strategy",
  "evidence_grade": "self_reported",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://mathoverflow.net/questions/499819/do-x-mapsto-ex-1-and-x-mapsto-x2-generate-a-free-group-on-mathbbr-to",
      "locator": "Editorial research route recorded 2026-08-01."
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://mathoverflow.net/questions/499819/do-x-mapsto-ex-1-and-x-mapsto-x2-generate-a-free-group-on-mathbbr-to",
    "locator": "Editorial research route recorded 2026-08-01."
  },
  "relations": [
    {
      "slug": "R1301",
      "title": "Current checked status and unresolved remainder",
      "object_type": "claim",
      "relation": "addresses",
      "direction": "outgoing"
    },
    {
      "slug": "exponential-square-free-group",
      "title": "exponential square free group",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}