{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1304",
  "content_hash": null,
  "slug": "finite-order-integer-matrix-ternary-conjugate-next-route-20260801",
  "type": "attempt",
  "title": "Complete the stated acceptance conditions",
  "summary": "For a positive answer, prove that every finite-order element of every \\(\\operatorname{GL}_n(\\mathbb Z)\\) has an integrally conjugate ternary representative. For a negative answer, give a finite-order integral matrix in the least possible dimension and prove that no integral conjugate is ternary; also certify all smaller dimensions.",
  "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. For a positive answer, prove that every finite-order element of every \\(\\operatorname{GL}_n(\\mathbb Z)\\) has an integrally conjugate ternary representative. For a negative answer, give a finite-order integral matrix in the least possible dimension and prove that no integral conjugate is ternary; also certify all smaller dimensions. 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/346842/is-every-finite-order-unimodular-matrix-conjugate-to-a-0-1-1-matrix",
      "locator": "Editorial research route recorded 2026-08-01."
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://mathoverflow.net/questions/346842/is-every-finite-order-unimodular-matrix-conjugate-to-a-0-1-1-matrix",
    "locator": "Editorial research route recorded 2026-08-01."
  },
  "relations": [
    {
      "slug": "R1305",
      "title": "Current checked status and unresolved remainder",
      "object_type": "claim",
      "relation": "addresses",
      "direction": "outgoing"
    },
    {
      "slug": "finite-order-integer-matrix-ternary-conjugate",
      "title": "finite order integer matrix ternary conjugate",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}