{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1772",
  "content_hash": null,
  "slug": "tarski-monster-exponent-five-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 MathOverflow page has no answers and its comments connect the case to the small odd-exponent Burnside problem. The checked modern theorem proves infinitude for much larger odd exponents and does not reach exponent five. Exact unresolved remainder: For a positive answer, construct a group \\(G\\) and prove infinitude, exponent five, and the assertion that every nontrivial proper subgroup is cyclic of order five. For a negative answer, prove that no infinite exponent-five group can have the stated subgroup structure.",
  "relevance": "For A Tarski monster of exponent five, 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 MathOverflow page has no answers and its comments connect the case to the small odd-exponent Burnside problem. The checked modern theorem proves infinitude for much larger odd exponents and does not reach exponent five.\n\nExact unresolved remainder: For a positive answer, construct a group \\(G\\) and prove infinitude, exponent five, and the assertion that every nontrivial proper subgroup is cyclic of order five. For a negative answer, prove that no infinite exponent-five group can have the stated subgroup structure.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://arxiv.org/abs/2303.15997",
      "locator": "abstract and main theorem proving B(m,n) infinite for m >= 2 and odd n >= 557"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2303.15997",
    "locator": "abstract and main theorem proving B(m,n) infinite for m >= 2 and odd n >= 557"
  },
  "models": [],
  "relations": [
    {
      "slug": "R1364",
      "title": "Current checked 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": "tarski-monster-exponent-five",
      "title": "tarski monster exponent five",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}