{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1771",
  "content_hash": null,
  "slug": "sum-of-three-cubes-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: Booker and Sutherland found explicit representations for 33 and 42, completing every admissible positive k<=100. Universal representability outside residues 4 and 5 modulo 9 remains open. Exact unresolved remainder: Prove representation for every admissible integer, or prove one admissible integer is not representable.",
  "relevance": "For Sum of three cubes 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: Booker and Sutherland found explicit representations for 33 and 42, completing every admissible positive k<=100. Universal representability outside residues 4 and 5 modulo 9 remains open.\n\nExact unresolved remainder: Prove representation for every admissible integer, or prove one admissible integer is not representable.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://arxiv.org/abs/2108.03398",
      "locator": "Abstract and introduction"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2108.03398",
    "locator": "Abstract and introduction"
  },
  "relations": [
    {
      "slug": "R1158",
      "title": "Current status and unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing"
    },
    {
      "slug": "sum-of-three-cubes-problem",
      "title": "sum of three cubes problem",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}