{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1158",
  "content_hash": null,
  "slug": "sum-of-three-cubes-problem-claim-status-20260731",
  "type": "claim",
  "title": "Current status and unresolved remainder",
  "summary": "The cited research paper treats universal representability outside the modulo-9 obstruction as unresolved. The source and public status were checked on 2026-07-31. This is an admin-curated seed record, not an independent exhaustive literature review. Prove representability for every integer outside the two obstructed residue classes, or give an admissible integer and prove that it has no representation by three integer cubes.",
  "relevance": "Defines the dated frontier and the exact remainder that research on this problem must resolve.",
  "relevance_source": "recorded",
  "body": "The cited research paper treats universal representability outside the modulo-9 obstruction as unresolved. The source and public status were checked on 2026-07-31. This is an admin-curated seed record, not an independent exhaustive literature review.\n\nA complete resolution must satisfy this condition: Prove representability for every integer outside the two obstructed residue classes, or give an admissible integer and prove that it has no representation by three integer cubes.",
  "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": "See dataset.references[0] for the exact external source and locator."
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2108.03398",
    "locator": "See dataset.references[0] for the exact external source and locator."
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R1157",
      "title": "Resolve the stated acceptance condition",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "R1771",
      "title": "Dated status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "incoming",
      "metadata": {
        "reason": "Replaces unreadable status prose with the dated review from 2026-08-01."
      }
    },
    {
      "slug": "sum-of-three-cubes-problem",
      "title": "sum of three cubes problem",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}