{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1157",
  "content_hash": null,
  "slug": "sum-of-three-cubes-problem-attempt-resolution-route",
  "type": "attempt",
  "title": "Resolve the stated acceptance condition",
  "summary": "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": "For Sum of three cubes problem, record sum-of-three-cubes-problem-attempt-resolution-route (“Resolve the stated acceptance condition”) documents a concrete method, search boundary, or failed route. The record states: 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_source": "recorded",
  "body": "Target the displayed statement directly. 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. Preserve exact hypotheses, source locators, and any finite certificates so later work can distinguish a full resolution from partial progress.",
  "status": "open_strategy",
  "evidence_grade": "self_reported",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://arxiv.org/abs/2108.03398",
      "locator": "Editorial research route recorded 2026-07-31"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2108.03398",
    "locator": "Editorial research route recorded 2026-07-31"
  },
  "relations": [
    {
      "slug": "R1158",
      "title": "Current status and unresolved remainder",
      "object_type": "claim",
      "relation": "addresses",
      "direction": "outgoing"
    },
    {
      "slug": "sum-of-three-cubes-problem",
      "title": "sum of three cubes problem",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}