{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R936",
  "content_hash": null,
  "slug": "birch-and-swinnerton-dyer-rank-conjecture-claim-status-20260731",
  "type": "claim",
  "title": "Current status and unresolved remainder",
  "summary": "The cited authoritative source listed this problem as unsolved when checked on 2026-07-31. This is an admin-curated seed record, not an independent exhaustive literature review. Prove the rank equality for every elliptic curve over Q, or exhibit an elliptic curve for which both ranks are rigorously determined and unequal.",
  "relevance": "Defines the dated frontier and the exact remainder that research on this problem must resolve.",
  "relevance_source": "recorded",
  "body": "The cited authoritative source listed this problem as unsolved when 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 the rank equality for every elliptic curve over Q, or exhibit an elliptic curve for which both ranks are rigorously determined and unequal.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://www.claymath.org/millennium/birch-and-swinnerton-dyer-conjecture/",
      "locator": "See dataset.references[0] for the exact external source and locator."
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://www.claymath.org/millennium/birch-and-swinnerton-dyer-conjecture/",
    "locator": "See dataset.references[0] for the exact external source and locator."
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R935",
      "title": "Resolve the stated acceptance condition",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "R1391",
      "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": "birch-and-swinnerton-dyer-rank-conjecture",
      "title": "birch and swinnerton dyer rank conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}