{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1796",
  "content_hash": null,
  "slug": "unbounded-integral-points-minimal-elliptic-curves-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: Large explicit examples and average bounds are known, but the checked sources do not prove unboundedness across global minimal models or an absolute uniform bound. Exact unresolved remainder: For unboundedness, construct or prove the existence of elliptic curves \\(E_r/\\mathbb Q\\) with certified global minimal equations and \\(N(E_r)\\to\\infty\\). For boundedness, give an absolute constant \\(C\\) and prove \\(N(E)\\le C\\) for every elliptic curve over \\(\\mathbb Q\\) on its global minimal integral model.",
  "relevance": "For Unbounded numbers of integral points on global minimal elliptic curves, 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: Large explicit examples and average bounds are known, but the checked sources do not prove unboundedness across global minimal models or an absolute uniform bound.\n\nExact unresolved remainder: For unboundedness, construct or prove the existence of elliptic curves \\(E_r/\\mathbb Q\\) with certified global minimal equations and \\(N(E_r)\\to\\infty\\). For boundedness, give an absolute constant \\(C\\) and prove \\(N(E)\\le C\\) for every elliptic curve over \\(\\mathbb Q\\) on its global minimal integral model.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://arxiv.org/abs/1807.03761",
      "locator": "abstract and bounded-second-moment theorem for numbers of S-integral points in height-ordered elliptic-curve families"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/1807.03761",
    "locator": "abstract and bounded-second-moment theorem for numbers of S-integral points in height-ordered elliptic-curve families"
  },
  "relations": [
    {
      "slug": "R1372",
      "title": "Current checked status and unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing"
    },
    {
      "slug": "unbounded-integral-points-minimal-elliptic-curves",
      "title": "unbounded integral points minimal elliptic curves",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}