{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1672",
  "content_hash": null,
  "slug": "normalized-prime-gap-limit-set-claim-status-20260801",
  "type": "claim",
  "title": "Current status and exact unresolved remainder",
  "summary": "OPEN as checked on 2026-08-01. Strongest checked neighboring result: The maintained survey records \\(0\\) and \\(\\infty\\) as limit points, arbitrarily large finite limit points, an interval \\([0,c]\\), positive density of the limit set, and bounded gaps in that set. Exact unresolved remainder: It is unknown whether every finite \\(C\\ge0\\) is a limit point.",
  "relevance": "This is the dated publication status for the canonical target All nonnegative limits of normalized consecutive-prime gaps.",
  "relevance_source": "recorded",
  "body": "The problem was checked as open on 2026-08-01.\n\nThe strongest neighboring result found in the cited sources is: The maintained survey records \\(0\\) and \\(\\infty\\) as limit points, arbitrarily large finite limit points, an interval \\([0,c]\\), positive density of the limit set, and bounded gaps in that set.\n\nThe exact unresolved remainder is: It is unknown whether every finite \\(C\\ge0\\) is a limit point.\n\nA complete resolution must meet the following acceptance conditions:\n- For a proof, construct or establish a convergent subsequence for every \\(C\\ge0\\).\n- For a disproof, exhibit a specific \\(C\\ge0\\) and prove that no normalized-gap subsequence converges to it.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://www.erdosproblems.com/5",
      "locator": "Thomas F. Bloom, Erdős Problem #5, Erdős Problems database (living entry), accessed 2026-08-01. Problem #5, OPEN banner, statement, remarks, and bibliography"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://www.erdosproblems.com/5",
    "locator": "Thomas F. Bloom, Erdős Problem #5, Erdős Problems database (living entry), accessed 2026-08-01. Problem #5, OPEN banner, statement, remarks, and bibliography"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R1671",
      "title": "Strongest checked neighboring result",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R1669",
      "title": "Dated source and duplicate audit",
      "object_type": "attempt",
      "relation": "evidences",
      "direction": "incoming"
    },
    {
      "slug": "R1670",
      "title": "Work at the unresolved boundary",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "normalized-prime-gap-limit-set",
      "title": "normalized prime gap limit set",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}