{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1671",
  "content_hash": null,
  "slug": "normalized-prime-gap-limit-set-claim-literature-frontier",
  "type": "claim",
  "title": "Strongest checked neighboring result",
  "summary": "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.",
  "relevance": "Locates the present research frontier immediately below All nonnegative limits of normalized consecutive-prime gaps.",
  "relevance_source": "recorded",
  "body": "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\nThis leaves the following boundary unresolved: It is unknown whether every finite \\(C\\ge0\\) is a limit point. The distinction is retained here so a restricted theorem, finite computation, or neighboring case is not presented as a solution of the full target.",
  "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": "R1672",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "normalized-prime-gap-limit-set",
      "title": "normalized prime gap limit set",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}