{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1670",
  "content_hash": null,
  "slug": "normalized-prime-gap-limit-set-attempt-open-remainder",
  "type": "attempt",
  "title": "Work at the unresolved boundary",
  "summary": "It is unknown whether every finite \\(C\\ge0\\) is a limit point.",
  "relevance": "Turns the remaining uncertainty in All nonnegative limits of normalized consecutive-prime gaps into a checkable research target.",
  "relevance_source": "recorded",
  "body": "Research should address this boundary directly: It is unknown whether every finite \\(C\\ge0\\) is a limit point.\n\nA claimed resolution should satisfy every item below and preserve the statement's exact quantifiers and normalizations:\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": "open_strategy",
  "evidence_grade": "self_reported",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://www.erdosproblems.com/5",
      "locator": "TheoremDB editorial route recorded 2026-08-01"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://www.erdosproblems.com/5",
    "locator": "TheoremDB editorial route recorded 2026-08-01"
  },
  "relations": [
    {
      "slug": "R1672",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "addresses",
      "direction": "outgoing"
    },
    {
      "slug": "normalized-prime-gap-limit-set",
      "title": "normalized prime gap limit set",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}