{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1483",
  "content_hash": null,
  "slug": "cramers-prime-gap-conjecture-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: Baker, Harman, and Pintz proved unconditionally that every sufficiently large interval [x-x^0.525,x] contains a prime. Consequently p_(n+1)-p_n = O(p_n^0.525). Cramer's O((log p_n)^2) bound remains open. Exact unresolved remainder: Prove a uniform C(log p_n)^2 upper bound for every sufficiently large consecutive-prime gap, or prove that limsup (p_(n+1)-p_n)/(log p_n)^2 is infinite.",
  "relevance": "For Cramér's prime-gap conjecture, 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: Baker, Harman, and Pintz proved unconditionally that every sufficiently large interval [x-x^0.525,x] contains a prime. Consequently p_(n+1)-p_n = O(p_n^0.525). Cramer's O((log p_n)^2) bound remains open.\n\nExact unresolved remainder: Prove a uniform C(log p_n)^2 upper bound for every sufficiently large consecutive-prime gap, or prove that limsup (p_(n+1)-p_n)/(log p_n)^2 is infinite.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://primegap-list-project.github.io/faq/",
      "locator": "Cramér conjecture and record-gap sections"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://primegap-list-project.github.io/faq/",
    "locator": "Cramér conjecture and record-gap sections"
  },
  "relations": [
    {
      "slug": "R946",
      "title": "Current status and unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing"
    },
    {
      "slug": "cramers-prime-gap-conjecture",
      "title": "cramers prime gap conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}