{
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  "ref": "R1659",
  "content_hash": null,
  "slug": "navier-stokes-existence-and-smoothness-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: Global Leray-Hopf weak solutions exist in three dimensions. Smooth solutions are global in two dimensions and local, or global for suitable small data, in three dimensions. Exact unresolved remainder: For every admissible smooth finite-energy three-dimensional datum, prove global smooth existence and uniqueness, or construct admissible data producing finite-time breakdown.",
  "relevance": "For Navier-Stokes existence and smoothness, 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: Global Leray-Hopf weak solutions exist in three dimensions. Smooth solutions are global in two dimensions and local, or global for suitable small data, in three dimensions.\n\nExact unresolved remainder: For every admissible smooth finite-energy three-dimensional datum, prove global smooth existence and uniqueness, or construct admissible data producing finite-time breakdown.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://www.claymath.org/millennium/navier-stokes-equation/",
      "locator": "Unsolved label and official overview"
    },
    "missing": [
      "source",
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      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://www.claymath.org/millennium/navier-stokes-equation/",
    "locator": "Unsolved label and official overview"
  },
  "relations": [
    {
      "slug": "R1106",
      "title": "Current status and unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing"
    },
    {
      "slug": "navier-stokes-existence-and-smoothness",
      "title": "navier stokes existence and smoothness",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}