{
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  "ref": "R1394",
  "content_hash": null,
  "slug": "birkhoff-billiard-conjecture-claim-literature-frontier",
  "type": "claim",
  "title": "Strongest checked neighboring result",
  "summary": "Local rigidity is known near many ellipses and under symmetry or perturbative hypotheses.",
  "relevance": "Locates the present research frontier immediately below Birkhoff conjecture for integrable convex billiards.",
  "relevance_source": "recorded",
  "body": "Local rigidity is known near many ellipses and under symmetry or perturbative hypotheses.\n\nThis leaves the following boundary unresolved: The global classification of all smooth strictly convex integrable tables remains open. 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://doi.org/10.1007/s00222-025-01397-y",
      "locator": "Illya Koval, “Local strong Birkhoff conjecture and local spectral uniqueness of almost every ellipse,” Inventiones Mathematicae 244(1) (2026), 221–298. main local strong Birkhoff theorem"
    },
    "missing": [
      "source",
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    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1007/s00222-025-01397-y",
    "locator": "Illya Koval, “Local strong Birkhoff conjecture and local spectral uniqueness of almost every ellipse,” Inventiones Mathematicae 244(1) (2026), 221–298. main local strong Birkhoff theorem"
  },
  "relations": [
    {
      "slug": "R1395",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "birkhoff-billiard-conjecture",
      "title": "birkhoff billiard conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}