{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1392",
  "content_hash": null,
  "slug": "birkhoff-billiard-conjecture-attempt-dated-source-audit",
  "type": "attempt",
  "title": "Dated source and duplicate audit",
  "summary": "The exact target, equivalent terminology, and 2025-2026 status evidence were checked on 2026-08-01. Strongest checked result: Local rigidity is known near many ellipses and under symmetry or perturbative hypotheses. Unresolved remainder: The global classification of all smooth strictly convex integrable tables remains open.",
  "relevance": "Documents why Birkhoff conjecture for integrable convex billiards was treated as a distinct open target on 2026-08-01.",
  "relevance_source": "recorded",
  "body": "The audit ran on 2026-08-01 across the cited primary literature and problem collections, Crossref, arXiv, and stable publisher records, TheoremDB published, prospecting, packet, formal, and retired corpus. It checked the exact statement, its named or normalized variants, recent status evidence, and the controlled TheoremDB corpus.\n\nQueries included:\n- Birkhoff billiard conjecture integrable ellipse open 2026\n- local strong Birkhoff conjecture almost every ellipse 2025\n\nThe exact target, equivalent terminology, and 2025-2026 status evidence were checked on 2026-08-01. Strongest checked result: Local rigidity is known near many ellipses and under symmetry or perturbative hypotheses. Unresolved remainder: The global classification of all smooth strictly convex integrable tables remains open.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "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",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "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": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "birkhoff-billiard-conjecture",
      "title": "birkhoff billiard conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}