{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1763",
  "content_hash": null,
  "slug": "standard-map-positive-metric-entropy-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: Positive entropy can be created by nearby conservative perturbations, and hyperbolic sets of zero area are known for many parameters. Unresolved remainder: Positive Lebesgue metric entropy for the exact standard map at any K remains unproved.",
  "relevance": "Documents why Positive metric entropy for the standard map 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- standard map positive metric entropy exists parameter open 2026\n- Chirikov standard map Lebesgue entropy positive proof\n\nThe exact target, equivalent terminology, and 2025-2026 status evidence were checked on 2026-08-01. Strongest checked result: Positive entropy can be created by nearby conservative perturbations, and hyperbolic sets of zero area are known for many parameters. Unresolved remainder: Positive Lebesgue metric entropy for the exact standard map at any K remains unproved.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://people.math.harvard.edu/~knill/books/KnillDissertation.pdf",
      "locator": "O. Knill, dissertation discussion of the standard-map entropy problem. standard map open problem discussion"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://people.math.harvard.edu/~knill/books/KnillDissertation.pdf",
    "locator": "O. Knill, dissertation discussion of the standard-map entropy problem. standard map open problem discussion"
  },
  "relations": [
    {
      "slug": "R1766",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "standard-map-positive-metric-entropy",
      "title": "standard map positive metric entropy",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}