{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1765",
  "content_hash": null,
  "slug": "standard-map-positive-metric-entropy-claim-literature-frontier",
  "type": "claim",
  "title": "Strongest checked neighboring result",
  "summary": "Positive entropy can be created by nearby conservative perturbations, and hyperbolic sets of zero area are known for many parameters.",
  "relevance": "Locates the present research frontier immediately below Positive metric entropy for the standard map.",
  "relevance_source": "recorded",
  "body": "Positive entropy can be created by nearby conservative perturbations, and hyperbolic sets of zero area are known for many parameters.\n\nThis leaves the following boundary unresolved: Positive Lebesgue metric entropy for the exact standard map at any K remains unproved. 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://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"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R1766",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "standard-map-positive-metric-entropy",
      "title": "standard map positive metric entropy",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}