{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1568",
  "content_hash": null,
  "slug": "generic-analytic-arnold-diffusion-apriori-stable-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: Generic diffusion is proved in broad a priori unstable systems and in several stable models or regularity classes. Unresolved remainder: A general analytic genericity theorem for a priori stable steep systems remains open.",
  "relevance": "Documents why Generic analytic Arnold diffusion in a priori stable systems 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- generic analytic Arnold diffusion a priori stable open problem\n- Arnold diffusion analytic genericity stable Hamiltonian\n\nThe exact target, equivalent terminology, and 2025-2026 status evidence were checked on 2026-08-01. Strongest checked result: Generic diffusion is proved in broad a priori unstable systems and in several stable models or regularity classes. Unresolved remainder: A general analytic genericity theorem for a priori stable steep systems remains open.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://arxiv.org/abs/1203.2893",
      "locator": "P. Bernard, Arnold's diffusion: from the a priori unstable to the a priori stable case. a priori stable discussion"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/1203.2893",
    "locator": "P. Bernard, Arnold's diffusion: from the a priori unstable to the a priori stable case. a priori stable discussion"
  },
  "models": [],
  "relations": [
    {
      "slug": "R1571",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "generic-analytic-arnold-diffusion-apriori-stable",
      "title": "generic analytic arnold diffusion apriori stable",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}