{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1571",
  "content_hash": null,
  "slug": "generic-analytic-arnold-diffusion-apriori-stable-claim-status-20260801",
  "type": "claim",
  "title": "Current status and exact unresolved remainder",
  "summary": "OPEN as checked on 2026-08-01. Strongest checked neighboring result: Generic diffusion is proved in broad a priori unstable systems and in several stable models or regularity classes. Exact unresolved remainder: A general analytic genericity theorem for a priori stable steep systems remains open.",
  "relevance": "This is the dated publication status for the canonical target Generic analytic Arnold diffusion in a priori stable systems.",
  "relevance_source": "recorded",
  "body": "The problem was checked as open on 2026-08-01.\n\nThe strongest neighboring result found in the cited sources is: Generic diffusion is proved in broad a priori unstable systems and in several stable models or regularity classes.\n\nThe exact unresolved remainder is: A general analytic genericity theorem for a priori stable steep systems remains open.\n\nA complete resolution must meet the following acceptance conditions:\n- State a standard Baire or prevalence notion of genericity and prove order-one diffusion for the corresponding analytic perturbations.\n- Or disprove the generic claim by an open or residual obstruction class under the same topology.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "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": "R1570",
      "title": "Strongest checked neighboring result",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R1568",
      "title": "Dated source and duplicate audit",
      "object_type": "attempt",
      "relation": "evidences",
      "direction": "incoming"
    },
    {
      "slug": "R1569",
      "title": "Work at the unresolved boundary",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "generic-analytic-arnold-diffusion-apriori-stable",
      "title": "generic analytic arnold diffusion apriori stable",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}