{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1519",
  "content_hash": null,
  "slug": "euler-material-line-exponential-growth-claim-status-20260801",
  "type": "claim",
  "title": "Current status and exact unresolved remainder",
  "summary": "OPEN as checked on 2026-08-01. Strongest checked neighboring result: Very fast vorticity-gradient growth and substantial finite-time material deformation are known. Exact unresolved remainder: A single smooth example with a uniform exponential arclength lower bound for every time remains open in the checked record.",
  "relevance": "This is the dated publication status for the canonical target Persistent exponential stretching of a material line in two-dimensional Euler flow.",
  "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: Very fast vorticity-gradient growth and substantial finite-time material deformation are known.\n\nThe exact unresolved remainder is: A single smooth example with a uniform exponential arclength lower bound for every time remains open in the checked record.\n\nA complete resolution must meet the following acceptance conditions:\n- Construct a domain and smooth Euler solution with the stated all-time arclength lower bound.\n- Or prove an obstruction excluding such all-time exponential stretching.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://aimath.org/pastworkshops/smallscalefluidrep.pdf",
      "locator": "AIM, Small scales and singularity formation in fluid dynamics, workshop report, Problem 4. Problem 4"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://aimath.org/pastworkshops/smallscalefluidrep.pdf",
    "locator": "AIM, Small scales and singularity formation in fluid dynamics, workshop report, Problem 4. Problem 4"
  },
  "models": [],
  "relations": [
    {
      "slug": "R1518",
      "title": "Strongest checked neighboring result",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R1516",
      "title": "Dated source and duplicate audit",
      "object_type": "attempt",
      "relation": "evidences",
      "direction": "incoming"
    },
    {
      "slug": "R1517",
      "title": "Work at the unresolved boundary",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "euler-material-line-exponential-growth",
      "title": "euler material line exponential growth",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}