{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1663",
  "content_hash": null,
  "slug": "navier-stokes-half-space-backward-self-similar-claim-status-20260801",
  "type": "claim",
  "title": "Current status and exact unresolved remainder",
  "summary": "OPEN as checked on 2026-08-01. Strongest checked neighboring result: Tsai-type theorems rule out broad classes of whole-space profiles, and half-space results exist under stronger decay or regularity. Exact unresolved remainder: The scale-critical half-space statement above remains open in the checked sources.",
  "relevance": "This is the dated publication status for the canonical target Backward self-similar Navier-Stokes profiles in a half-space.",
  "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: Tsai-type theorems rule out broad classes of whole-space profiles, and half-space results exist under stronger decay or regularity.\n\nThe exact unresolved remainder is: The scale-critical half-space statement above remains open in the checked sources.\n\nA complete resolution must meet the following acceptance conditions:\n- Prove U=0 under a precisely stated critical hypothesis no stronger than the packet's target.\n- Or construct a nonzero profile meeting all equations, boundary conditions, and integrability assumptions.",
  "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 2. Problem 2"
    },
    "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 2. Problem 2"
  },
  "relations": [
    {
      "slug": "R1662",
      "title": "Strongest checked neighboring result",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R1660",
      "title": "Dated source and duplicate audit",
      "object_type": "attempt",
      "relation": "evidences",
      "direction": "incoming"
    },
    {
      "slug": "R1661",
      "title": "Work at the unresolved boundary",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "navier-stokes-half-space-backward-self-similar",
      "title": "navier stokes half space backward self similar",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}