{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1806",
  "content_hash": null,
  "slug": "whitehead-asphericity-claim-status-20260801",
  "type": "claim",
  "title": "Current status and exact unresolved remainder",
  "summary": "OPEN as checked on 2026-08-01. Strongest checked neighboring result: Many group-theoretic, one-relator, and rational or p-adic analogues are known; recent claimed proofs have not produced consensus closure. Exact unresolved remainder: The general integral two-complex statement remains open in current peer-reviewed literature.",
  "relevance": "This is the dated publication status for the canonical target Whitehead asphericity conjecture.",
  "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: Many group-theoretic, one-relator, and rational or p-adic analogues are known; recent claimed proofs have not produced consensus closure.\n\nThe exact unresolved remainder is: The general integral two-complex statement remains open in current peer-reviewed literature.\n\nA complete resolution must meet the following acceptance conditions:\n- Prove every connected subcomplex Y is aspherical.\n- Or give an explicit aspherical two-complex with a connected subcomplex having nonzero π₂.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://www.mathnet.ru/links/4fbc817a2c66e119ba5013f03fd81599/im9597_eng.pdf",
      "locator": "A. Mikhovich, Rational and p-adic analogues of J. H. C. Whitehead's conjecture, Izvestiya: Mathematics 89 (2025). introduction"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://www.mathnet.ru/links/4fbc817a2c66e119ba5013f03fd81599/im9597_eng.pdf",
    "locator": "A. Mikhovich, Rational and p-adic analogues of J. H. C. Whitehead's conjecture, Izvestiya: Mathematics 89 (2025). introduction"
  },
  "relations": [
    {
      "slug": "R1805",
      "title": "Strongest checked neighboring result",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R1803",
      "title": "Dated source and duplicate audit",
      "object_type": "attempt",
      "relation": "evidences",
      "direction": "incoming"
    },
    {
      "slug": "R1804",
      "title": "Work at the unresolved boundary",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "whitehead-asphericity",
      "title": "whitehead asphericity",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}