{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1622",
  "content_hash": null,
  "slug": "kashaev-volume-conjecture-claim-status-20260801",
  "type": "claim",
  "title": "Current status and exact unresolved remainder",
  "summary": "OPEN as checked on 2026-08-01. Strongest checked neighboring result: The conjecture is proved for several knot families and supported by extensive asymptotic calculations and geometric refinements. Exact unresolved remainder: A proof or counterexample for arbitrary hyperbolic knots remains unknown.",
  "relevance": "This is the dated publication status for the canonical target Kashaev volume conjecture for hyperbolic knots.",
  "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: The conjecture is proved for several knot families and supported by extensive asymptotic calculations and geometric refinements.\n\nThe exact unresolved remainder is: A proof or counterexample for arbitrary hyperbolic knots remains unknown.\n\nA complete resolution must meet the following acceptance conditions:\n- Prove existence of the limit and the stated equality for every hyperbolic knot.\n- Or give a hyperbolic knot for which the limit fails to exist or differs from hyperbolic volume.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://doi.org/10.1023/A:1007364912784",
      "locator": "R. Kashaev, The hyperbolic volume of knots from the quantum dilogarithm, Letters in Mathematical Physics 39 (1997). volume-growth conjecture"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1023/A:1007364912784",
    "locator": "R. Kashaev, The hyperbolic volume of knots from the quantum dilogarithm, Letters in Mathematical Physics 39 (1997). volume-growth conjecture"
  },
  "relations": [
    {
      "slug": "R1621",
      "title": "Strongest checked neighboring result",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R1619",
      "title": "Dated source and duplicate audit",
      "object_type": "attempt",
      "relation": "evidences",
      "direction": "incoming"
    },
    {
      "slug": "R1620",
      "title": "Work at the unresolved boundary",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "kashaev-volume-conjecture",
      "title": "kashaev volume conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}