{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1554",
  "content_hash": null,
  "slug": "fp-laurent-series-theory-decidability-claim-status-20260801",
  "type": "claim",
  "title": "Current status and exact unresolved remainder",
  "summary": "OPEN as checked on 2026-08-01. Strongest checked neighboring result: Conditional quantifier-elimination routes and decidability results for related extensions and languages are known. Exact unresolved remainder: Unconditional decidability in the pure ring language remains open in the checked sources.",
  "relevance": "This is the dated publication status for the canonical target Decidability of the first-order theory of F_p((t)).",
  "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: Conditional quantifier-elimination routes and decidability results for related extensions and languages are known.\n\nThe exact unresolved remainder is: Unconditional decidability in the pure ring language remains open in the checked sources.\n\nA complete resolution must meet the following acceptance conditions:\n- Give a terminating correct decision algorithm for all ring-language sentences.\n- Or prove the theory undecidable by an effective interpretation or reduction.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://doi.org/10.2140/ant.2016.10.665",
      "locator": "S. Anscombe and A. Fehm, “The existential theory of equicharacteristic henselian valued fields,” Algebra & Number Theory 10(3) (2016), 665–683. abstract and main existential Ax–Kochen–Ershov theorem"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.2140/ant.2016.10.665",
    "locator": "S. Anscombe and A. Fehm, “The existential theory of equicharacteristic henselian valued fields,” Algebra & Number Theory 10(3) (2016), 665–683. abstract and main existential Ax–Kochen–Ershov theorem"
  },
  "relations": [
    {
      "slug": "R1553",
      "title": "Strongest checked neighboring result",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R1551",
      "title": "Dated source and duplicate audit",
      "object_type": "attempt",
      "relation": "evidences",
      "direction": "incoming"
    },
    {
      "slug": "R1552",
      "title": "Work at the unresolved boundary",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "fp-laurent-series-theory-decidability",
      "title": "fp laurent series theory decidability",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}