{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1551",
  "content_hash": null,
  "slug": "fp-laurent-series-theory-decidability-attempt-dated-source-audit",
  "type": "attempt",
  "title": "Dated source and duplicate audit",
  "summary": "The exact target, equivalent terminology, and 2025-2026 status evidence were checked on 2026-08-01. Strongest checked result: Conditional quantifier-elimination routes and decidability results for related extensions and languages are known. Unresolved remainder: Unconditional decidability in the pure ring language remains open in the checked sources.",
  "relevance": "Documents why Decidability of the first-order theory of F_p((t)) was treated as a distinct open target on 2026-08-01.",
  "relevance_source": "recorded",
  "body": "The audit ran on 2026-08-01 across the cited primary literature and problem collections, Crossref, arXiv, and stable publisher records, TheoremDB published, prospecting, packet, formal, and retired corpus. It checked the exact statement, its named or normalized variants, recent status evidence, and the controlled TheoremDB corpus.\n\nQueries included:\n- decidability first order theory F_p((t)) open problem 2026\n- quantifier elimination Laurent series field positive characteristic decidability\n\nThe exact target, equivalent terminology, and 2025-2026 status evidence were checked on 2026-08-01. Strongest checked result: Conditional quantifier-elimination routes and decidability results for related extensions and languages are known. Unresolved remainder: Unconditional decidability in the pure ring language remains open in the checked sources.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "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": "R1554",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "fp-laurent-series-theory-decidability",
      "title": "fp laurent series theory decidability",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}