{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1631",
  "content_hash": null,
  "slug": "linear-recurrence-positivity-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: Decidability is known through order five, for simple sequences through order nine, and for additional reversible or dominant-root subclasses. Unresolved remainder: A decision procedure for unrestricted order, already beyond the low-order frontier, remains open.",
  "relevance": "Documents why Decidability of positivity for linear recurrence sequences 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- positivity problem linear recurrence sequences general decidability open 2026\n- linear recurrence positivity order 6 Diophantine approximation\n\nThe exact target, equivalent terminology, and 2025-2026 status evidence were checked on 2026-08-01. Strongest checked result: Decidability is known through order five, for simple sequences through order nine, and for additional reversible or dominant-root subclasses. Unresolved remainder: A decision procedure for unrestricted order, already beyond the low-order frontier, remains open.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.1137/1.9781611973402.27",
      "locator": "J. Ouaknine and J. Worrell, Positivity Problems for Low-Order Linear Recurrence Sequences, SODA 2014. main decidability theorems"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1137/1.9781611973402.27",
    "locator": "J. Ouaknine and J. Worrell, Positivity Problems for Low-Order Linear Recurrence Sequences, SODA 2014. main decidability theorems"
  },
  "relations": [
    {
      "slug": "R1634",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "linear-recurrence-positivity-decidability",
      "title": "linear recurrence positivity decidability",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}