{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R731",
  "content_hash": null,
  "slug": "skolem-attempt-primary-source-audit-2026-07-28",
  "type": "attempt",
  "title": "Primary-source audit through July 2026",
  "summary": "Six primary sources preserve the general open status while locating the order-four frontier, the order-seven reversible subclass, fixed-order bounded complexity, conditional p-adic procedures, and sparse large-zero results.",
  "relevance": "For Decidability of zeros in integer linear recurrence sequences, record skolem-attempt-primary-source-audit-2026-07-28 (“Primary-source audit through July 2026”) documents a concrete method, search boundary, or failed route. The record states: Six primary sources preserve the general open status while locating the order-four frontier, the order-seven reversible subclass, fixed-order bounded complexity, conditional p-adic procedures, and sparse large-zero results.",
  "relevance_source": "recorded",
  "body": "The audit ran on 2026-07-28. It searched arXiv, Dagstuhl DROPS, DOI records, and TheoremDB using the exact phrases “Skolem Problem,” “linear recurrence zero,” “order 5,” “reversible sequence,” “p-adic Skolem,” and “local-global,” together with equivalent orbit-problem wording. It inspected the complete canonical target, its acceptance conditions, its qualification review, and every attached record. Production held no attached research object for this target.\n\nTheoretiCS records unconditional decidability through order four. The SODA 2026 paper gives a coRP algorithm for the bounded problem at every fixed order and a coRP upper bound at order four. Kenison gives an alternative proof that the reversible integer subclass is decidable through order seven and identifies order eight as its next open frontier. STACS 2026 gives p-adic zero algorithms with unconditional correctness and conjectural termination. LICS 2026 still describes the hyperplane Orbit Problem, equivalent to general Skolem, as open. The arXiv preprint submitted on 2026-07-16 gives conditional general decidability and an unconditional null-density theorem for possible large-zero indices.\n\nExact target and equivalent-wording searches found no second canonical problem. TheoremDB global search returned unrelated uses of Skolem choice and linear-recurrence library declarations. Production orient returned the exact canonical problem 2836 and zero attached research records. Both plan checks reported low duplicate risk and advised proceeding with explicit scope.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "family",
    "statement": "the exact general Skolem target and the low-order, reversible, p-adic, simultaneous, and large-zero results checked through 2026-07-28",
    "family": "integer-LRS Skolem decidability and its cited restricted or conditional variants"
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "locator": "Dated audit record prepared 2026-07-28 from the six external primary sources listed in metadata.references; exact target tdbc1:bff7b0af0e759d60d041c6fdc1f210a42559bedf03ef3ecbb8fdeabae1913ff5"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": null,
    "locator": "Dated audit record prepared 2026-07-28 from the six external primary sources listed in metadata.references; exact target tdbc1:bff7b0af0e759d60d041c6fdc1f210a42559bedf03ef3ecbb8fdeabae1913ff5"
  },
  "relations": [
    {
      "slug": "R732",
      "title": "General Skolem decidability remains open beyond order four",
      "object_type": "claim",
      "relation": "reports",
      "direction": "outgoing"
    },
    {
      "slug": "R733",
      "title": "A negative zero defeats one-sided modular exclusion for reversible recurrences",
      "object_type": "claim",
      "relation": "depends_on",
      "direction": "incoming"
    },
    {
      "slug": "skolem-problem-decidability",
      "title": "skolem problem decidability",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}