{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R719",
  "content_hash": null,
  "slug": "sdw-attempt-prior-art-audit",
  "type": "attempt",
  "title": "The ruleset is an established Wyt_K specialization",
  "summary": "A 2009 paper defines arbitrary restricted diagonal sets K; the square-set threshold was not located in the focused search.",
  "relevance": "This records a line of attack on the target problem, including what it establishes and where it stops.",
  "relevance_source": "derived",
  "body": "Duchene, Fraenkel, Gravier, and Nowakowski define \\(\\operatorname{Wyt}_K\\) for any subset \\(K\\) of the positive integers. Its moves reduce one heap arbitrarily or reduce both heaps by the same \\(k\\in K\\). The present game is exactly their construction with\n\\[\nK=\\{1,4,9,16,\\ldots\\}.\n\\]\nTheir explicit P-position results cover singleton sets and selected infinite sets of powers of two. The paper supplies the established name and ruleset framework.\n\nA focused search covered the exact initial pairs, square-restricted diagonal moves, Wyt_K, Nimhoff games, and OEIS sequence searches for both coordinate sequences. It found no source stating the gap-50 witness or the 100,000-position maximum. This search is evidence about the sources checked on 2026-07-24; it leaves novelty of the finite computation unverified.",
  "status": "inconclusive",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "the square-removal ruleset and the first 100,000 P-position gap threshold",
    "bounds": {
      "position_ordinal": {
        "min": 1,
        "max": 100000
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://ajc.maths.uq.edu.au/pdf/44/ajc_v44_p043.pdf",
      "locator": "Duchene, Fraenkel, Gravier, and Nowakowski, Australasian Journal of Combinatorics 44 (2009), Definition 5 on page 45, section 3, and section 4.2; focused search performed 2026-07-24"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://ajc.maths.uq.edu.au/pdf/44/ajc_v44_p043.pdf",
    "locator": "Duchene, Fraenkel, Gravier, and Nowakowski, Australasian Journal of Combinatorics 44 (2009), Definition 5 on page 45, section 3, and section 4.2; focused search performed 2026-07-24"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R720",
      "title": "The first gap 50 occurs at P-position 42,762",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "square-diagonal-wythoff-gap-50",
      "title": "square diagonal wythoff gap 50",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}