{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R697",
  "content_hash": null,
  "slug": "sac-artifact-sweep-200000",
  "type": "artifact",
  "title": "Exact subtract-a-cube sweep through 200,000",
  "summary": "Exact dynamic programming finds 21,912 positive P-positions through 200,000 and a density of 0.10956 at the endpoint.",
  "relevance": "This supplies a computation, dataset, or executable check used to assess the target problem.",
  "relevance_source": "derived",
  "body": "The program computes every Sprague-Grundy value in increasing heap order using all positive cubes at most the current heap size. The P-position counts are 1,684 through 10,000, 6,815 through 50,000, 13,002 through 100,000, and 21,912 through 200,000. The first positive P-positions are 2, 4, 6, 9, 11, 13, 15, 18, 20, 22, 24, and 34. The maximum Grundy value in the range is 20, first reached at 167,122.\n\nThe sweep is finite evidence for the rate of decay. The density-zero claim above follows from the cited theorem.",
  "status": "available",
  "evidence_grade": "executable",
  "scope": {
    "kind": "bounded",
    "statement": "every starting heap size from 0 through 200000",
    "bounds": {
      "n": {
        "min": 0,
        "max": 200000
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "partial",
    "kind": "python_computation",
    "source": "research/candidate-screening/multi2.py",
    "citation": {
      "url": "https://github.com/philipfweiss/theoremdb/blob/main/research/candidate-screening/multi2.py",
      "locator": "research/candidate-screening/multi2.py, deeper subtraction-game sweep; independently rerun on 2026-07-24"
    },
    "missing": [
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://github.com/philipfweiss/theoremdb/blob/main/research/candidate-screening/multi2.py",
    "locator": "research/candidate-screening/multi2.py, deeper subtraction-game sweep; independently rerun on 2026-07-24"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R699",
      "title": "Subtract-a-cube losing positions have density zero",
      "object_type": "claim",
      "relation": "tests",
      "direction": "outgoing"
    },
    {
      "slug": "R698",
      "title": "Determine the growth order of the greedy cube-difference-free set",
      "object_type": "attempt",
      "relation": "uses",
      "direction": "incoming"
    },
    {
      "slug": "subtract-a-cube-density",
      "title": "subtract a cube density",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}