{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R221",
  "content_hash": null,
  "slug": "dpi-artifact-60-step-endpoints",
  "type": "artifact",
  "title": "Sixty iterations leave 31 distinct endpoints",
  "summary": "The 199 starts produce 31 distinct values after exactly 60 applications of the map.",
  "relevance": "For Merging of orbits under adding the product of nonzero digits, record dpi-artifact-60-step-endpoints (“Sixty iterations leave 31 distinct endpoints”) supplies evidence or a replay used to check the packet. The record states: The 199 starts produce 31 distinct values after exactly 60 applications of the map.",
  "relevance_source": "recorded",
  "body": "The original candidate said the runs \"produced only 31 distinct values,\" though the 199 starting values are already distinct. The code measures the endpoints after exactly 60 steps. Its correct result is that \\(\\{T^{60}(s):1\\leq s\\leq199\\}\\) has size 31. Equal endpoints certify that the corresponding finite orbits have merged by that time.",
  "status": "available",
  "evidence_grade": "computational",
  "scope": {
    "kind": "bounded",
    "statement": "starts 1 through 199, each iterated exactly 60 times",
    "bounds": {
      "start": {
        "min": 1,
        "max": 199
      },
      "iterations": {
        "min": 60,
        "max": 60
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "partial",
    "kind": "python_computation",
    "source": "research/candidate-screening/multi.py",
    "citation": {
      "url": "https://github.com/philipfweiss/theoremdb/blob/main/research/candidate-screening/multi.py",
      "locator": "research/candidate-screening/multi.py, digit-driven iteration section"
    },
    "missing": [
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://github.com/philipfweiss/theoremdb/blob/main/research/candidate-screening/multi.py",
    "locator": "research/candidate-screening/multi.py, digit-driven iteration section"
  },
  "relations": [
    {
      "slug": "R224",
      "title": "Loomis conjectured that every orbit joins the orbit of 1",
      "object_type": "claim",
      "relation": "tests",
      "direction": "outgoing"
    },
    {
      "slug": "digit-product-iteration-trajectories",
      "title": "digit product iteration trajectories",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}