{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R225",
  "content_hash": null,
  "slug": "dpi-claim-oeis-identification",
  "type": "claim",
  "title": "The map and principal orbit have OEIS records",
  "summary": "OEIS A063114 records the map, while A063108 records the orbit of 1.",
  "relevance": "For Merging of orbits under adding the product of nonzero digits, record dpi-claim-oeis-identification (“The map and principal orbit have OEIS records”) records a bound, answer, status fact, or structural consequence. The record states: OEIS A063114 records the map, while A063108 records the orbit of 1.",
  "relevance_source": "recorded",
  "body": "OEIS A063114 is the transformation \\(n\\mapsto n+p(n)\\). OEIS A063108 is its orbit beginning at 1, and A096287 records joining times for individual starts. These records cite Loomis and preserve the conjectural status of universal joining.",
  "status": "established",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "universal",
    "statement": "the map and the orbit beginning at 1"
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://oeis.org/A063108",
      "locator": "OEIS A063108, A063114, and A096287"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://oeis.org/A063108",
    "locator": "OEIS A063108, A063114, and A096287"
  },
  "models": [],
  "relations": [
    {
      "slug": "R224",
      "title": "Loomis conjectured that every orbit joins the orbit of 1",
      "object_type": "claim",
      "relation": "supports",
      "direction": "outgoing"
    },
    {
      "slug": "digit-product-iteration-trajectories",
      "title": "digit product iteration trajectories",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}