{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R224",
  "content_hash": null,
  "slug": "dpi-claim-loomis-conjecture",
  "type": "claim",
  "title": "Loomis conjectured that every orbit joins the orbit of 1",
  "summary": "The published conjecture gives a single eventual trajectory, which is stronger than the candidate's finite-trajectory question.",
  "relevance": "For Merging of orbits under adding the product of nonzero digits, record dpi-claim-loomis-conjecture (“Loomis conjectured that every orbit joins the orbit of 1”) records a bound, answer, status fact, or structural consequence. The record states: The published conjecture gives a single eventual trajectory, which is stronger than the candidate's finite-trajectory question.",
  "relevance_source": "recorded",
  "body": "For \\(T(n)=n+p(n)\\), with zero digits omitted from the product, Paul Loomis conjectured that every positive starting value eventually enters the orbit beginning at 1. This exact map and conjecture appeared in his article on digit product sequences and on the companion page's section \"Sequences That Join.\" The candidate independently rediscovered a weaker consequence. The reviewed sources still describe universal joining as a conjecture.",
  "status": "conjectured",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "universal",
    "statement": "every positive starting value under the digit-product map"
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://plouffe.fr/OEIS/citations/itseq4.pdf",
      "locator": "Paul A. Loomis, An Introduction to Digit Product Sequences, Journal of Recreational Mathematics 32 (2003-2004), pages 147-151; companion page section III"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://plouffe.fr/OEIS/citations/itseq4.pdf",
    "locator": "Paul A. Loomis, An Introduction to Digit Product Sequences, Journal of Recreational Mathematics 32 (2003-2004), pages 147-151; companion page section III"
  },
  "relations": [
    {
      "slug": "R225",
      "title": "The map and principal orbit have OEIS records",
      "object_type": "claim",
      "relation": "supports",
      "direction": "incoming"
    },
    {
      "slug": "R222",
      "title": "Loomis reports a million-start joining check",
      "object_type": "artifact",
      "relation": "tests",
      "direction": "incoming"
    },
    {
      "slug": "R221",
      "title": "Sixty iterations leave 31 distinct endpoints",
      "object_type": "artifact",
      "relation": "tests",
      "direction": "incoming"
    },
    {
      "slug": "R223",
      "title": "Separate the finite-orbit question from Loomis's conjecture",
      "object_type": "attempt",
      "relation": "uses",
      "direction": "incoming"
    },
    {
      "slug": "digit-product-iteration-trajectories",
      "title": "digit product iteration trajectories",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}