{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R212",
  "content_hash": null,
  "slug": "dfb100-claim-oeis-identification",
  "type": "claim",
  "title": "OEIS already records the bounded maximum sequence",
  "summary": "A065677 is the same maximum; its inverse sequence places stopping time 13 at bound 44 and stopping time 14 at bound 105.",
  "relevance": "For Longest four-number Ducci trajectory in the 100 box, record dfb100-claim-oeis-identification (“OEIS already records the bounded maximum sequence”) records a bound, answer, status fact, or structural consequence. The record states: A065677 is the same maximum; its inverse sequence places stopping time 13 at bound 44 and stopping time 14 at bound 105.",
  "relevance_source": "recorded",
  "body": "OEIS A065677 defines \\(a(n)\\) as the maximal Ducci length among nonnegative quadruples whose entries are at most \\(n\\). This is the present problem with \\(n=100\\). Its inverse, A065678, records the least bound at which a given length occurs. The two relevant values are\n\\[\nA065678(13)=44,\\qquad A065678(14)=105.\n\\]\nIt follows that \\(A065677(100)=13\\). The independently computed values through bound 20 in the candidate record agree term for term with A065677.\n\nThe literature also explains the quotient used in the certificate. Behn, Kribs-Zaleta, and Ponomarenko treat translation, positive scaling, rotation, and reflection as equivalences and classify four-number longevity in a canonical two-dimensional region. The exhaustive computation here supplies the finite-box multiplicities and complete list of maximizers.",
  "status": "established",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "the maximum four-number Ducci stopping time for coordinate bounds through 100",
    "bounds": {
      "coordinate_bound": {
        "min": 0,
        "max": 100
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://oeis.org/A065677",
      "locator": "OEIS A065677, Maximal Diffy_length for quadruples of numbers <= n; inverse A065678; Behn, Kribs-Zaleta, and Ponomarenko, The Convergence of Difference Boxes, American Mathematical Monthly 112 (2005), 426-439, DOI 10.2307/30037493"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://oeis.org/A065677",
    "locator": "OEIS A065677, Maximal Diffy_length for quadruples of numbers <= n; inverse A065678; Behn, Kribs-Zaleta, and Ponomarenko, The Convergence of Difference Boxes, American Mathematical Monthly 112 (2005), 426-439, DOI 10.2307/30037493"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R211",
      "title": "The longest trajectory in the 100 box has 13 steps",
      "object_type": "claim",
      "relation": "supports",
      "direction": "outgoing"
    },
    {
      "slug": "ducci-four-box-100",
      "title": "ducci four box 100",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}