{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-13T02:58:53Z",
    "providers": [
      "Claude"
    ],
    "breadth": "written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify",
    "pass": 2,
    "wave": 3,
    "engine": "claude",
    "enrichment": {
      "pass": 3,
      "engine": "claude",
      "producedAt": "2026-10-06T10:00:00Z",
      "ingestedAt": "2026-10-06T07:04:52+00:00",
      "fields": [
        "agent_conduct",
        "ethics",
        "owners"
      ]
    },
    "gate": {
      "passed": true,
      "version": "1.0",
      "at": "2026-10-06T19:51:57+00:00",
      "evidence": [
        "completeness 1.00",
        "sense: Wikidata description",
        "2 live sources",
        "review by codex: pass"
      ]
    }
  },
  "metaModel": {
    "id": "THING-Q2297602",
    "registryId": "vr.tr.integer-sequence",
    "name": "integer sequence",
    "version": "0.2.0-wave.3",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.QLT"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q2297602/",
  "model": {
    "registry_id": "vr.tr.integer-sequence",
    "name": "integer sequence",
    "purpose": "Let an agent explain integer sequences and how they are defined, relay notable examples and the OEIS from mathematical references, describe their uses across mathematics, and route to entries for specific sequences.",
    "definition": "An ordered list of integers, finite or infinite, defined by a formula, a recurrence, a property of its members or a construction, such as the primes, the Fibonacci numbers, degree sequences of graphs, Goodstein sequences that eventually reach zero despite explosive growth, Hofstadter sequences defined by nested recurrences, Piatetski-Shapiro sequences of floor functions of powers, and the Sindel sequence of the Prague astronomical clock; integer sequences are catalogued in the On-Line Encyclopedia of Integer Sequences.",
    "what_it_is_for": "Not applicable; a mathematical concept.",
    "affordances": [
      "explain definitions",
      "relay notable examples",
      "describe the OEIS",
      "route to specific sequences"
    ],
    "distinguishing_features": [
      "Ordered integers",
      "Definition by rule",
      "Catalogued in OEIS",
      "Cross-mathematical role"
    ],
    "appearance": "Not a visible object; lists of integers.",
    "visual_identification": [
      "Ordered lists of integers",
      "Primes, Fibonacci, Goodstein, Hofstadter, Piatetski-Shapiro, Sindel and degree sequences",
      "Real sequences and series are broader; a set of integers is unordered"
    ],
    "physical_properties": [
      {
        "quantity": "OEIS entries",
        "typical_range": "over 380000",
        "unit": "count",
        "note": "2025"
      },
      {
        "quantity": "OEIS founded",
        "typical_range": "1964 as a card file, online 1996",
        "unit": "year",
        "note": "Neil Sloane"
      }
    ],
    "families_and_kinds": [
      "sequences defined by formulas",
      "recurrence sequences such as Fibonacci and Hofstadter sequences",
      "sequences defined by properties such as primes and perfect numbers",
      "combinatorial sequences such as degree sequences",
      "sequences from logic such as Goodstein sequences",
      "number-theoretic sequences such as Piatetski-Shapiro sequences",
      "sequences from applications such as the Sindel sequence"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "number sequence",
        "why": "in registry terms"
      },
      {
        "relation": "is catalogued in",
        "target": "OEIS",
        "why": "the On-Line Encyclopedia of Integer Sequences"
      },
      {
        "relation": "includes",
        "target": "Fibonacci sequence",
        "why": "as a classic example"
      },
      {
        "relation": "is studied in",
        "target": "number theory",
        "why": "and combinatorics"
      }
    ],
    "identifiers": [],
    "standards_and_regulation": [
      "No regulation; OEIS editorial standards for entries"
    ],
    "failure_modes_and_hazards": [
      "Guessing rules from few terms",
      "Confusing sequences with sets or series",
      "Mislabelled sequences"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Compute, list and check terms of an integer sequence from its definition.",
        "Cite a sequence with its standard reference and give its first terms."
      ],
      "must_not": [
        "Claim a pattern holds for all terms on the evidence of a few computed ones.",
        "Present a conjectured formula as proved.",
        "Fabricate terms, references or catalogue entries for a sequence.",
        "Confuse two sequences that share initial terms."
      ],
      "requires_human": [
        "Publishing a new sequence or a correction to a shared reference catalogue."
      ]
    },
    "ethics": {
      "considerations": [
        "Reference catalogues of sequences are relied on by researchers; errors spread widely.",
        "Credit for discovering sequences and results belongs to those who found them."
      ],
      "affected_parties": [
        "Mathematicians and students",
        "Maintainers of reference catalogues"
      ]
    },
    "owners": {
      "steward": "Nobody owns the concept; editors of reference catalogues answer for their entries.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q2297602: integer sequence",
      "url": "https://www.wikidata.org/wiki/Q2297602",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Integer sequence",
      "url": "https://en.wikipedia.org/wiki/Integer_sequence",
      "url_status": "live",
      "what_it_supports": "general description of the item",
      "checked_by": "wikidata-api sitelink"
    }
  ],
  "structure": {
    "bundles": [
      {
        "id": "understand",
        "name": "Understand",
        "description": "What an integer sequence is.",
        "rationale": "Mathematics.",
        "layers": [
          {
            "id": "definition",
            "name": "Definition",
            "description": "Definition.",
            "findings": [
              {
                "id": "definition-finding",
                "name": "Definition",
                "description": "Definition.",
                "questions": [
                  {
                    "text": "What is an integer sequence, and how are sequences defined by formulas, recurrences and properties?",
                    "kind": "definition"
                  },
                  {
                    "text": "Is the question about integer sequences in general or a specific sequence?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "examples",
            "name": "Examples",
            "description": "Notable examples.",
            "findings": [
              {
                "id": "examples-finding",
                "name": "Examples",
                "description": "Examples.",
                "questions": [
                  {
                    "text": "What are Goodstein, Hofstadter, Piatetski-Shapiro and Sindel sequences and degree sequences?",
                    "kind": "definition"
                  },
                  {
                    "text": "Which entry fits the specific sequence?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "explore",
        "name": "Explore",
        "description": "Exploring sequences.",
        "rationale": "Practice.",
        "layers": [
          {
            "id": "oeis",
            "name": "OEIS",
            "description": "The OEIS.",
            "findings": [
              {
                "id": "oeis-finding",
                "name": "OEIS",
                "description": "OEIS.",
                "questions": [
                  {
                    "text": "How does the OEIS work, and how can a sequence be looked up or submitted?",
                    "kind": "action"
                  },
                  {
                    "text": "Which references are standard?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "analysis",
            "name": "Analysis",
            "description": "Analysing sequences.",
            "findings": [
              {
                "id": "analysis-finding",
                "name": "Analysis",
                "description": "Analysis.",
                "questions": [
                  {
                    "text": "How are growth rates, generating functions and recurrences used to analyse sequences?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits generating function?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "apply",
        "name": "Apply",
        "description": "Applications.",
        "rationale": "Mathematics.",
        "layers": [
          {
            "id": "mathematics",
            "name": "Mathematics",
            "description": "In mathematics.",
            "findings": [
              {
                "id": "mathematics-finding",
                "name": "Mathematics",
                "description": "Mathematics.",
                "questions": [
                  {
                    "text": "How do integer sequences appear in number theory, combinatorics, logic and graph theory?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which sources are cited?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "applications",
            "name": "Applications",
            "description": "Beyond mathematics.",
            "findings": [
              {
                "id": "applications-finding",
                "name": "Applications",
                "description": "Applications.",
                "questions": [
                  {
                    "text": "How are integer sequences used in computing, physics and devices such as the Prague astronomical clock?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits the specific application?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "context",
        "name": "Context",
        "description": "History and culture.",
        "rationale": "Context.",
        "layers": [
          {
            "id": "history",
            "name": "History",
            "description": "History.",
            "findings": [
              {
                "id": "history-finding",
                "name": "History",
                "description": "History.",
                "questions": [
                  {
                    "text": "How have integer sequences been studied from antiquity to the OEIS?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits the history of number theory?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "culture",
            "name": "Culture",
            "description": "Puzzles and culture.",
            "findings": [
              {
                "id": "culture-finding",
                "name": "Culture",
                "description": "Culture.",
                "questions": [
                  {
                    "text": "How do integer sequences appear in puzzles, tests and popular mathematics?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits recreational mathematics?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Should notable sequences be separate entries?",
    "How should the OEIS be linked?",
    "The registry entry has merged aliases naming specific sequences; should they be split off?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}