{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-12T19:51:39Z",
    "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": "2026-10-06T00:10:00Z",
      "ingestedAt": "2026-10-05T20:57:14+00:00",
      "fields": [
        "agent_conduct",
        "ethics",
        "owners"
      ]
    },
    "gate": {
      "passed": true,
      "version": "1.0",
      "at": "2026-10-06T19:51:54+00:00",
      "evidence": [
        "completeness 1.00",
        "sense: Wikidata description",
        "2 live sources",
        "review by codex: pass"
      ]
    }
  },
  "metaModel": {
    "id": "THING-Q1478274",
    "registryId": "vr.tr.kaprekar-number",
    "name": "Kaprekar number",
    "version": "0.2.0-wave.3",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.QTY"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q1478274/",
  "model": {
    "registry_id": "vr.tr.kaprekar-number",
    "name": "Kaprekar number",
    "purpose": "Let an agent define Kaprekar numbers precisely, test whether a number is one, list the small examples, relate them to the Kaprekar routine and constant, and point to sequence references.",
    "definition": "A non-negative integer whose square, written in a given base, can be split into two parts that add up to the original number, such as 45, since 45 squared is 2025 and 20 plus 25 is 45; named after the Indian mathematician D. R. Kaprekar and studied in recreational number theory.",
    "what_it_is_for": "Not for anything; a curiosity in number theory.",
    "affordances": [
      "test whether an integer is a Kaprekar number",
      "list examples in base ten and other bases",
      "explain the definition and edge cases",
      "distinguish it from the Kaprekar routine and constant 6174"
    ],
    "distinguishing_features": [
      "Defined by a splitting of the square",
      "Depends on the base",
      "Conventions differ on zero parts and on 1",
      "Named after Kaprekar, like the unrelated routine"
    ],
    "appearance": "Not visible; a property of integers.",
    "visual_identification": [
      "Square splits into two parts summing to the number",
      "Examples 1, 9, 45, 55, 99, 297, 703, 999",
      "The Kaprekar constant 6174 comes from a different procedure"
    ],
    "physical_properties": [
      {
        "quantity": "smallest examples in base ten",
        "typical_range": "1, 9, 45, 55, 99",
        "unit": "integers",
        "note": "with the convention that the right part is nonzero"
      }
    ],
    "families_and_kinds": [
      "Kaprekar numbers in base ten",
      "Kaprekar numbers in other bases",
      "generalised Kaprekar numbers for higher powers",
      "related: the Kaprekar routine and constant"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "non-negative integer",
        "why": "a property of integers"
      },
      {
        "relation": "is confused with",
        "target": "Kaprekar constant",
        "why": "a different object named after the same person"
      },
      {
        "relation": "is listed in",
        "target": "On-Line Encyclopedia of Integer Sequences",
        "why": "sequence A006886"
      },
      {
        "relation": "is studied by",
        "target": "recreational mathematics",
        "why": "the field"
      }
    ],
    "identifiers": [
      {
        "scheme": "OEIS",
        "value_or_pattern": "A006886",
        "note": "sequence of Kaprekar numbers in base ten"
      }
    ],
    "standards_and_regulation": [
      "No regulation; definitions follow the literature and the OEIS"
    ],
    "failure_modes_and_hazards": [
      "Inconsistent conventions about zero parts",
      "Confusing the number with the routine",
      "Base-dependent claims stated as absolute"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Explain Kaprekar numbers with examples and check whether a number is one.",
        "Generate lists in a given base and show the working."
      ],
      "must_not": [
        "Present a number as a Kaprekar number without checking the definition in the stated base.",
        "Confuse Kaprekar numbers with Kaprekar's routine or constant.",
        "Attach mystical or predictive meaning to these numbers as fact."
      ],
      "requires_human": [
        "Publishing new results about them."
      ]
    },
    "ethics": {
      "considerations": [
        "Correct attribution credits a self-taught mathematician.",
        "Numerology can mislead people into harmful decisions."
      ],
      "affected_parties": [
        "Students",
        "Mathematicians"
      ]
    },
    "owners": {
      "steward": "Nobody: a mathematical concept held in common.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q1478274: Kaprekar number",
      "url": "https://www.wikidata.org/wiki/Q1478274",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Kaprekar number",
      "url": "https://en.wikipedia.org/wiki/Kaprekar_number",
      "url_status": "live",
      "what_it_supports": "general description of the item",
      "checked_by": "wikidata-api sitelink"
    }
  ],
  "structure": {
    "bundles": [
      {
        "id": "define",
        "name": "Define",
        "description": "The definition.",
        "rationale": "Precision.",
        "layers": [
          {
            "id": "definition",
            "name": "Definition",
            "description": "Definition.",
            "findings": [
              {
                "id": "definition-finding",
                "name": "Definition",
                "description": "Definition.",
                "questions": [
                  {
                    "text": "What exactly makes an integer a Kaprekar number, and how are zero parts and the number 1 handled?",
                    "kind": "definition"
                  },
                  {
                    "text": "Is the question about Kaprekar numbers or about the Kaprekar routine?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "base",
            "name": "Base",
            "description": "Base dependence.",
            "findings": [
              {
                "id": "base-finding",
                "name": "Base",
                "description": "Base.",
                "questions": [
                  {
                    "text": "How does the property depend on the base?",
                    "kind": "definition"
                  },
                  {
                    "text": "Which base is assumed?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "compute",
        "name": "Compute",
        "description": "Testing and listing.",
        "rationale": "Computation.",
        "layers": [
          {
            "id": "test",
            "name": "Test",
            "description": "Testing.",
            "findings": [
              {
                "id": "test-finding",
                "name": "Test",
                "description": "Test.",
                "questions": [
                  {
                    "text": "How is a given integer tested, and what is the result for the number in question?",
                    "kind": "action"
                  },
                  {
                    "text": "What are the examples below a given bound?",
                    "kind": "measurement"
                  }
                ]
              }
            ]
          },
          {
            "id": "sequence",
            "name": "Sequence",
            "description": "The sequence.",
            "findings": [
              {
                "id": "sequence-finding",
                "name": "Sequence",
                "description": "Sequence.",
                "questions": [
                  {
                    "text": "Where is the sequence recorded, and what is known about its growth?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits integer sequences?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "theory",
        "name": "Theory",
        "description": "Properties.",
        "rationale": "Theory.",
        "layers": [
          {
            "id": "properties",
            "name": "Properties",
            "description": "Known results.",
            "findings": [
              {
                "id": "properties-finding",
                "name": "Properties",
                "description": "Properties.",
                "questions": [
                  {
                    "text": "What is known about the structure of Kaprekar numbers, such as their relation to unitary divisors of powers of ten?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which references are standard?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "generalise",
            "name": "Generalise",
            "description": "Generalisations.",
            "findings": [
              {
                "id": "generalise-finding",
                "name": "Generalise",
                "description": "Generalise.",
                "questions": [
                  {
                    "text": "What generalisations exist to other powers and splittings?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Should a generalisation be a separate entry?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "context",
        "name": "Context",
        "description": "History and teaching.",
        "rationale": "Context.",
        "layers": [
          {
            "id": "history",
            "name": "History",
            "description": "Kaprekar.",
            "findings": [
              {
                "id": "history-finding",
                "name": "History",
                "description": "History.",
                "questions": [
                  {
                    "text": "Who was Kaprekar, and how did the numbers get their name?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits the person?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "teach",
            "name": "Teach",
            "description": "Teaching.",
            "findings": [
              {
                "id": "teach-finding",
                "name": "Teach",
                "description": "Teaching.",
                "questions": [
                  {
                    "text": "How are Kaprekar numbers used in teaching and puzzles?",
                    "kind": "action"
                  },
                  {
                    "text": "Which misconceptions arise?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Which convention on zero parts should the entry adopt?",
    "How should OEIS entries be linked?",
    "Should generalisations be separate entries?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}