{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-12T20:49:56Z",
    "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": "2026-10-06T07:00:59+00:00",
      "fields": [
        "agent_conduct",
        "ethics",
        "owners"
      ]
    },
    "gate": {
      "passed": true,
      "version": "1.0",
      "at": "2026-10-06T19:52:02+00:00",
      "evidence": [
        "completeness 1.00",
        "sense: Wikidata description",
        "2 live sources",
        "review by codex: pass"
      ]
    }
  },
  "metaModel": {
    "id": "THING-Q854503",
    "registryId": "vr.tr.kaprekar-s-constant",
    "name": "Kaprekar's constant",
    "version": "0.2.0-wave.3",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.QTY"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q854503/",
  "model": {
    "registry_id": "vr.tr.kaprekar-s-constant",
    "name": "Kaprekar's constant",
    "purpose": "Let an agent define the Kaprekar routine and constant precisely, run the routine on a given number, state the conditions and the corresponding constants for other digit lengths, and distinguish the constant from Kaprekar numbers.",
    "definition": "The number 6174, the fixed point of the Kaprekar routine on four-digit numbers: take any four-digit number with at least two different digits, arrange its digits in descending and ascending order, subtract the smaller from the larger, and repeat; the process reaches 6174 within at most seven steps and then stays there, a result found by D. R. Kaprekar in 1949.",
    "what_it_is_for": "Not for anything; a curiosity in recreational mathematics.",
    "affordances": [
      "run the routine on a given number",
      "state the conditions and step bound",
      "relay constants for other digit lengths",
      "distinguish the constant from Kaprekar numbers"
    ],
    "distinguishing_features": [
      "Fixed point of a digit-sorting subtraction routine",
      "Universal for four-digit inputs with two distinct digits",
      "Bounded number of steps",
      "No single constant for most other lengths"
    ],
    "appearance": "Not visible; the number 6174.",
    "visual_identification": [
      "Fixed point of the four-digit Kaprekar routine",
      "Reached within seven steps from any valid start",
      "Kaprekar numbers such as 45 are a different notion"
    ],
    "physical_properties": [
      {
        "quantity": "value",
        "typical_range": "6174",
        "unit": "integer",
        "note": ""
      },
      {
        "quantity": "maximum steps",
        "typical_range": "7",
        "unit": "iterations",
        "note": "for four-digit inputs"
      },
      {
        "quantity": "three-digit constant",
        "typical_range": "495",
        "unit": "integer",
        "note": ""
      }
    ],
    "families_and_kinds": [
      "the four-digit constant 6174",
      "the three-digit constant 495",
      "cycles rather than constants for other digit lengths",
      "Kaprekar routine in other bases"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "fixed point",
        "why": "of the Kaprekar routine"
      },
      {
        "relation": "is produced by",
        "target": "Kaprekar routine",
        "why": "the procedure"
      },
      {
        "relation": "is confused with",
        "target": "Kaprekar number",
        "why": "a different property"
      },
      {
        "relation": "is listed in",
        "target": "On-Line Encyclopedia of Integer Sequences",
        "why": "sequence A099009 for fixed points"
      }
    ],
    "identifiers": [
      {
        "scheme": "OEIS",
        "value_or_pattern": "A099009",
        "note": "fixed points of the Kaprekar map"
      }
    ],
    "standards_and_regulation": [
      "No regulation; definitions follow the literature"
    ],
    "failure_modes_and_hazards": [
      "Forgetting the two-distinct-digit condition",
      "Dropping leading zeros incorrectly",
      "Confusing with Kaprekar numbers"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Run the Kaprekar routine on a four-digit number and show each step.",
        "Explain why 6174 is the fixed point."
      ],
      "must_not": [
        "Forget the condition that the number has at least two different digits.",
        "Drop leading zeros in a way that breaks the routine.",
        "Confuse Kaprekar's constant with Kaprekar numbers.",
        "Present the constant as having uses it does not have."
      ],
      "requires_human": [
        "Using the routine in assessed teaching where errors carry marks."
      ]
    },
    "ethics": {
      "considerations": [
        "Mathematical curiosities are often padded with false claims; accuracy keeps trust."
      ],
      "affected_parties": [
        "Learners and puzzle readers",
        "Teachers"
      ]
    },
    "owners": {
      "steward": "Nobody owns the concept; it belongs to the shared body of mathematics.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q854503: Kaprekar's constant",
      "url": "https://www.wikidata.org/wiki/Q854503",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Kaprekar's constant",
      "url": "https://en.wikipedia.org/wiki/Kaprekar%27s_constant",
      "url_status": "live",
      "what_it_supports": "general description of the item",
      "checked_by": "wikidata-api sitelink"
    }
  ],
  "structure": {
    "bundles": [
      {
        "id": "define",
        "name": "Define",
        "description": "The routine and constant.",
        "rationale": "Precision.",
        "layers": [
          {
            "id": "routine",
            "name": "Routine",
            "description": "The routine.",
            "findings": [
              {
                "id": "routine-finding",
                "name": "Routine",
                "description": "Routine.",
                "questions": [
                  {
                    "text": "How does the Kaprekar routine work, and what inputs are allowed?",
                    "kind": "definition"
                  },
                  {
                    "text": "Is the question about the constant 6174 or about Kaprekar numbers?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "constant",
            "name": "Constant",
            "description": "The constant.",
            "findings": [
              {
                "id": "constant-finding",
                "name": "Constant",
                "description": "Constant.",
                "questions": [
                  {
                    "text": "Why is 6174 a fixed point, and why does every valid input reach it?",
                    "kind": "definition"
                  },
                  {
                    "text": "Which entry fits fixed points generally?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "compute",
        "name": "Compute",
        "description": "Running the routine.",
        "rationale": "Computation.",
        "layers": [
          {
            "id": "run",
            "name": "Run",
            "description": "Running.",
            "findings": [
              {
                "id": "run-finding",
                "name": "Run",
                "description": "Run.",
                "questions": [
                  {
                    "text": "What sequence does a given number produce, and in how many steps?",
                    "kind": "action"
                  },
                  {
                    "text": "What is the result for the number in question?",
                    "kind": "measurement"
                  }
                ]
              }
            ]
          },
          {
            "id": "bound",
            "name": "Bound",
            "description": "Step bound.",
            "findings": [
              {
                "id": "bound-finding",
                "name": "Bound",
                "description": "Bound.",
                "questions": [
                  {
                    "text": "How is the seven-step bound established?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which references are standard?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "generalise",
        "name": "Generalise",
        "description": "Other lengths and bases.",
        "rationale": "Theory.",
        "layers": [
          {
            "id": "lengths",
            "name": "Lengths",
            "description": "Other digit lengths.",
            "findings": [
              {
                "id": "lengths-finding",
                "name": "Lengths",
                "description": "Lengths.",
                "questions": [
                  {
                    "text": "What happens for three, five and more digits, and which produce constants or cycles?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits the three-digit constant?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "bases",
            "name": "Bases",
            "description": "Other bases.",
            "findings": [
              {
                "id": "bases-finding",
                "name": "Bases",
                "description": "Bases.",
                "questions": [
                  {
                    "text": "What is known about the routine in other bases?",
                    "kind": "provenance"
                  },
                  {
                    "text": "What is proven versus computed?",
                    "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 he find the constant?",
                    "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 is the constant used in teaching and puzzles?",
                    "kind": "action"
                  },
                  {
                    "text": "Which misconceptions arise?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Should the Kaprekar routine be a separate entry?",
    "How should OEIS entries be linked?",
    "How should results for other bases be recorded?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}