{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-12T23:27:52Z",
    "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": "2026-10-06T07:03:09+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-Q777616",
    "registryId": "vr.tr.narcissistic-number",
    "name": "narcissistic number",
    "version": "0.2.0-wave.3",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.QTY"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q777616/",
  "model": {
    "registry_id": "vr.tr.narcissistic-number",
    "name": "narcissistic number",
    "purpose": "Let an agent define narcissistic numbers, list examples and the finite set in base 10, explain why the set is finite and base-dependent, and help test or generate them.",
    "definition": "A number that equals the sum of its own digits each raised to the power of the number of digits, such as 153, which equals 1 cubed plus 5 cubed plus 3 cubed, also called an Armstrong number or pluperfect digital invariant; in base 10 there are exactly 88 such numbers, the largest with 39 digits, and the concept is a recreational curiosity that depends on the base rather than a deep property of numbers.",
    "what_it_is_for": "Recreational number theory and programming exercises.",
    "affordances": [
      "define and list examples",
      "explain finiteness and base dependence",
      "help test or generate numbers",
      "distinguish related digit invariants"
    ],
    "distinguishing_features": [
      "Digit-power invariant",
      "Finite in any base",
      "Base dependent",
      "Recreational status"
    ],
    "appearance": "Not a visible object; integers such as 153, 370, 371 and 407.",
    "visual_identification": [
      "Sum of digits to the power of digit count equals the number",
      "88 in base 10, largest 39 digits",
      "Perfect digital invariants use a fixed power; happy numbers use iteration"
    ],
    "physical_properties": [
      {
        "quantity": "three-digit examples",
        "typical_range": "153, 370, 371, 407",
        "unit": "set",
        "note": ""
      },
      {
        "quantity": "count in base 10",
        "typical_range": "88",
        "unit": "count",
        "note": "including single digits"
      }
    ],
    "families_and_kinds": [
      "narcissistic numbers in base 10",
      "narcissistic numbers in other bases",
      "perfect digital invariants with fixed power",
      "related curiosities such as Dudeney and Kaprekar numbers"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "perfect digital invariant",
        "why": "in registry terms"
      },
      {
        "relation": "is a kind of",
        "target": "integer",
        "why": "a special class"
      },
      {
        "relation": "is related to",
        "target": "happy number",
        "why": "another digit-based class"
      },
      {
        "relation": "is studied in",
        "target": "recreational mathematics",
        "why": "the field"
      }
    ],
    "identifiers": [
      {
        "scheme": "OEIS",
        "value_or_pattern": "A005188",
        "note": "narcissistic numbers in base 10"
      }
    ],
    "standards_and_regulation": [
      "No regulation; the OEIS is the reference database"
    ],
    "failure_modes_and_hazards": [
      "Treating the property as mathematically deep",
      "Confusing with other digit invariants",
      "Overflow in naive computation of large cases"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Compute and check narcissistic numbers and explain the definition.",
        "Cite the full list from recognised integer sequence references."
      ],
      "must_not": [
        "State a wrong count or a wrong largest member without checking a source.",
        "Confuse the term with narcissism as a personality trait.",
        "Fabricate properties or proofs."
      ],
      "requires_human": [
        "Publishing new claims about the sequence."
      ]
    },
    "ethics": {
      "considerations": [
        "Recreational maths builds interest, and errors erode trust.",
        "Using a clinical-sounding name for a number should not trivialise the personality disorder."
      ],
      "affected_parties": [
        "Learners",
        "Puzzle and maths readers",
        "Researchers"
      ]
    },
    "owners": {
      "steward": "Nobody owns a number; it is held in common.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q777616: narcissistic number",
      "url": "https://www.wikidata.org/wiki/Q777616",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Narcissistic number",
      "url": "https://en.wikipedia.org/wiki/Narcissistic_number",
      "url_status": "live",
      "what_it_supports": "general description of the item",
      "checked_by": "wikidata-api sitelink"
    }
  ],
  "structure": {
    "bundles": [
      {
        "id": "define",
        "name": "Define",
        "description": "What narcissistic numbers are.",
        "rationale": "Definition.",
        "layers": [
          {
            "id": "definition",
            "name": "Definition",
            "description": "Definition and examples.",
            "findings": [
              {
                "id": "definition-finding",
                "name": "Definition",
                "description": "Definition.",
                "questions": [
                  {
                    "text": "What is a narcissistic number, and what are the examples in base 10?",
                    "kind": "definition"
                  },
                  {
                    "text": "Is the question about narcissistic numbers or another digit-based class?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "finite",
            "name": "Finite",
            "description": "Why the set is finite.",
            "findings": [
              {
                "id": "finite-finding",
                "name": "Finite",
                "description": "Finite.",
                "questions": [
                  {
                    "text": "Why are there finitely many narcissistic numbers in any base, and how is the bound found?",
                    "kind": "definition"
                  },
                  {
                    "text": "Which entry fits perfect digital invariant?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "compute",
        "name": "Compute",
        "description": "Testing and generating.",
        "rationale": "Computation.",
        "layers": [
          {
            "id": "test",
            "name": "Test",
            "description": "Testing a number.",
            "findings": [
              {
                "id": "test-finding",
                "name": "Test",
                "description": "Test.",
                "questions": [
                  {
                    "text": "How is a number tested for the property, and how are all such numbers generated?",
                    "kind": "action"
                  },
                  {
                    "text": "Is the number in question narcissistic?",
                    "kind": "measurement"
                  }
                ]
              }
            ]
          },
          {
            "id": "programming",
            "name": "Programming",
            "description": "Programming exercise.",
            "findings": [
              {
                "id": "programming-finding",
                "name": "Programming",
                "description": "Programming.",
                "questions": [
                  {
                    "text": "Why are Armstrong numbers a common programming exercise, and what pitfalls arise?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which references are standard?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "theory",
        "name": "Theory",
        "description": "Related classes.",
        "rationale": "Theory.",
        "layers": [
          {
            "id": "bases",
            "name": "Bases",
            "description": "Other bases.",
            "findings": [
              {
                "id": "bases-finding",
                "name": "Bases",
                "description": "Bases.",
                "questions": [
                  {
                    "text": "How do narcissistic numbers differ across bases?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which sources are cited?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "related",
            "name": "Related",
            "description": "Related curiosities.",
            "findings": [
              {
                "id": "related-finding",
                "name": "Related",
                "description": "Related.",
                "questions": [
                  {
                    "text": "How do happy, Kaprekar, Dudeney and other digit-based numbers relate?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits the specific class?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "context",
        "name": "Context",
        "description": "History and status.",
        "rationale": "Context.",
        "layers": [
          {
            "id": "history",
            "name": "History",
            "description": "History.",
            "findings": [
              {
                "id": "history-finding",
                "name": "History",
                "description": "History.",
                "questions": [
                  {
                    "text": "Who studied these numbers, and where does the name Armstrong come from?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits recreational mathematics?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "status",
            "name": "Status",
            "description": "Mathematical status.",
            "findings": [
              {
                "id": "status-finding",
                "name": "Status",
                "description": "Status.",
                "questions": [
                  {
                    "text": "Why do mathematicians regard the property as a curiosity, with positions attributed?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Is the presentation neutral?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Should perfect digital invariant be the primary entry?",
    "How should the OEIS be linked?",
    "How should base-dependent sets be recorded?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}