{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.narcissistic-number","code":"thing-q777616","url":"https://ver.cy/models/thing/q777616/","name":"narcissistic number","alternateNames":[],"kind":"thing","status":"published","version":"0.2.0-wave.3","language":"en","classifiers":{"family":"Thing Registry","category":"Cross-cutting context","entryKind":"thing","plane":"XCT","domain":["XCT.QTY"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"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.","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.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Digit-power invariant","Finite in any base","Base dependent","Recreational status"],"structure":{"bundles":[{"id":"define","name":"Define","description":"What narcissistic numbers are.","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.","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.","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.","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"}]}]}]}]},"agentConduct":{"may":["Compute and check narcissistic numbers and explain the definition.","Cite the full list from recognised integer sequence references."],"mustNot":["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."],"requiresHuman":["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."],"affectedParties":["Learners","Puzzle and maths readers","Researchers"]},"owners":{"steward":"Nobody owns a number; it is held in common.","roles":[],"masterSystems":[]},"relations":[{"target":"Q85792806","type":"parent","note":"registry parent class"},{"target":"perfect digital invariant","type":"related","note":"in registry terms"},{"target":"integer","type":"related","note":"a special class"},{"target":"happy number","type":"related","note":"another digit-based class"},{"target":"recreational mathematics","type":"related","note":"the field"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.narcissistic-number","Wikidata: Q777616 (https://www.wikidata.org/wiki/Q777616)","OEIS: A005188 narcissistic numbers in base 10"]},"properties":{"applicability":"not-applicable","items":["three-digit examples: 153, 370, 371, 407 set","count in base 10: 88 count - including single digits"]},"recognition":{"applicability":"optional","items":["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","Not a visible object; integers such as 153, 370, 371 and 407."]},"capabilities":{"applicability":"required","items":["define and list examples","explain finiteness and base dependence","help test or generate numbers","distinguish related digit invariants"]},"hazards":{"applicability":"required","items":["Treating the property as mathematically deep","Confusing with other digit invariants","Overflow in naive computation of large cases"]},"interfaces":{"applicability":"required","items":["No regulation; the OEIS is the reference database"]},"context":{"applicability":"required","items":["Recreational number theory and programming exercises.","narcissistic numbers in base 10","narcissistic numbers in other bases","perfect digital invariants with fixed power","related curiosities such as Dudeney and Kaprekar numbers"]}},"sources":[{"title":"Wikidata item Q777616: narcissistic number","url":"https://www.wikidata.org/wiki/Q777616","note":"identity and sense of the item"},{"title":"Wikipedia: Narcissistic number","url":"https://en.wikipedia.org/wiki/Narcissistic_number","note":"general description of the item"}],"openQuestions":["Should perfect digital invariant be the primary entry?","How should the OEIS be linked?","How should base-dependent sets be recorded?"],"resources":{"spec":"/models/things/publications/thing-q777616/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q777616/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-12T23:27:52Z","builder":"tools/build_cards.py@1.0.0"},"completeness":{"sections":{"classifiers":"filled","whatItIs":"filled","purpose":"filled","distinguishingFeatures":"filled","structure":"filled","agentConduct":"filled","ethics":"filled","owners":"filled","relations":"filled","interaction.identity":"filled","interaction.properties":"not-applicable","interaction.recognition":"filled","interaction.capabilities":"filled","interaction.hazards":"filled","interaction.interfaces":"filled","interaction.context":"filled","sources":"filled"},"notes":{"_gate":"Published through the thing publication gate 1.0 on 2026-10-06T19:52:02+00:00: completeness 1.00; sense: Wikidata description; 2 live sources; review by codex: pass","interaction.properties":"Plane XCT: no invented physical properties."},"score":1.0}}