{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.kaprekar-number","code":"thing-q1478274","url":"https://ver.cy/models/thing/q1478274/","name":"Kaprekar 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 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.","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.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["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"],"structure":{"bundles":[{"id":"define","name":"Define","description":"The definition.","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.","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.","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.","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"}]}]}]}]},"agentConduct":{"may":["Explain Kaprekar numbers with examples and check whether a number is one.","Generate lists in a given base and show the working."],"mustNot":["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."],"requiresHuman":["Publishing new results about them."]},"ethics":{"considerations":["Correct attribution credits a self-taught mathematician.","Numerology can mislead people into harmful decisions."],"affectedParties":["Students","Mathematicians"]},"owners":{"steward":"Nobody: a mathematical concept held in common.","roles":[],"masterSystems":[]},"relations":[{"target":"Q28920052","type":"parent","note":"registry parent class"},{"target":"non-negative integer","type":"related","note":"a property of integers"},{"target":"Kaprekar constant","type":"related","note":"a different object named after the same person"},{"target":"On-Line Encyclopedia of Integer Sequences","type":"related","note":"sequence A006886"},{"target":"recreational mathematics","type":"related","note":"the field"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.kaprekar-number","Wikidata: Q1478274 (https://www.wikidata.org/wiki/Q1478274)","OEIS: A006886 sequence of Kaprekar numbers in base ten"]},"properties":{"applicability":"not-applicable","items":["smallest examples in base ten: 1, 9, 45, 55, 99 integers - with the convention that the right part is nonzero"]},"recognition":{"applicability":"optional","items":["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","Not visible; a property of integers."]},"capabilities":{"applicability":"required","items":["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"]},"hazards":{"applicability":"required","items":["Inconsistent conventions about zero parts","Confusing the number with the routine","Base-dependent claims stated as absolute"]},"interfaces":{"applicability":"required","items":["No regulation; definitions follow the literature and the OEIS"]},"context":{"applicability":"required","items":["Not for anything; a curiosity in number theory.","Kaprekar numbers in base ten","Kaprekar numbers in other bases","generalised Kaprekar numbers for higher powers","related: the Kaprekar routine and constant"]}},"sources":[{"title":"Wikidata item Q1478274: Kaprekar number","url":"https://www.wikidata.org/wiki/Q1478274","note":"identity and sense of the item"},{"title":"Wikipedia: Kaprekar number","url":"https://en.wikipedia.org/wiki/Kaprekar_number","note":"general description of the item"}],"openQuestions":["Which convention on zero parts should the entry adopt?","How should OEIS entries be linked?","Should generalisations be separate entries?"],"resources":{"spec":"/models/things/publications/thing-q1478274/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q1478274/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-12T19:51:39Z","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 2026-10-06T19:51:54+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}}