{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.kaprekar-s-constant","code":"thing-q854503","url":"https://ver.cy/models/thing/q854503/","name":"Kaprekar's constant","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":"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.","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.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["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"],"structure":{"bundles":[{"id":"define","name":"Define","description":"The routine and constant.","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.","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.","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.","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"}]}]}]}]},"agentConduct":{"may":["Run the Kaprekar routine on a four-digit number and show each step.","Explain why 6174 is the fixed point."],"mustNot":["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."],"requiresHuman":["Using the routine in assessed teaching where errors carry marks."]},"ethics":{"considerations":["Mathematical curiosities are often padded with false claims; accuracy keeps trust."],"affectedParties":["Learners and puzzle readers","Teachers"]},"owners":{"steward":"Nobody owns the concept; it belongs to the shared body of mathematics.","roles":[],"masterSystems":[]},"relations":[{"target":"Q217608","type":"parent","note":"registry parent class"},{"target":"Q28920052","type":"parent","note":"registry parent class"},{"target":"fixed point","type":"related","note":"of the Kaprekar routine"},{"target":"Kaprekar routine","type":"related","note":"the procedure"},{"target":"Kaprekar number","type":"related","note":"a different property"},{"target":"On-Line Encyclopedia of Integer Sequences","type":"related","note":"sequence A099009 for fixed points"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.kaprekar-s-constant","Wikidata: Q854503 (https://www.wikidata.org/wiki/Q854503)","OEIS: A099009 fixed points of the Kaprekar map"]},"properties":{"applicability":"not-applicable","items":["value: 6174 integer","maximum steps: 7 iterations - for four-digit inputs","three-digit constant: 495 integer"]},"recognition":{"applicability":"optional","items":["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","Not visible; the number 6174."]},"capabilities":{"applicability":"required","items":["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"]},"hazards":{"applicability":"required","items":["Forgetting the two-distinct-digit condition","Dropping leading zeros incorrectly","Confusing with Kaprekar numbers"]},"interfaces":{"applicability":"required","items":["No regulation; definitions follow the literature"]},"context":{"applicability":"required","items":["Not for anything; a curiosity in recreational mathematics.","the four-digit constant 6174","the three-digit constant 495","cycles rather than constants for other digit lengths","Kaprekar routine in other bases"]}},"sources":[{"title":"Wikidata item Q854503: Kaprekar's constant","url":"https://www.wikidata.org/wiki/Q854503","note":"identity and sense of the item"},{"title":"Wikipedia: Kaprekar's constant","url":"https://en.wikipedia.org/wiki/Kaprekar%27s_constant","note":"general description of the item"}],"openQuestions":["Should the Kaprekar routine be a separate entry?","How should OEIS entries be linked?","How should results for other bases be recorded?"],"resources":{"spec":"/models/things/publications/thing-q854503/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q854503/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-12T20:49:56Z","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}}