{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.highly-composite-number","code":"thing-q629958","url":"https://ver.cy/models/thing/q629958/","name":"highly composite number","alternateNames":["superior highly composite number"],"kind":"thing","status":"published","version":"0.2.0-wave.2","language":"en","classifiers":{"family":"Thing Registry","category":"Cross-cutting context","entryKind":"thing","plane":"XCT","domain":["XCT.QTY"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"A positive integer with more divisors than any smaller positive integer, such as 1, 2, 4, 6, 12, 24, 36, 48, 60 and 120, studied by Ramanujan, together with the related superior highly composite numbers that maximise a scaled divisor count; highly composite numbers have prime factorisations with non-increasing exponents over consecutive primes, explain the historical choice of numbers like 12 and 60 in measurement, and appear in number theory and computing.","purpose":"Let an agent explain highly composite numbers and their properties, test and generate them, describe superior highly composite numbers, and relate them to history and applications.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Record divisor count","Structured factorisation","Ramanujan study","Practical origins"],"structure":{"bundles":[{"id":"understand","name":"Understand","description":"What highly composite numbers are.","layers":[{"id":"definition","name":"Definition","description":"Definition and examples.","findings":[{"id":"definition-finding","name":"Definition","description":"Definition.","questions":[{"text":"What defines a highly composite number, and what are the first members of the sequence?","kind":"definition"},{"text":"How do they differ from abundant and superabundant numbers?","kind":"definition"}]}]},{"id":"structure","name":"Structure","description":"Factorisation structure.","findings":[{"id":"structure-finding","name":"Structure","description":"Structure.","questions":[{"text":"Why do highly composite numbers have prime factorisations with non-increasing exponents over consecutive primes?","kind":"definition"},{"text":"What are superior highly composite numbers?","kind":"definition"}]}]}]},{"id":"compute","name":"Compute","description":"Computing.","layers":[{"id":"test","name":"Test","description":"Testing and generating.","findings":[{"id":"test-finding","name":"Test","description":"Testing.","questions":[{"text":"Is this number highly composite, and how can the sequence be generated efficiently?","kind":"action"},{"text":"Which entry fits divisor functions?","kind":"action"}]}]},{"id":"growth","name":"Growth","description":"Growth and distribution.","findings":[{"id":"growth-finding","name":"Growth","description":"Growth.","questions":[{"text":"How do highly composite numbers grow, and what did Ramanujan prove about them?","kind":"provenance"},{"text":"Which references are standard?","kind":"provenance"}]}]}]},{"id":"apply","name":"Apply","description":"Applications and history.","layers":[{"id":"measurement","name":"Measurement","description":"Measurement systems.","findings":[{"id":"measurement-finding","name":"Measurement","description":"Measurement.","questions":[{"text":"Why were numbers such as 12, 60 and 360 favoured in historical measurement and time systems?","kind":"provenance"},{"text":"Which entry fits sexagesimal systems?","kind":"action"}]}]},{"id":"computing","name":"Computing","description":"Computing uses.","findings":[{"id":"computing-finding","name":"Computing","description":"Computing.","questions":[{"text":"Where do highly composite numbers appear in computing, such as grid sizes and fast transforms?","kind":"provenance"},{"text":"Which entry fits a specific application?","kind":"action"}]}]}]},{"id":"learn","name":"Learn","description":"History and teaching.","layers":[{"id":"history","name":"History","description":"History.","findings":[{"id":"history-finding","name":"History","description":"History.","questions":[{"text":"How did Ramanujan study highly composite numbers, and what followed?","kind":"provenance"},{"text":"Which entry fits Ramanujan?","kind":"action"}]}]},{"id":"teach","name":"Teach","description":"Teaching.","findings":[{"id":"teach-finding","name":"Teach","description":"Teaching.","questions":[{"text":"How can highly composite numbers be used to teach divisors and factorisation?","kind":"action"},{"text":"Which misconceptions arise?","kind":"provenance"}]}]}]}]},"agentConduct":{"may":["List highly composite numbers and verify their divisor counts.","Explain why numbers such as 12, 60 and 360 have historically been used for division."],"mustNot":["Confuse divisor count with divisor sum or with abundant numbers.","List a number as highly composite without checking all smaller numbers.","Attribute results to Ramanujan or others without a source.","Overstate what is proved about the distribution of these numbers."],"requiresHuman":["Publishing new results or tables as verified mathematics."]},"ethics":{"considerations":["Mathematical errors spread when tables are copied without checking.","Credit for results should go to those who proved them."],"affectedParties":["Students and researchers","Readers of mathematics"]},"owners":{"steward":"Nobody owns it; it is held in common by mathematics.","roles":[],"masterSystems":[]},"relations":[{"target":"Q16317911","type":"parent","note":"registry parent class"},{"target":"positive integer","type":"related","note":"category"},{"target":"deficient number","type":"related","note":"another divisor-based classification"},{"target":"sociable number","type":"related","note":"another divisor-based entry"},{"target":"liquid unit","type":"related","note":"measurement systems using 12 and 60"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.highly-composite-number","Wikidata: Q629958 (https://www.wikidata.org/wiki/Q629958)"]},"properties":{"applicability":"not-applicable","items":[]},"recognition":{"applicability":"optional","items":["More divisors than any smaller number","1, 2, 4, 6, 12, 24, 36, 48, 60, 120","Abundant numbers have large divisor sums rather than counts","Not physical; a sequence of integers."]},"capabilities":{"applicability":"required","items":["explain the definition and properties","test and generate numbers","describe superior variants","relate to history and applications"]},"hazards":{"applicability":"required","items":["Confusing divisor count with divisor sum","Errors in factorisation","Overstating structural results"]},"interfaces":{"applicability":"required","items":["Mathematical definitions and notation","Sequence database conventions"]},"context":{"applicability":"required","items":["Integers with record numbers of divisors.","highly composite numbers","superior highly composite numbers","largely composite numbers","related divisor-record sequences","highly composite numbers in measurement systems"]}},"sources":[{"title":"Wikidata item Q629958: highly composite number","url":"https://www.wikidata.org/wiki/Q629958","note":"identity and sense of the item"},{"title":"Wikipedia: Highly composite number","url":"https://en.wikipedia.org/wiki/Highly_composite_number","note":"general description of the item"}],"openQuestions":["Should superior highly composite numbers be a separate entry?","How should sequence databases be linked?","How should Ramanujan work be linked?"],"resources":{"spec":"/models/things/publications/thing-q629958/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q629958/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-12T01:48:32Z","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 2026-10-06T19:52:01+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}}