{ "model": { "rank": 17872, "code": "thing-q375355", "model_id": "vr.tr.harshad-number", "name": "harshad number", "purpose": "Let an agent define harshad numbers, test and generate them in any base, present known results and open questions, and support recreational mathematics learning.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QTY", "industry": "", "version": "", "url": "/models/thing/q375355/", "tier": 2, "score": 30, "payload": { "layer": "wikidata", "aliases": [ "self-descriptive number" ], "aliasCount": 1, "merged": 1, "knownIn": 30, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q375355", "url": "https://www.wikidata.org/wiki/Q375355", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-11T23:17:24Z", "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": 2, "engine": "claude" }, "metaModel": { "id": "THING-Q375355", "registryId": "vr.tr.harshad-number", "name": "harshad number", "version": "0.2.0-wave.2", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QTY" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q375355/", "model": { "registry_id": "vr.tr.harshad-number", "name": "harshad number", "purpose": "Let an agent define harshad numbers, test and generate them in any base, present known results and open questions, and support recreational mathematics learning.", "definition": "A positive integer that is divisible by the sum of its digits in a given base, such as 18, whose digits sum to 9, also called a Niven number, with variants such as multiple harshad numbers and base-dependent properties; harshad numbers are studied in recreational and elementary number theory, where questions about consecutive harshad numbers and their distribution have been answered or remain open.", "what_it_is_for": "A class of integers in number theory.", "affordances": [ "define and test harshad numbers", "generate them in a base", "present results and open problems", "support learning" ], "distinguishing_features": [ "Digit-sum divisibility", "Base-dependent", "Recreational interest", "Known results" ], "appearance": "Not physical; integers with a divisibility property.", "visual_identification": [ "Divisible by its digit sum", "Base-dependent", "Self-descriptive numbers are a different concept despite the alias" ], "physical_properties": [], "families_and_kinds": [ "harshad numbers in base ten", "harshad numbers in other bases", "multiple harshad numbers", "consecutive harshad numbers", "all-harshad numbers" ], "related_models": [ { "relation": "is a kind of", "target": "positive integer", "why": "category" }, { "relation": "is related to", "target": "radix", "why": "base dependence" }, { "relation": "is related to", "target": "sum", "why": "digit sums" }, { "relation": "is related to", "target": "amicable numbers", "why": "another recreational number class" } ], "identifiers": [], "standards_and_regulation": [ "Mathematical notation conventions" ], "failure_modes_and_hazards": [ "Confusing with self-descriptive or Niven variants", "Forgetting base dependence", "Overstating open problems as solved" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "define", "name": "Define", "description": "What harshad 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 harshad number, and why are 18 and 21 harshad while 11 is not?", "kind": "definition" }, { "text": "Why does the property depend on the base?", "kind": "definition" } ] } ] }, { "id": "test", "name": "Test", "description": "Testing a number.", "findings": [ { "id": "test-finding", "name": "Test", "description": "Testing.", "questions": [ { "text": "Is this number harshad in the given base?", "kind": "action" }, { "text": "How can harshad numbers be generated by computer?", "kind": "action" } ] } ] } ] }, { "id": "theory", "name": "Theory", "description": "Results and problems.", "rationale": "Mathematics.", "layers": [ { "id": "results", "name": "Results", "description": "Known results.", "findings": [ { "id": "results-finding", "name": "Results", "description": "Results.", "questions": [ { "text": "What is known about consecutive harshad numbers, multiple harshad numbers and their density?", "kind": "provenance" }, { "text": "What are all-harshad numbers?", "kind": "definition" } ] } ] }, { "id": "open", "name": "Open", "description": "Open questions.", "findings": [ { "id": "open-finding", "name": "Open", "description": "Open questions.", "questions": [ { "text": "Which questions about harshad numbers remain open?", "kind": "provenance" }, { "text": "Which sequence databases record them?", "kind": "provenance" } ] } ] } ] }, { "id": "history", "name": "History", "description": "Origins.", "rationale": "Context.", "layers": [ { "id": "naming", "name": "Naming", "description": "Names and history.", "findings": [ { "id": "naming-finding", "name": "Naming", "description": "Naming.", "questions": [ { "text": "Where do the names harshad and Niven come from, and who studied these numbers?", "kind": "provenance" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] }, { "id": "related", "name": "Related", "description": "Related classes.", "findings": [ { "id": "related-finding", "name": "Related", "description": "Related classes.", "questions": [ { "text": "How do harshad numbers relate to digit-based classes such as self-descriptive and Smith numbers?", "kind": "definition" }, { "text": "Which entry fits a related class?", "kind": "action" } ] } ] } ] }, { "id": "learn", "name": "Learn", "description": "Teaching.", "rationale": "Education.", "layers": [ { "id": "teach", "name": "Teach", "description": "Teaching with harshad numbers.", "findings": [ { "id": "teach-finding", "name": "Teach", "description": "Teaching.", "questions": [ { "text": "How can harshad numbers be used to teach divisibility and programming?", "kind": "action" }, { "text": "Which misconceptions arise?", "kind": "provenance" } ] } ] }, { "id": "puzzles", "name": "Puzzles", "description": "Puzzles.", "findings": [ { "id": "puzzles-finding", "name": "Puzzles", "description": "Puzzles.", "questions": [ { "text": "Which puzzles and exercises involve harshad numbers?", "kind": "action" }, { "text": "How can they be extended?", "kind": "action" } ] } ] } ] } ] }, "openQuestions": [ "Should recreational number classes be a single entry?", "How should integer sequence databases be linked?", "How should open problems be tracked?" ], "statistics": { "bundles": 4, "layers": 8, "findings": 8, "questions": 16 } }, "draft": { "generator": "vr.draft.v3", "status": "draft-generated", "researched": false, "archetype": "unit, quantity or measure", "method": "Written from the archetype playbook - what this kind of thing needs beyond identity and provenance - and from the structure that recurred across 6,333 models already researched by two engines. Applied to this entry by rule. No source was read for this thing and no claim here is researched. This entry carries no facets of its own, so they were inferred from its domain - a guess about a whole domain applied to one thing.", "facetsInferred": true, "nextPass": "A researcher replaces this draft with a sourced specification. Treat every sentence below as a proposal to argue with.", "purpose": "Give an agent a durable, checkable way to recognise a harshad number, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent define harshad numbers, test and generate them in any base, present known results and open questions, and support recreational mathematics learning.", "characteristics": { "substance": "abstract", "origin": "conceptual", "agency": "inert" }, "whatYouCanDoWithIt": [ "observed and measured" ], "distinguishingFeatures": [ "Names folded into this entry, which a task may need to split apart again: self-descriptive number.", "1 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 30 Wikipedia languages, which is a measure of how widely the thing is known, not of how important it is." ], "openQuestionsForResearch": [ "Which of the bundles below does a real task actually need, and which are ceremony?", "What does this thing have that the facets do not capture at all?", "Which neighbouring kind is most often confused with a harshad number, and on what evidence are they told apart?" ], "whatItIsMadeOf": "an abstraction with no physical instance", "physicalCharacter": [ "Does nothing on its own; everything it does, something else did to it.", "These come from the domain this entry sits in rather than from the entry itself, so treat them as a first guess about the whole domain applied to one thing." ], "whatCanBeDoneWithIt": [ "observe it, measure it, record its state" ], "howItIsRecognised": [ "Nothing to see: a unit is a convention. What is seen is an instrument reading in it." ], "relatedModels": [ { "relation": "covers", "note": "Finer kinds folded into this entry because telling them apart needs a task that asks for it. Each is a model waiting to be split out when one does.", "targets": [ "self-descriptive number" ] } ], "standing": "Described in 30 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 1 finer distinctions are held inside this entry as names rather than as separate models.", "structure": { "bundles": [ { "id": "identity-and-classification", "name": "Identity, naming and classification", "description": "How an agent tells one harshad number from another, and a harshad number from things that resemble it.", "rationale": "Recognition comes before every other claim. Without stable identity nothing else in the model can be trusted to be about the same thing twice.", "layers": [ { "id": "naming-and-identifiers", "name": "Names and identifiers", "description": "The names this thing goes by and the identifiers that survive translation and time.", "findings": [ { "id": "preferred-name-and-aliases", "name": "Preferred name, aliases and local names", "description": "Which name to use, which names mean the same thing, and which merely sound similar.", "questions": [ { "id": "preferred-name-and-aliases-q01", "text": "What identifies and describes the name of a harshad number, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "preferred-name-and-aliases-q02", "text": "Who or what asserted this about the name of a harshad number, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "preferred-name-and-aliases-q03", "text": "What may an agent decide or do once the name of a harshad number is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] }, { "id": "stable-identifiers", "name": "Stable identifiers and external keys", "description": "Identifiers that keep pointing at this kind of thing across systems and languages.", "questions": [ { "id": "stable-identifiers-q01", "text": "What identifies and describes an identifier for a harshad number, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "stable-identifiers-q02", "text": "Who or what asserted this about an identifier for a harshad number, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "stable-identifiers-q03", "text": "What may an agent decide or do once an identifier for a harshad number is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] }, { "id": "classification-and-granularity", "name": "Classification and granularity", "description": "Where a harshad number sits among kinds, and how finely a task needs to cut it.", "findings": [ { "id": "kind-and-parents", "name": "Kind, parents and neighbouring kinds", "description": "The classes this thing belongs to and the ones it is next to.", "questions": [ { "id": "kind-and-parents-q01", "text": "What identifies and describes the kind of a harshad number, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "kind-and-parents-q02", "text": "Who or what asserted this about the kind of a harshad number, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "kind-and-parents-q03", "text": "What may an agent decide or do once the kind of a harshad number is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] }, { "id": "distinguishing-features", "name": "Distinguishing features", "description": "What separates a harshad number from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a harshad number, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "distinguishing-features-q02", "text": "Who or what asserted this about what distinguishes a harshad number, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "distinguishing-features-q03", "text": "What may an agent decide or do once what distinguishes a harshad number is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] }, { "id": "state-and-lifecycle", "name": "State and lifecycle", "description": "The states a harshad number passes through and the events that move it between them.", "rationale": "Most decisions about a thing depend on what state it is in now, which is a claim with a time on it, not a property.", "layers": [ { "id": "lifecycle-stages", "name": "Lifecycle stages", "description": "From coming into existence to ceasing to be one of these.", "findings": [ { "id": "stages-and-transitions", "name": "Stages and transitions", "description": "The stages worth naming and what moves a harshad number between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a harshad number, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "stages-and-transitions-q02", "text": "Who or what asserted this about the lifecycle of a harshad number, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "stages-and-transitions-q03", "text": "What may an agent decide or do once the lifecycle of a harshad number is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] }, { "id": "observations-and-status", "name": "Observations and current status", "description": "What is observed about a harshad number, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a harshad number is recorded so that it can be superseded rather than overwritten.", "questions": [ { "id": "observation-record-q01", "text": "What identifies and describes an observation of a harshad number, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "observation-record-q02", "text": "Who or what asserted this about an observation of a harshad number, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "observation-record-q03", "text": "What may an agent decide or do once an observation of a harshad number is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] }, { "id": "definition-and-realisation", "name": "Definition, dimension and realisation", "description": "What harshad number is defined as and how it is realised in practice.", "rationale": "A unit is not the quantity it measures, and its definition has a history that older data still depends on.", "layers": [ { "id": "definition", "name": "Definition and dimension", "description": "The defining relation and the quantity it measures.", "findings": [ { "id": "definition-record", "name": "Definition, body and date", "description": "What defines it now, and what defined it before.", "questions": [ { "id": "definition-record-q01", "text": "How is harshad number defined, by which body, and since when?", "kind": "definition" }, { "id": "definition-record-q02", "text": "What was the previous definition, and what data still depends on it?", "kind": "provenance" } ] } ] }, { "id": "conversion", "name": "Conversion and compatibility", "description": "Relations to other units, exact or approximate.", "findings": [ { "id": "conversion-record", "name": "Conversions and their exactness", "description": "Factors, and whether each is exact by definition.", "questions": [ { "id": "conversion-record-q01", "text": "What conversions relate harshad number to other units, and which are exact by definition?", "kind": "measurement" }, { "id": "conversion-record-q02", "text": "Where does rounding a conversion change a decision, and how should that be recorded?", "kind": "action" } ] } ] } ] }, { "id": "provenance-and-evidence", "name": "Provenance, evidence and time", "description": "Where every claim about a harshad number came from and when it held.", "rationale": "A claim without a source and a time cannot be superseded, only overwritten, and an agent that overwrites loses the ability to explain itself.", "layers": [ { "id": "source-and-authority", "name": "Source and authority", "description": "Who said it, on what evidence, and how strongly.", "findings": [ { "id": "claim-provenance", "name": "Claim provenance and confidence", "description": "The authority behind each claim about a harshad number and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a harshad number, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "claim-provenance-q02", "text": "Who or what asserted this about a claim about a harshad number, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "claim-provenance-q03", "text": "What may an agent decide or do once a claim about a harshad number is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] }, { "id": "time-and-versions", "name": "Time, versions and supersession", "description": "When a claim was true, when it was learnt, and what replaced it.", "findings": [ { "id": "validity-and-supersession", "name": "Validity period and supersession", "description": "How an old claim about a harshad number is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a harshad number, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "validity-and-supersession-q02", "text": "Who or what asserted this about the validity of a claim about a harshad number, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "validity-and-supersession-q03", "text": "What may an agent decide or do once the validity of a claim about a harshad number is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] } ] }, "statistics": { "bundles": 4, "layers": 8, "findings": 10, "questions": 28 } } } }