{ "model": { "rank": 3655, "code": "thing-q131752", "model_id": "vr.tr.greatest-common-divisor", "name": "greatest common divisor", "purpose": "Let an agent handle the greatest common divisor by definition, computation, properties and applications.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QTY", "industry": "", "version": "", "url": "/models/thing/q131752/", "tier": 2, "score": 83, "payload": { "layer": "wikidata", "aliases": [], "aliasCount": 0, "merged": 0, "knownIn": 83, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q131752", "url": "https://www.wikidata.org/wiki/Q131752", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-11T10:18:59Z", "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": 1, "engine": "claude" }, "metaModel": { "id": "THING-Q131752", "registryId": "vr.tr.greatest-common-divisor", "name": "greatest common divisor", "version": "0.2.0-wave.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QTY" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q131752/", "model": { "registry_id": "vr.tr.greatest-common-divisor", "name": "greatest common divisor", "purpose": "Let an agent handle the greatest common divisor by definition, computation, properties and applications.", "definition": "The largest positive integer that divides each of two or more integers without remainder, written gcd(a, b); computed efficiently by the Euclidean algorithm, and used to simplify fractions.", "what_it_is_for": "Simplifying fractions, number theory and cryptography.", "affordances": [ "compute gcd by the Euclidean algorithm", "simplify fractions", "find Bezout coefficients", "relate gcd and lcm" ], "distinguishing_features": [ "Largest shared divisor", "Efficient algorithm", "gcd(a, b) x lcm(a, b) = |a x b|", "Basis of coprimality" ], "appearance": "A number resulting from computation.", "visual_identification": [ "Notation gcd(a, b)", "Also called highest common factor", "Least common multiple is the related dual" ], "physical_properties": [], "families_and_kinds": [ "gcd of integers", "gcd of polynomials", "extended Euclidean algorithm", "binary gcd algorithm" ], "related_models": [ { "relation": "is a kind of", "target": "common divisor", "why": "category" }, { "relation": "is computed by", "target": "Euclidean algorithm", "why": "method" }, { "relation": "is related to", "target": "least common multiple", "why": "dual" }, { "relation": "is related to", "target": "divisor", "why": "concept" } ], "identifiers": [], "standards_and_regulation": [ "ISO 80000-2 notation" ], "failure_modes_and_hazards": [ "Arithmetic errors", "Confusing gcd and lcm" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "compute", "name": "Compute", "description": "Finding it.", "rationale": "Algorithms compute gcd.", "layers": [ { "id": "value", "name": "Value", "description": "Result.", "findings": [ { "id": "value-finding", "name": "Value", "description": "GCD value.", "questions": [ { "text": "What is the gcd of these numbers?", "kind": "measurement" }, { "text": "Which algorithm was used?", "kind": "definition" } ] } ] }, { "id": "steps", "name": "Steps", "description": "Euclidean algorithm.", "findings": [ { "id": "steps-finding", "name": "Steps", "description": "Algorithm steps.", "questions": [ { "text": "What are the steps of the Euclidean algorithm here?", "kind": "action" }, { "text": "How many steps are needed?", "kind": "measurement" } ] } ] } ] }, { "id": "properties", "name": "Properties", "description": "Theory.", "rationale": "Properties enable proofs.", "layers": [ { "id": "bezout", "name": "Bezout", "description": "Coefficients.", "findings": [ { "id": "bezout-finding", "name": "Bezout", "description": "Bezout identity.", "questions": [ { "text": "What integers x and y satisfy ax + by = gcd(a, b)?", "kind": "measurement" }, { "text": "How are they found?", "kind": "action" } ] } ] }, { "id": "coprime", "name": "Coprime", "description": "gcd equals 1.", "findings": [ { "id": "coprime-finding", "name": "Coprime", "description": "Coprimality.", "questions": [ { "text": "Are the numbers coprime?", "kind": "boundary" }, { "text": "Why does it matter?", "kind": "definition" } ] } ] } ] }, { "id": "applications", "name": "Applications", "description": "Uses.", "rationale": "gcd appears widely.", "layers": [ { "id": "fractions", "name": "Fractions", "description": "Simplifying.", "findings": [ { "id": "fractions-finding", "name": "Fractions", "description": "Simplifying fractions.", "questions": [ { "text": "How does the gcd simplify this fraction?", "kind": "action" }, { "text": "Is the result in lowest terms?", "kind": "boundary" } ] } ] }, { "id": "crypto", "name": "Cryptography", "description": "RSA.", "findings": [ { "id": "crypto-finding", "name": "Cryptography", "description": "Cryptography.", "questions": [ { "text": "How is the gcd used in cryptographic algorithms such as RSA key generation?", "kind": "definition" }, { "text": "Which step uses it?", "kind": "definition" } ] } ] } ] }, { "id": "learning", "name": "Learning", "description": "Teaching.", "rationale": "Clear terms help.", "layers": [ { "id": "terms", "name": "Terms", "description": "HCF and GCD.", "findings": [ { "id": "terms-finding", "name": "Terms", "description": "Terminology.", "questions": [ { "text": "Is it called gcd or highest common factor in this curriculum?", "kind": "provenance" }, { "text": "Are they the same?", "kind": "definition" } ] } ] }, { "id": "lcm", "name": "LCM", "description": "Relation.", "findings": [ { "id": "lcm-finding", "name": "LCM", "description": "Relation to lcm.", "questions": [ { "text": "How are gcd and lcm related?", "kind": "definition" }, { "text": "Can the relation be checked on an example?", "kind": "action" } ] } ] } ] } ] }, "openQuestions": [ "Should the Euclidean algorithm be a separate entry?", "How should polynomial gcd be linked?", "How should terminology variants be recorded?" ], "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 greatest common divisor, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent handle the greatest common divisor by definition, computation, properties and applications.", "characteristics": { "substance": "abstract", "origin": "conceptual", "agency": "inert" }, "whatYouCanDoWithIt": [ "observed and measured" ], "distinguishingFeatures": [ "Described in 83 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 greatest common divisor, 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": [], "standing": "Described in 83 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is.", "structure": { "bundles": [ { "id": "identity-and-classification", "name": "Identity, naming and classification", "description": "How an agent tells one greatest common divisor from another, and a greatest common divisor 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 greatest common divisor, 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 greatest common divisor, 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 greatest common divisor 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 greatest common divisor, 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 greatest common divisor, 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 greatest common divisor 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 greatest common divisor 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 greatest common divisor, 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 greatest common divisor, 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 greatest common divisor 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 greatest common divisor from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a greatest common divisor, 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 greatest common divisor, 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 greatest common divisor 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 greatest common divisor 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 greatest common divisor between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a greatest common divisor, 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 greatest common divisor, 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 greatest common divisor 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 greatest common divisor, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a greatest common divisor 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 greatest common divisor, 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 greatest common divisor, 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 greatest common divisor 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 greatest common divisor 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 greatest common divisor 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 greatest common divisor 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 greatest common divisor 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 greatest common divisor and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a greatest common divisor, 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 greatest common divisor, 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 greatest common divisor 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 greatest common divisor is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a greatest common divisor, 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 greatest common divisor, 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 greatest common divisor 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 } } } }