{ "model": { "rank": 4771, "code": "thing-q50707", "model_id": "vr.tr.composite-number", "name": "composite number", "purpose": "Let an agent handle composite numbers mathematically, with factorisation, tests and their role in cryptography.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QTY", "industry": "", "version": "", "url": "/models/thing/q50707/", "tier": 2, "score": 72, "payload": { "layer": "wikidata", "aliases": [ "RSA number", "pseudoprime", "unitary perfect number", "Lucas–Carmichael number", "positive power of ten", "Fibonacci pseudoprime", "Fermat pseudoprime", "Lucas pseudoprime", "strong pseudoprime", "Catalan pseudoprime", "product of four distinct primes", "product of five distinct primes", "product of six distinct primes", "Giuga number", "sphenic number", "antisquare number", "Unprimeable numbers", "Smith number", "pseudoperfect number", "vampire number", "Knödel number", "Zumkeller number", "semiprime", "sublime number", "Poulet number", "Blum integer" ], "aliasCount": 26, "merged": 26, "knownIn": 72, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": "vr.tr.composite-number", "source": { "dataset": "wikidata", "item": "Q50707", "url": "https://www.wikidata.org/wiki/Q50707", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-11T06:19:08Z", "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-Q50707", "registryId": "vr.tr.composite-number", "name": "composite number", "version": "0.2.0-wave.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QTY" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q50707/", "model": { "registry_id": "vr.tr.composite-number", "name": "composite number", "purpose": "Let an agent handle composite numbers mathematically, with factorisation, tests and their role in cryptography.", "definition": "A positive integer greater than 1 that has at least one divisor other than 1 and itself, and so can be factored into smaller primes, such as 4, 6, 9 and RSA numbers.", "what_it_is_for": "Composite numbers are studied in number theory and are central to factoring-based cryptography.", "affordances": [ "factor it into primes", "test compositeness", "study special classes such as pseudoprimes", "use hard-to-factor composites in cryptography" ], "distinguishing_features": [ "Not prime and greater than 1", "Unique prime factorisation", "Some pass primality tests falsely (pseudoprimes)", "Factoring large ones is hard" ], "appearance": "Numbers; notable composites such as RSA challenge numbers.", "visual_identification": [ "Has a divisor other than 1 and itself", "Prime factorisation", "Classes such as Carmichael numbers or pseudoprimes" ], "physical_properties": [], "families_and_kinds": [ "semiprimes such as RSA numbers", "pseudoprimes and Carmichael numbers", "perfect and unitary perfect numbers", "powers of ten" ], "related_models": [ { "relation": "is a kind of", "target": "integer", "why": "positive integer" }, { "relation": "is the complement of", "target": "prime number", "why": "among integers above 1" }, { "relation": "is used in", "target": "cryptographic key", "why": "RSA" }, { "relation": "is studied by", "target": "mathematics", "why": "number theory" } ], "identifiers": [ { "scheme": "OEIS A002808", "value_or_pattern": "composite numbers", "note": "sequence" } ], "standards_and_regulation": [ "FIPS 186 key generation rules" ], "failure_modes_and_hazards": [ "Mistaking a pseudoprime for a prime", "Weak composites in cryptography" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "definition", "name": "Definition", "description": "What makes it composite.", "rationale": "Definition is exact.", "layers": [ { "id": "test", "name": "Test", "description": "Compositeness.", "findings": [ { "id": "test-finding", "name": "Test", "description": "Compositeness.", "questions": [ { "text": "Is this number composite, by which test?", "kind": "measurement" }, { "text": "Is the result certain?", "kind": "boundary" } ] } ] }, { "id": "factors", "name": "Factors", "description": "Factorisation.", "findings": [ { "id": "factors-finding", "name": "Factors", "description": "Prime factorisation.", "questions": [ { "text": "What is its prime factorisation?", "kind": "measurement" }, { "text": "How long did factoring take?", "kind": "measurement" } ] } ] } ] }, { "id": "classes", "name": "Classes", "description": "Special composites.", "rationale": "Classes have properties.", "layers": [ { "id": "class", "name": "Class", "description": "Semiprime, pseudoprime.", "findings": [ { "id": "class-finding", "name": "Class", "description": "Class membership.", "questions": [ { "text": "Does it belong to a special class?", "kind": "definition" }, { "text": "Which property defines it?", "kind": "definition" } ] } ] }, { "id": "records", "name": "Records", "description": "Factoring records.", "findings": [ { "id": "records-finding", "name": "Records", "description": "Factoring records.", "questions": [ { "text": "Which RSA numbers have been factored?", "kind": "provenance" }, { "text": "When?", "kind": "provenance" } ] } ] } ] }, { "id": "cryptography", "name": "Cryptography", "description": "Security.", "rationale": "Factoring hardness secures keys.", "layers": [ { "id": "keys", "name": "Keys", "description": "RSA moduli.", "findings": [ { "id": "keys-finding", "name": "Keys", "description": "Key sizes.", "questions": [ { "text": "How large must RSA moduli be for current security?", "kind": "boundary" }, { "text": "Which guidance applies?", "kind": "provenance" } ] } ] }, { "id": "threats", "name": "Threats", "description": "Quantum computing.", "findings": [ { "id": "threats-finding", "name": "Threats", "description": "Threats.", "questions": [ { "text": "How would quantum computers affect factoring?", "kind": "boundary" }, { "text": "What is the migration advice?", "kind": "provenance" } ] } ] } ] }, { "id": "teaching", "name": "Teaching", "description": "Explaining.", "rationale": "Clear explanations.", "layers": [ { "id": "explanation", "name": "Explanation", "description": "Concepts.", "findings": [ { "id": "explanation-finding", "name": "Explanation", "description": "Explaining.", "questions": [ { "text": "How can composites be explained simply?", "kind": "action" }, { "text": "What are common misconceptions?", "kind": "boundary" } ] } ] }, { "id": "computation", "name": "Computation", "description": "Tools.", "findings": [ { "id": "computation-finding", "name": "Computation", "description": "Tools.", "questions": [ { "text": "Which tools factor numbers reliably?", "kind": "definition" }, { "text": "What are their limits?", "kind": "boundary" } ] } ] } ] } ] }, "openQuestions": [ "Should special classes be separate entries?", "How should factoring records be tracked?", "How should quantum threats be described?" ], "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 composite number, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent handle composite numbers mathematically, with factorisation, tests and their role in cryptography.", "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: RSA number, pseudoprime, unitary perfect number, Lucas–Carmichael number, positive power of ten, Fibonacci pseudoprime, Fermat pseudoprime, Lucas pseudoprime, strong pseudoprime, Catalan pseudoprime, product of four distinct primes, product of five distinct primes.", "26 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 72 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 composite 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": [ "RSA number", "pseudoprime", "unitary perfect number", "Lucas–Carmichael number", "positive power of ten", "Fibonacci pseudoprime", "Fermat pseudoprime", "Lucas pseudoprime", "strong pseudoprime", "Catalan pseudoprime", "product of four distinct primes", "product of five distinct primes" ] } ], "standing": "Described in 72 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 26 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 composite number from another, and a composite 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 composite 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 composite 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 composite 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 composite 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 composite 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 composite 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 composite 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 composite 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 composite 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 composite 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 composite number from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a composite 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 composite 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 composite 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 composite 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 composite number between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a composite 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 composite 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 composite 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 composite number, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a composite 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 composite 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 composite 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 composite 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 composite 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 composite 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 composite 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 composite 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 composite number and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a composite 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 composite 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 composite 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 composite number is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a composite 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 composite 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 composite 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 } } } }