{ "model": { "rank": 5208, "code": "thing-q170043", "model_id": "vr.tr.perfect-number", "name": "perfect number", "purpose": "Let an agent handle perfect numbers by definition, known examples, relation to Mersenne primes and open problems.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QTY", "industry": "", "version": "", "url": "/models/thing/q170043/", "tier": 2, "score": 69, "payload": { "layer": "wikidata", "aliases": [ "odd perfect number", "multiply perfect number" ], "aliasCount": 2, "merged": 2, "knownIn": 69, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q170043", "url": "https://www.wikidata.org/wiki/Q170043", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-11T10:36:56Z", "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-Q170043", "registryId": "vr.tr.perfect-number", "name": "perfect number", "version": "0.2.0-wave.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QTY" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q170043/", "model": { "registry_id": "vr.tr.perfect-number", "name": "perfect number", "purpose": "Let an agent handle perfect numbers by definition, known examples, relation to Mersenne primes and open problems.", "definition": "A positive integer equal to the sum of its proper divisors, such as 6 = 1 + 2 + 3 and 28; all known perfect numbers are even and correspond to Mersenne primes, and whether any odd perfect number exists is an open problem.", "what_it_is_for": "Number theory and recreational mathematics.", "affordances": [ "test whether a number is perfect", "list known perfect numbers", "relate them to Mersenne primes", "describe open problems accurately" ], "distinguishing_features": [ "Sum of proper divisors equals itself", "All known ones are even", "Linked to Mersenne primes", "Odd perfect numbers unknown" ], "appearance": "Integers such as 6, 28, 496 and 8128.", "visual_identification": [ "Sum of proper divisors equals the number", "Euclid-Euler form 2^(p-1)(2^p - 1)", "Abundant and deficient numbers are related" ], "physical_properties": [], "families_and_kinds": [ "even perfect numbers", "hypothetical odd perfect numbers", "multiply perfect numbers (related)" ], "related_models": [ { "relation": "is a kind of", "target": "natural number", "why": "category" }, { "relation": "is related to", "target": "Mersenne prime", "why": "construction" }, { "relation": "is defined by", "target": "divisor", "why": "concept" }, { "relation": "is studied in", "target": "number theory", "why": "field" } ], "identifiers": [ { "scheme": "OEIS", "value_or_pattern": "A000396", "note": "integer sequence" } ], "standards_and_regulation": [], "failure_modes_and_hazards": [ "Stating that no odd perfect numbers exist as proved", "Outdated counts of known perfect numbers" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "test", "name": "Test", "description": "Is it perfect.", "rationale": "Divisors decide.", "layers": [ { "id": "check", "name": "Check", "description": "Sum of divisors.", "findings": [ { "id": "check-finding", "name": "Check", "description": "Perfectness test.", "questions": [ { "text": "Is this number perfect, abundant or deficient?", "kind": "boundary" }, { "text": "What is the sum of its proper divisors?", "kind": "measurement" } ] } ] }, { "id": "form", "name": "Form", "description": "Euclid-Euler.", "findings": [ { "id": "form-finding", "name": "Form", "description": "Euclid-Euler form.", "questions": [ { "text": "Can it be written in the Euclid-Euler form?", "kind": "definition" }, { "text": "Which Mersenne prime generates it?", "kind": "definition" } ] } ] } ] }, { "id": "known", "name": "Known", "description": "Examples.", "rationale": "Counts change.", "layers": [ { "id": "list", "name": "List", "description": "Known perfect numbers.", "findings": [ { "id": "list-finding", "name": "List", "description": "Known perfect numbers.", "questions": [ { "text": "How many perfect numbers are known, according to current records?", "kind": "provenance" }, { "text": "Which was found most recently?", "kind": "provenance" } ] } ] }, { "id": "search", "name": "Search", "description": "Mersenne searches.", "findings": [ { "id": "search-finding", "name": "Search", "description": "Searches.", "questions": [ { "text": "How are new Mersenne primes and perfect numbers found?", "kind": "definition" }, { "text": "Which project coordinates the search?", "kind": "provenance" } ] } ] } ] }, { "id": "open", "name": "Open problems", "description": "Unknowns.", "rationale": "Accuracy about open problems matters.", "layers": [ { "id": "odd", "name": "Odd", "description": "Odd perfect numbers.", "findings": [ { "id": "odd-finding", "name": "Odd", "description": "Odd perfect numbers.", "questions": [ { "text": "Is the existence of odd perfect numbers still open?", "kind": "provenance" }, { "text": "What lower bounds are known?", "kind": "measurement" } ] } ] }, { "id": "infinitude", "name": "Infinitude", "description": "Infinitely many.", "findings": [ { "id": "infinitude-finding", "name": "Infinitude", "description": "Infinitely many.", "questions": [ { "text": "Is it known whether there are infinitely many perfect numbers?", "kind": "provenance" }, { "text": "What would settle it?", "kind": "definition" } ] } ] } ] }, { "id": "learning", "name": "Learning", "description": "Teaching.", "rationale": "Perfect numbers engage learners.", "layers": [ { "id": "history", "name": "History", "description": "Euclid and Euler.", "findings": [ { "id": "history-finding", "name": "History", "description": "History.", "questions": [ { "text": "What did Euclid and Euler prove about perfect numbers?", "kind": "provenance" }, { "text": "Which sources explain it?", "kind": "provenance" } ] } ] }, { "id": "activities", "name": "Activities", "description": "Exercises.", "findings": [ { "id": "activities-finding", "name": "Activities", "description": "Activities.", "questions": [ { "text": "Which exercises help learners explore perfect numbers?", "kind": "action" }, { "text": "How can divisors be listed quickly?", "kind": "action" } ] } ] } ] } ] }, "openQuestions": [ "Should multiply perfect numbers be separate?", "How should Mersenne prime searches be linked?", "How should the count be kept current?" ], "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 perfect number, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent handle perfect numbers by definition, known examples, relation to Mersenne primes and open problems.", "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: odd perfect number, multiply perfect number.", "2 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 69 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 perfect 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": [ "odd perfect number", "multiply perfect number" ] } ], "standing": "Described in 69 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 2 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 perfect number from another, and a perfect 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 perfect 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 perfect 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 perfect 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 perfect 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 perfect 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 perfect 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 perfect 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 perfect 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 perfect 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 perfect 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 perfect number from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a perfect 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 perfect 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 perfect 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 perfect 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 perfect number between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a perfect 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 perfect 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 perfect 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 perfect number, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a perfect 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 perfect 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 perfect 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 perfect 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 perfect 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 perfect 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 perfect 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 perfect 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 perfect number and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a perfect 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 perfect 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 perfect 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 perfect number is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a perfect 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 perfect 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 perfect 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 } } } }