{ "model": { "rank": 12985, "code": "thing-q467511", "model_id": "vr.tr.deficient-number", "name": "deficient number", "purpose": "Let an agent explain deficient numbers and their relation to perfect and abundant numbers, test whether a number is deficient, describe known results and distribution, and support number theory learning.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QTY", "industry": "", "version": "", "url": "/models/thing/q467511/", "tier": 2, "score": 38, "payload": { "layer": "wikidata", "aliases": [], "aliasCount": 0, "merged": 0, "knownIn": 38, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q467511", "url": "https://www.wikidata.org/wiki/Q467511", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-12T01:28:50Z", "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-Q467511", "registryId": "vr.tr.deficient-number", "name": "deficient number", "version": "0.2.0-wave.2", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QTY" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q467511/", "model": { "registry_id": "vr.tr.deficient-number", "name": "deficient number", "purpose": "Let an agent explain deficient numbers and their relation to perfect and abundant numbers, test whether a number is deficient, describe known results and distribution, and support number theory learning.", "definition": "A positive integer for which the sum of its proper divisors is less than the number itself, such as 8, whose proper divisors 1, 2 and 4 sum to 7, in contrast to perfect numbers where the sum equals the number and abundant numbers where it exceeds it; all prime numbers and prime powers are deficient, deficient numbers form the majority of integers, and the classification dates to ancient Greek number theory.", "what_it_is_for": "Integers with small divisor sums.", "affordances": [ "explain the definition", "test numbers", "describe results and distribution", "support learning" ], "distinguishing_features": [ "Aliquot sum classification", "Includes primes", "Majority of integers", "Ancient origin" ], "appearance": "Not physical; a class of integers.", "visual_identification": [ "Sum of proper divisors less than the number", "Includes all primes", "Perfect numbers equal their divisor sum; abundant exceed it" ], "physical_properties": [], "families_and_kinds": [ "prime numbers as deficient numbers", "prime powers", "deficient composite numbers", "almost perfect numbers", "deficient numbers in aliquot sequences" ], "related_models": [ { "relation": "is a kind of", "target": "positive integer", "why": "category" }, { "relation": "is related to", "target": "sociable number", "why": "another aliquot classification" }, { "relation": "is related to", "target": "Catalan number", "why": "another integer sequence entry" }, { "relation": "is related to", "target": "Fermat number", "why": "numbers that are prime or composite" } ], "identifiers": [], "standards_and_regulation": [ "Mathematical definitions and notation", "Sequence database conventions" ], "failure_modes_and_hazards": [ "Including the number itself in the divisor sum", "Confusing deficient with abundant", "Overstating what is proven" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "understand", "name": "Understand", "description": "What deficient numbers are.", "rationale": "Mathematics.", "layers": [ { "id": "definition", "name": "Definition", "description": "Definition and examples.", "findings": [ { "id": "definition-finding", "name": "Definition", "description": "Definition.", "questions": [ { "text": "What makes a number deficient, and how do deficient, perfect and abundant numbers partition the integers?", "kind": "definition" }, { "text": "Which entry fits perfect or abundant numbers?", "kind": "action" } ] } ] }, { "id": "properties", "name": "Properties", "description": "Properties.", "findings": [ { "id": "properties-finding", "name": "Properties", "description": "Properties.", "questions": [ { "text": "Why are all primes and prime powers deficient, and what are almost perfect numbers?", "kind": "definition" }, { "text": "Which results about divisors of deficient numbers are known?", "kind": "provenance" } ] } ] } ] }, { "id": "compute", "name": "Compute", "description": "Testing numbers.", "rationale": "Practice.", "layers": [ { "id": "test", "name": "Test", "description": "Testing deficiency.", "findings": [ { "id": "test-finding", "name": "Test", "description": "Testing.", "questions": [ { "text": "Is this number deficient, and what is its aliquot sum?", "kind": "action" }, { "text": "Which entry fits divisor functions?", "kind": "action" } ] } ] }, { "id": "distribution", "name": "Distribution", "description": "Distribution.", "findings": [ { "id": "distribution-finding", "name": "Distribution", "description": "Distribution.", "questions": [ { "text": "What proportion of integers are deficient, and how is the density known?", "kind": "provenance" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] } ] }, { "id": "connect", "name": "Connect", "description": "Connections.", "rationale": "Theory.", "layers": [ { "id": "aliquot", "name": "Aliquot", "description": "Aliquot sequences.", "findings": [ { "id": "aliquot-finding", "name": "Aliquot", "description": "Aliquot.", "questions": [ { "text": "How do deficient numbers behave in aliquot sequences?", "kind": "definition" }, { "text": "Which entry fits aliquot sequences?", "kind": "action" } ] } ] }, { "id": "open", "name": "Open", "description": "Open problems.", "findings": [ { "id": "open-finding", "name": "Open", "description": "Open problems.", "questions": [ { "text": "Which open problems involve deficient numbers and the divisor sum function?", "kind": "boundary" }, { "text": "Which findings are recent?", "kind": "provenance" } ] } ] } ] }, { "id": "learn", "name": "Learn", "description": "History and teaching.", "rationale": "Education.", "layers": [ { "id": "history", "name": "History", "description": "History.", "findings": [ { "id": "history-finding", "name": "History", "description": "History.", "questions": [ { "text": "How did Nicomachus and other ancient mathematicians classify deficient, perfect and abundant numbers?", "kind": "provenance" }, { "text": "Which entry fits history of number theory?", "kind": "action" } ] } ] }, { "id": "teach", "name": "Teach", "description": "Teaching.", "findings": [ { "id": "teach-finding", "name": "Teach", "description": "Teaching.", "questions": [ { "text": "How can divisor classifications be used to teach factors?", "kind": "action" }, { "text": "Which misconceptions arise?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Should abundant and perfect numbers be linked as separate entries?", "How should sequence databases be linked?", "How should open problems be documented?" ], "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 deficient number, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain deficient numbers and their relation to perfect and abundant numbers, test whether a number is deficient, describe known results and distribution, and support number theory learning.", "characteristics": { "substance": "abstract", "origin": "conceptual", "agency": "inert" }, "whatYouCanDoWithIt": [ "observed and measured" ], "distinguishingFeatures": [ "Described in 38 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 deficient 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": [], "standing": "Described in 38 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 deficient number from another, and a deficient 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 deficient 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 deficient 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 deficient 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 deficient 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 deficient 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 deficient 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 deficient 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 deficient 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 deficient 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 deficient 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 deficient number from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a deficient 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 deficient 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 deficient 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 deficient 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 deficient number between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a deficient 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 deficient 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 deficient 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 deficient number, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a deficient 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 deficient 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 deficient 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 deficient 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 deficient 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 deficient 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 deficient 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 deficient 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 deficient number and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a deficient 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 deficient 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 deficient 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 deficient number is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a deficient 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 deficient 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 deficient 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 } } } }