{ "model": { "rank": 10668, "code": "thing-q3176558", "model_id": "vr.tr.positive-real-number", "name": "positive real number", "purpose": "Let an agent define positive real numbers and their properties, distinguish them from non-negative and nonzero reals, explain their algebraic and order structure, and separate the set from particular large numbers listed as aliases.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q3176558/", "tier": 2, "score": 44, "payload": { "layer": "wikidata", "aliases": [ "number of strongly connected digraphs with n labeled nodes", "large number", "quintillion", "nonillion", "octillion", "sextillion", "10^96", "quadrillion", "centillion", "septillion", "positive integer", "aspiring number", "near-perfect number", "deficient perfect number", "graph dimension", "autobiographical number", "rough number", "Ackermann number", "highly touchable number", "Zuckerman number", "amenable number", "Cunningham number", "cyclic number", "sum-product number", "amino acid position", "nonhypotenuse number", "totative", "Trofimov number", "number of steps", "Pisot–Vijayaraghavan number", "negative power of ten", "power of 1000", "Histogramm-Differenz", "conjugate index", "module of an automorphism" ], "aliasCount": 35, "merged": 35, "knownIn": 44, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q3176558", "url": "https://www.wikidata.org/wiki/Q3176558", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-12T22:09:37Z", "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": 3, "engine": "claude" }, "metaModel": { "id": "THING-Q3176558", "registryId": "vr.tr.positive-real-number", "name": "positive real number", "version": "0.2.0-wave.3", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q3176558/", "model": { "registry_id": "vr.tr.positive-real-number", "name": "positive real number", "purpose": "Let an agent define positive real numbers and their properties, distinguish them from non-negative and nonzero reals, explain their algebraic and order structure, and separate the set from particular large numbers listed as aliases.", "definition": "A real number greater than zero, forming the set denoted R plus or R greater than zero, which is closed under addition, multiplication and division, has no smallest element, and serves as the domain of logarithms, the range of exponentials and the natural setting for magnitudes such as lengths and probabilities of positive events; the registry entry also gathers aliases naming large numbers such as quintillion and a combinatorial sequence, which are particular positive numbers rather than the set.", "what_it_is_for": "A basic number set in mathematics.", "affordances": [ "define the set and its properties", "distinguish from related sets", "explain algebraic and order structure", "separate from particular numbers" ], "distinguishing_features": [ "Strictly positive", "Closed under multiplication and division", "Multiplicative group", "Domain of the logarithm" ], "appearance": "Not a visible object; the open ray from zero to infinity on the number line.", "visual_identification": [ "Real numbers strictly greater than zero", "Open ray excluding zero", "Non-negative reals include zero; nonzero reals include negatives" ], "physical_properties": [ { "quantity": "infimum", "typical_range": "0", "unit": "value", "note": "not attained" }, { "quantity": "cardinality", "typical_range": "continuum", "unit": "cardinal", "note": "same as the reals" } ], "families_and_kinds": [ "positive rationals and irrationals", "positive integers as a subset", "large named numbers such as sextillion, octillion and nonillion, as particular members", "positive reals as a group under multiplication and an ordered semifield" ], "related_models": [ { "relation": "is a kind of", "target": "non-negative real number", "why": "excluding zero" }, { "relation": "is a kind of", "target": "nonzero real number", "why": "excluding negatives" }, { "relation": "is a subset of", "target": "real number", "why": "the reals" }, { "relation": "is the domain of", "target": "logarithm", "why": "the function" } ], "identifiers": [ { "scheme": "notation", "value_or_pattern": "R plus, R greater than zero, or R sub greater than zero", "note": "varies by convention" } ], "standards_and_regulation": [ "ISO 80000-2 notation for number sets" ], "failure_modes_and_hazards": [ "Confusing positive with non-negative", "Notation ambiguity between conventions", "Sense confusion with particular large numbers" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "define", "name": "Define", "description": "What the set is.", "rationale": "Definition.", "layers": [ { "id": "definition", "name": "Definition", "description": "Definition and notation.", "findings": [ { "id": "definition-finding", "name": "Definition", "description": "Definition.", "questions": [ { "text": "What are the positive real numbers, and how are they denoted?", "kind": "definition" }, { "text": "Is the question about the set or about a particular large number?", "kind": "boundary" } ] } ] }, { "id": "relations", "name": "Relations", "description": "Related sets.", "findings": [ { "id": "relations-finding", "name": "Relations", "description": "Relations.", "questions": [ { "text": "How do positive, non-negative and nonzero reals differ?", "kind": "definition" }, { "text": "Which entry fits the related set?", "kind": "action" } ] } ] } ] }, { "id": "structure", "name": "Structure", "description": "Structure.", "rationale": "Theory.", "layers": [ { "id": "algebra", "name": "Algebra", "description": "Algebraic structure.", "findings": [ { "id": "algebra-finding", "name": "Algebra", "description": "Algebra.", "questions": [ { "text": "What algebraic structure do the positive reals form, and how does the logarithm map them to the reals?", "kind": "definition" }, { "text": "Which entry fits ordered group?", "kind": "action" } ] } ] }, { "id": "order", "name": "Order", "description": "Order and topology.", "findings": [ { "id": "order-finding", "name": "Order", "description": "Order.", "questions": [ { "text": "What are the order and topological properties of the positive reals?", "kind": "provenance" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] } ] }, { "id": "use", "name": "Use", "description": "Uses.", "rationale": "Application.", "layers": [ { "id": "magnitudes", "name": "Magnitudes", "description": "Magnitudes.", "findings": [ { "id": "magnitudes-finding", "name": "Magnitudes", "description": "Magnitudes.", "questions": [ { "text": "Where do positive reals serve as the natural domain, such as lengths, rates and scales?", "kind": "provenance" }, { "text": "What constraints apply in the case in question?", "kind": "measurement" } ] } ] }, { "id": "large", "name": "Large", "description": "Large numbers.", "findings": [ { "id": "large-finding", "name": "Large", "description": "Large.", "questions": [ { "text": "How are large numbers such as quintillion named in short and long scales?", "kind": "provenance" }, { "text": "Which entry fits names of large numbers?", "kind": "action" } ] } ] } ] }, { "id": "context", "name": "Context", "description": "Teaching.", "rationale": "Context.", "layers": [ { "id": "teach", "name": "Teach", "description": "Teaching.", "findings": [ { "id": "teach-finding", "name": "Teach", "description": "Teaching.", "questions": [ { "text": "How are positive reals introduced in teaching, and which misconceptions arise?", "kind": "provenance" }, { "text": "Which entry fits mathematics education?", "kind": "action" } ] } ] }, { "id": "history", "name": "History", "description": "History.", "findings": [ { "id": "history-finding", "name": "History", "description": "History.", "questions": [ { "text": "How did the concept of positive magnitude develop before negative numbers were accepted?", "kind": "provenance" }, { "text": "Which entry fits the history of numbers?", "kind": "action" } ] } ] } ] } ] }, "openQuestions": [ "Should large named numbers be separate entries?", "How should notation conventions be recorded?", "The registry entry has merged aliases naming specific numbers and a sequence; should they be split off?" ], "statistics": { "bundles": 4, "layers": 8, "findings": 8, "questions": 16 } }, "draft": { "generator": "vr.draft.v3", "status": "draft-generated", "researched": false, "archetype": "abstract concept", "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 positive real number, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent define positive real numbers and their properties, distinguish them from non-negative and nonzero reals, explain their algebraic and order structure, and separate the set from particular large numbers listed as aliases.", "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: number of strongly connected digraphs with n labeled nodes, large number, quintillion, nonillion, octillion, sextillion, 10^96, quadrillion, centillion, septillion, positive integer, aspiring number.", "35 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 44 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 positive real 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. What is recognised is an instance of it, and which instances count is exactly what is argued about." ], "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": [ "number of strongly connected digraphs with n labeled nodes", "large number", "quintillion", "nonillion", "octillion", "sextillion", "10^96", "quadrillion", "centillion", "septillion", "positive integer", "aspiring number" ] } ], "standing": "Described in 44 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 35 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 positive real number from another, and a positive real 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 positive real 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 positive real 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 positive real 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 positive real 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 positive real 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 positive real 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 positive real 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 positive real 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 positive real 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 positive real 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 positive real number from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a positive real 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 positive real 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 positive real 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 positive real 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 positive real number between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a positive real 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 positive real 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 positive real 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 positive real number, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a positive real 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 positive real 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 positive real 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 positive real number is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] }, { "id": "definitions-in-contest", "name": "Definitions and who holds them", "description": "What positive real number is taken to mean, and by whom.", "rationale": "When a field disagrees about a concept, the disagreement is the content. A model that picks one definition silently destroys the information.", "layers": [ { "id": "competing-definitions", "name": "Competing definitions", "description": "The main readings and the traditions behind them.", "findings": [ { "id": "definition-map", "name": "Definitions and their holders", "description": "Each definition with the school or body that holds it.", "questions": [ { "id": "definition-map-q01", "text": "Which definitions of positive real number are in use, and which tradition or body holds each?", "kind": "definition" }, { "id": "definition-map-q02", "text": "What turns on the difference between them in practice?", "kind": "boundary" } ] } ] }, { "id": "operationalisation", "name": "Operationalisation", "description": "How it is measured or applied when it has to be.", "findings": [ { "id": "operational-record", "name": "Measures and proxies", "description": "Instruments and indicators used to stand in for it.", "questions": [ { "id": "operational-record-q01", "text": "How is positive real number operationalised or measured in practice, and by what instrument?", "kind": "measurement" }, { "id": "operational-record-q02", "text": "What does that operationalisation leave out, and when does that matter?", "kind": "boundary" } ] } ] } ] }, { "id": "instances-and-use", "name": "Instances, use and consequence", "description": "What counts as an instance of positive real number and what follows from calling something that.", "rationale": "Applying a concept is an act with consequences, so a model must say what the label licenses and what it does not.", "layers": [ { "id": "instances", "name": "What counts as an instance", "description": "Clear cases, borderline cases and non-cases.", "findings": [ { "id": "instance-tests", "name": "Tests for an instance", "description": "What would settle whether something falls under it.", "questions": [ { "id": "instance-tests-q01", "text": "What would settle whether something is an instance of positive real number?", "kind": "boundary" }, { "id": "instance-tests-q02", "text": "Which borderline cases are argued about, and on what grounds?", "kind": "definition" } ] } ] }, { "id": "consequence", "name": "Consequence of application", "description": "Rights, duties or decisions that follow from the label.", "findings": [ { "id": "consequence-record", "name": "What the label licenses", "description": "What an agent may do once something is classified this way.", "questions": [ { "id": "consequence-record-q01", "text": "What follows practically once something is treated as positive real number?", "kind": "action" }, { "id": "consequence-record-q02", "text": "What must an agent not infer from the label alone?", "kind": "action" } ] } ] } ] }, { "id": "provenance-and-evidence", "name": "Provenance, evidence and time", "description": "Where every claim about a positive real 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 positive real number and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a positive real 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 positive real 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 positive real 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 positive real number is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a positive real 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 positive real 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 positive real number is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] } ] }, "statistics": { "bundles": 5, "layers": 10, "findings": 12, "questions": 32 } } } }