{ "model": { "rank": 2918, "code": "thing-q4440864", "model_id": "vr.tr.dimension", "name": "dimension", "purpose": "Let an agent explain mathematical dimension in its various senses, compute or identify the dimension of a given object, separate the measurement sense, and support learning across levels.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q4440864/", "tier": 2, "score": 94, "payload": { "layer": "wikidata", "aliases": [ "Krasnoselskii genus", "Krull dimension", "Weld size", "Leg size", "Throat thickness", "Root opening", "Groove angle", "Weld width", "Weld reinforcement", "fractal dimension", "Lebesgue covering dimension", "critical dimension", "dimension of an algebraic variety", "Gelfand–Kirillov dimension", "Hausdorff dimension", "dimension of a scheme", "inductive dimension" ], "aliasCount": 17, "merged": 17, "knownIn": 94, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": "vr.tr.dimension-cognition", "source": { "dataset": "wikidata", "item": "Q4440864", "url": "https://www.wikidata.org/wiki/Q4440864", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-11T21:59:31Z", "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-Q4440864", "registryId": "vr.tr.dimension", "name": "dimension", "version": "0.2.0-wave.2", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q4440864/", "model": { "registry_id": "vr.tr.dimension", "name": "dimension", "purpose": "Let an agent explain mathematical dimension in its various senses, compute or identify the dimension of a given object, separate the measurement sense, and support learning across levels.", "definition": "A mathematical property of a space or object giving the number of independent coordinates needed to specify a point, generalised to notions such as the dimension of a vector space, topological and fractal dimensions, the Krull dimension of a ring and other algebraic and analytic dimensions; the word also denotes measured sizes such as length, width and height and, in engineering, specified sizes such as weld leg and throat dimensions.", "what_it_is_for": "Degrees of freedom and measured sizes.", "affordances": [ "explain notions of dimension", "determine the dimension of a space or object", "separate measurement and engineering senses", "support learning" ], "distinguishing_features": [ "Degrees of freedom", "Many generalisations", "Integer or fractional", "Also a size measure" ], "appearance": "Not physical; a number attached to a space or a measurement of size.", "visual_identification": [ "Number of independent coordinates", "Generalised in many ways", "A measured length is the everyday sense" ], "physical_properties": [], "families_and_kinds": [ "dimension of vector spaces", "topological dimension", "fractal and Hausdorff dimension", "algebraic dimensions such as Krull dimension", "measured dimensions and engineering sizes" ], "related_models": [ { "relation": "is a kind of", "target": "mathematical property", "why": "category" }, { "relation": "is related to", "target": "ordered pair", "why": "coordinates" }, { "relation": "is related to", "target": "homomorphism", "why": "linear maps and rank" }, { "relation": "is related to", "target": "intensive quantity", "why": "dimensional analysis contrast" } ], "identifiers": [], "standards_and_regulation": [ "Mathematical conventions", "Engineering drawing and welding standards for sizes" ], "failure_modes_and_hazards": [ "Confusing senses of dimension", "Assuming dimension is always an integer", "Misreading engineering dimensions" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "define", "name": "Define", "description": "What dimension means.", "rationale": "Senses.", "layers": [ { "id": "senses", "name": "Senses", "description": "Which sense.", "findings": [ { "id": "senses-finding", "name": "Senses", "description": "Senses.", "questions": [ { "text": "Is the mathematical dimension of a space, a measured size, a physical dimension in unit analysis or an engineering specification meant?", "kind": "boundary" }, { "text": "Which entry fits?", "kind": "action" } ] } ] }, { "id": "basic", "name": "Basic", "description": "Dimension of a space.", "findings": [ { "id": "basic-finding", "name": "Basic", "description": "Basic notion.", "questions": [ { "text": "What is the dimension of a vector space or manifold, and why is it well defined?", "kind": "definition" }, { "text": "How is the dimension of this object computed?", "kind": "action" } ] } ] } ] }, { "id": "generalise", "name": "Generalise", "description": "Beyond the basics.", "rationale": "Advanced notions.", "layers": [ { "id": "topological", "name": "Topological", "description": "Topological and fractal.", "findings": [ { "id": "topological-finding", "name": "Topological", "description": "Topological and fractal.", "questions": [ { "text": "What are topological, Hausdorff and box-counting dimensions, and how can dimension be fractional?", "kind": "definition" }, { "text": "What is the dimension of a given fractal?", "kind": "action" } ] } ] }, { "id": "algebraic", "name": "Algebraic", "description": "Algebraic dimensions.", "findings": [ { "id": "algebraic-finding", "name": "Algebraic", "description": "Algebraic.", "questions": [ { "text": "What is the Krull dimension of a ring, and how does it relate to geometric dimension?", "kind": "definition" }, { "text": "Which other algebraic dimensions exist?", "kind": "definition" } ] } ] } ] }, { "id": "apply", "name": "Apply", "description": "Uses.", "rationale": "Applications.", "layers": [ { "id": "physics", "name": "Physics", "description": "Dimensions in physics.", "findings": [ { "id": "physics-finding", "name": "Physics", "description": "Physics.", "questions": [ { "text": "How is dimension used in physics, from spacetime to higher-dimensional theories, with speculative parts attributed?", "kind": "provenance" }, { "text": "What is the curse of dimensionality in data?", "kind": "definition" } ] } ] }, { "id": "engineering", "name": "Engineering", "description": "Engineering sizes.", "findings": [ { "id": "engineering-finding", "name": "Engineering", "description": "Engineering.", "questions": [ { "text": "What do weld dimensions such as leg size, throat thickness and root opening mean, and which standards specify them?", "kind": "provenance" }, { "text": "How are dimensions shown on drawings?", "kind": "provenance" } ] } ] } ] }, { "id": "learn", "name": "Learn", "description": "Teaching.", "rationale": "Education.", "layers": [ { "id": "teach", "name": "Teach", "description": "Teaching dimension.", "findings": [ { "id": "teach-finding", "name": "Teach", "description": "Teaching.", "questions": [ { "text": "How can dimension be taught from coordinates to fractals?", "kind": "action" }, { "text": "Which misconceptions arise?", "kind": "provenance" } ] } ] }, { "id": "history", "name": "History", "description": "History.", "findings": [ { "id": "history-finding", "name": "History", "description": "History.", "questions": [ { "text": "How did the concept of dimension develop, from Euclid to Cantor, Hausdorff and beyond?", "kind": "provenance" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Should each notion of dimension be a separate entry?", "How should engineering standards be linked?", "How should physical dimension analysis be linked?" ], "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 dimension, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain mathematical dimension in its various senses, compute or identify the dimension of a given object, separate the measurement sense, and support learning across levels.", "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: Krasnoselskii genus, Krull dimension, Weld size, Leg size, Throat thickness, Root opening, Groove angle, Weld width, Weld reinforcement, fractal dimension, Lebesgue covering dimension, critical dimension.", "17 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 94 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 dimension, 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": [ "Krasnoselskii genus", "Krull dimension", "Weld size", "Leg size", "Throat thickness", "Root opening", "Groove angle", "Weld width", "Weld reinforcement", "fractal dimension", "Lebesgue covering dimension", "critical dimension" ] } ], "standing": "Described in 94 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 17 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 dimension from another, and a dimension 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 dimension, 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 dimension, 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 dimension 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 dimension, 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 dimension, 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 dimension 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 dimension 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 dimension, 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 dimension, 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 dimension 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 dimension from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a dimension, 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 dimension, 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 dimension 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 dimension 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 dimension between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a dimension, 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 dimension, 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 dimension 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 dimension, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a dimension 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 dimension, 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 dimension, 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 dimension 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 dimension 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 dimension 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 dimension 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 dimension 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 dimension?", "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 dimension?", "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 dimension 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 dimension and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a dimension, 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 dimension, 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 dimension 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 dimension is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a dimension, 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 dimension, 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 dimension 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 } } } }