{ "model": { "rank": 8536, "code": "thing-q27058", "model_id": "vr.tr.approximation", "name": "approximation", "purpose": "Let an agent explain approximation as a concept and practice, relay how errors are bounded and reported, describe kinds across mathematics, science and everyday use, and separate the concept from unrelated aliases in the registry entry.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q27058/", "tier": 2, "score": 50, "payload": { "layer": "wikidata", "aliases": [ "overfitting", "scale analysis", "pressure altitude", "conventional date", "paraxial approximation", "approximate centre point", "approximations of π", "semiclassical approximation", "numerical solution", "staircase approximation", "small-angle approximation", "Korovkin approximation", "stationary phase approximation", "Whittle likelihood", "sigma approximation", "effective medium approximations", "approximate value", "empty lattice approximation", "point counting", "curve fitting", "least-squares function approximation", "minisuperspace", "two-stream approximation", "stochastic approximation", "curve interpolation" ], "aliasCount": 25, "merged": 25, "knownIn": 50, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q27058", "url": "https://www.wikidata.org/wiki/Q27058", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-12T22:59:37Z", "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-Q27058", "registryId": "vr.tr.approximation", "name": "approximation", "version": "0.2.0-wave.3", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q27058/", "model": { "registry_id": "vr.tr.approximation", "name": "approximation", "purpose": "Let an agent explain approximation as a concept and practice, relay how errors are bounded and reported, describe kinds across mathematics, science and everyday use, and separate the concept from unrelated aliases in the registry entry.", "definition": "A value, representation or model that is close to but not exactly equal to the true value or full description, used when exactness is unattainable, unnecessary or too costly, as in rounded decimals, approximate dates, simplified physical models such as the paraxial approximation and scale analysis, and estimated centre points; approximation is governed by error bounds and is studied in numerical analysis and approximation theory, while overfitting is a failure of approximation in statistics.", "what_it_is_for": "Working with values and models that are close enough for a purpose.", "affordances": [ "explain the concept and error bounds", "describe kinds across fields", "help choose and report approximations", "separate unrelated aliases" ], "distinguishing_features": [ "Bounded error", "Purpose-dependent accuracy", "Trade-off with cost", "Formal theory" ], "appearance": "Not a visible object; rounded numbers, simplified formulas and models.", "visual_identification": [ "Close but inexact value or model", "Numerical, physical, statistical and everyday forms", "An estimate is an approximation from incomplete data; an error is the difference from the truth" ], "physical_properties": [], "families_and_kinds": [ "numerical approximation and rounding", "approximation of functions and series", "physical approximations such as paraxial optics and scale analysis", "approximate dates and conventional dates in history", "geometric approximations such as approximate centre points", "model approximations, with overfitting as a failure mode" ], "related_models": [ { "relation": "is a kind of", "target": "method", "why": "in registry terms" }, { "relation": "is a kind of", "target": "decimal representation", "why": "in registry terms, for rounding" }, { "relation": "is bounded by", "target": "approximation error", "why": "the difference from the truth" }, { "relation": "is studied by", "target": "numerical analysis", "why": "and approximation theory" } ], "identifiers": [ { "scheme": "symbol", "value_or_pattern": "approximately equal sign", "note": "Unicode U+2248" } ], "standards_and_regulation": [ "ISO 80000 rules for rounding and significant figures", "Measurement uncertainty guidance such as the GUM", "Standards for reporting approximate dates in cataloguing" ], "failure_modes_and_hazards": [ "Unstated or underestimated error", "Approximations used outside their range of validity", "Overfitting in models", "Sense confusion with unrelated aliases" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "concept", "name": "Concept", "description": "What approximation is.", "rationale": "Definition.", "layers": [ { "id": "definition", "name": "Definition", "description": "Definition and error.", "findings": [ { "id": "definition-finding", "name": "Definition", "description": "Definition.", "questions": [ { "text": "What is an approximation, and how is its error defined and bounded?", "kind": "definition" }, { "text": "Is the question about approximation, estimation or measurement uncertainty?", "kind": "boundary" } ] } ] }, { "id": "kinds", "name": "Kinds", "description": "Kinds across fields.", "findings": [ { "id": "kinds-finding", "name": "Kinds", "description": "Kinds.", "questions": [ { "text": "What kinds of approximation are used in mathematics, physics, statistics and everyday life?", "kind": "definition" }, { "text": "Which entry fits the specific kind?", "kind": "action" } ] } ] } ] }, { "id": "apply", "name": "Apply", "description": "Choosing and reporting.", "rationale": "Computation.", "layers": [ { "id": "choose", "name": "Choose", "description": "Choosing an approximation.", "findings": [ { "id": "choose-finding", "name": "Choose", "description": "Choose.", "questions": [ { "text": "How is an appropriate approximation chosen for a given accuracy and cost?", "kind": "action" }, { "text": "What error applies in the case in question?", "kind": "measurement" } ] } ] }, { "id": "report", "name": "Report", "description": "Reporting.", "findings": [ { "id": "report-finding", "name": "Report", "description": "Report.", "questions": [ { "text": "How should approximations and their uncertainty be reported, per standards?", "kind": "action" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] } ] }, { "id": "theory", "name": "Theory", "description": "Theory.", "rationale": "Theory.", "layers": [ { "id": "numerical", "name": "Numerical", "description": "Numerical analysis.", "findings": [ { "id": "numerical-finding", "name": "Numerical", "description": "Numerical.", "questions": [ { "text": "How do numerical analysis and approximation theory treat convergence and error?", "kind": "provenance" }, { "text": "Which entry fits numerical analysis?", "kind": "action" } ] } ] }, { "id": "models", "name": "Models", "description": "Model approximation.", "findings": [ { "id": "models-finding", "name": "Models", "description": "Models.", "questions": [ { "text": "How do physical and statistical models approximate reality, and what is overfitting?", "kind": "provenance" }, { "text": "Which entry fits overfitting?", "kind": "action" } ] } ] } ] }, { "id": "context", "name": "Context", "description": "History and teaching.", "rationale": "Context.", "layers": [ { "id": "history", "name": "History", "description": "History.", "findings": [ { "id": "history-finding", "name": "History", "description": "History.", "questions": [ { "text": "How did approximation methods develop, from ancient estimates of pi to modern computation?", "kind": "provenance" }, { "text": "Which entry fits the history of mathematics?", "kind": "action" } ] } ] }, { "id": "teach", "name": "Teach", "description": "Teaching.", "findings": [ { "id": "teach-finding", "name": "Teach", "description": "Teaching.", "questions": [ { "text": "How is approximation taught, and which misconceptions arise?", "kind": "provenance" }, { "text": "Which sources are cited?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Should approximation theory and rounding be separate entries?", "How should uncertainty standards be linked?", "The registry entry has merged aliases for unrelated concepts such as pressure altitude; should they be removed?" ], "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 approximation, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain approximation as a concept and practice, relay how errors are bounded and reported, describe kinds across mathematics, science and everyday use, and separate the concept from unrelated aliases in the registry entry.", "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: overfitting, scale analysis, pressure altitude, conventional date, paraxial approximation, approximate centre point, approximations of π, semiclassical approximation, numerical solution, staircase approximation, small-angle approximation, Korovkin approximation.", "25 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 50 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 approximation, 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": [ "overfitting", "scale analysis", "pressure altitude", "conventional date", "paraxial approximation", "approximate centre point", "approximations of π", "semiclassical approximation", "numerical solution", "staircase approximation", "small-angle approximation", "Korovkin approximation" ] } ], "standing": "Described in 50 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 25 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 approximation from another, and a approximation 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 approximation, 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 approximation, 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 approximation 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 approximation, 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 approximation, 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 approximation 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 approximation 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 approximation, 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 approximation, 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 approximation 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 approximation from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a approximation, 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 approximation, 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 approximation 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 approximation 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 approximation between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a approximation, 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 approximation, 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 approximation 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 approximation, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a approximation 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 approximation, 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 approximation, 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 approximation 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 approximation 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 approximation 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 approximation 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 approximation 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 approximation?", "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 approximation?", "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 approximation 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 approximation and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a approximation, 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 approximation, 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 approximation 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 approximation is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a approximation, 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 approximation, 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 approximation 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 } } } }