{ "model": { "rank": 4860, "code": "thing-q131187", "model_id": "vr.tr.taylor-series", "name": "Taylor series", "purpose": "Let an agent handle Taylor series by function, centre, terms, convergence and error bounds.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.REL", "industry": "", "version": "", "url": "/models/thing/q131187/", "tier": 2, "score": 72, "payload": { "layer": "wikidata", "aliases": [ "Taylor expansions for the moments of functions of random variables", "MacLaurin series" ], "aliasCount": 2, "merged": 2, "knownIn": 72, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q131187", "url": "https://www.wikidata.org/wiki/Q131187", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-11T07:03:19Z", "providers": [ "Claude" ], "breadth": "written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify", "pass": 2, "wave": 1, "engine": "claude" }, "metaModel": { "id": "THING-Q131187", "registryId": "vr.tr.taylor-series", "name": "Taylor series", "version": "0.2.0-wave.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.REL" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q131187/", "model": { "registry_id": "vr.tr.taylor-series", "name": "Taylor series", "purpose": "Let an agent handle Taylor series by function, centre, terms, convergence and error bounds.", "definition": "A representation of a function as an infinite sum of terms computed from its derivatives at a single point; centred at zero it is called a Maclaurin series.", "what_it_is_for": "Approximating functions, analysing behaviour and computing numerically.", "affordances": [ "compute the series", "truncate to a polynomial approximation", "bound the remainder", "find the radius of convergence" ], "distinguishing_features": [ "Built from derivatives at a point", "Converges within a radius", "Remainder terms bound errors", "Not all smooth functions equal their series" ], "appearance": "A sum of terms f^(n)(a)/n! times (x - a)^n.", "visual_identification": [ "Factorials and powers of (x - a)", "Maclaurin series when a = 0", "Laurent series include negative powers" ], "physical_properties": [], "families_and_kinds": [ "Maclaurin series", "Taylor polynomials", "multivariable Taylor series", "Taylor expansions in statistics (delta method)" ], "related_models": [ { "relation": "is a kind of", "target": "power series", "why": "category" }, { "relation": "uses", "target": "derivative", "why": "ingredient" }, { "relation": "is generalised by", "target": "Laurent series", "why": "generalisation" }, { "relation": "is studied in", "target": "calculus", "why": "field" } ], "identifiers": [], "standards_and_regulation": [], "failure_modes_and_hazards": [ "Using outside the radius of convergence", "Ignoring remainder error", "Assuming analyticity" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "series", "name": "Series", "description": "Which expansion.", "rationale": "Function and centre define it.", "layers": [ { "id": "function", "name": "Function", "description": "What is expanded.", "findings": [ { "id": "function-finding", "name": "Function", "description": "Function and centre.", "questions": [ { "text": "Which function is expanded, about which point?", "kind": "definition" }, { "text": "What are the first terms?", "kind": "measurement" } ] } ] }, { "id": "terms", "name": "Terms", "description": "Coefficients.", "findings": [ { "id": "terms-finding", "name": "Terms", "description": "Coefficients.", "questions": [ { "text": "What is the general term?", "kind": "definition" }, { "text": "How are derivatives computed?", "kind": "action" } ] } ] } ] }, { "id": "convergence", "name": "Convergence", "description": "Where it works.", "rationale": "Convergence limits use.", "layers": [ { "id": "radius", "name": "Radius", "description": "Radius of convergence.", "findings": [ { "id": "radius-finding", "name": "Radius", "description": "Radius.", "questions": [ { "text": "What is the radius of convergence?", "kind": "measurement" }, { "text": "What happens at the boundary?", "kind": "boundary" } ] } ] }, { "id": "analyticity", "name": "Analyticity", "description": "Equality.", "findings": [ { "id": "analyticity-finding", "name": "Analyticity", "description": "Analyticity.", "questions": [ { "text": "Does the series equal the function in that region?", "kind": "boundary" }, { "text": "Is there a counterexample?", "kind": "boundary" } ] } ] } ] }, { "id": "approximation", "name": "Approximation", "description": "Truncation.", "rationale": "Truncation gives approximations.", "layers": [ { "id": "order", "name": "Order", "description": "Terms kept.", "findings": [ { "id": "order-finding", "name": "Order", "description": "Truncation order.", "questions": [ { "text": "How many terms are needed for the required accuracy?", "kind": "measurement" }, { "text": "Over what interval?", "kind": "boundary" } ] } ] }, { "id": "error", "name": "Error", "description": "Remainder.", "findings": [ { "id": "error-finding", "name": "Error", "description": "Error bound.", "questions": [ { "text": "What is the remainder bound?", "kind": "measurement" }, { "text": "Which remainder form is used?", "kind": "definition" } ] } ] } ] }, { "id": "applications", "name": "Applications", "description": "Uses.", "rationale": "Taylor series are everywhere.", "layers": [ { "id": "numerics", "name": "Numerics", "description": "Computation.", "findings": [ { "id": "numerics-finding", "name": "Numerics", "description": "Numerical use.", "questions": [ { "text": "How is the series used in numerical methods?", "kind": "definition" }, { "text": "Is it stable?", "kind": "boundary" } ] } ] }, { "id": "physics", "name": "Physics", "description": "Linearisation.", "findings": [ { "id": "physics-finding", "name": "Physics", "description": "Linearisation.", "questions": [ { "text": "How does linearisation use the first terms?", "kind": "definition" }, { "text": "When is it valid?", "kind": "boundary" } ] } ] } ] } ] }, "openQuestions": [ "Should Taylor polynomials be a separate entry?", "How should standard expansions be listed?", "How should the statistics use 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 Taylor series, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent handle Taylor series by function, centre, terms, convergence and error bounds.", "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: Taylor expansions for the moments of functions of random variables, MacLaurin series.", "2 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 72 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 Taylor series, 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": [ "Taylor expansions for the moments of functions of random variables", "MacLaurin series" ] } ], "standing": "Described in 72 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 2 finer distinctions are held inside this entry as names rather than as separate models.", "structure": { "bundles": [ { "id": "identity-and-classification", "name": "Identity, naming and classification", "description": "How an agent tells one Taylor series from another, and a Taylor series 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 Taylor series, 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 Taylor series, 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 Taylor series 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 Taylor series, 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 Taylor series, 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 Taylor series 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 Taylor series 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 Taylor series, 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 Taylor series, 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 Taylor series 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 Taylor series from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a Taylor series, 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 Taylor series, 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 Taylor series 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 Taylor series 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 Taylor series between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a Taylor series, 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 Taylor series, 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 Taylor series 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 Taylor series, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a Taylor series 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 Taylor series, 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 Taylor series, 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 Taylor series 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 Taylor series 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 Taylor series 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 Taylor series 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 Taylor series 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 Taylor series?", "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 Taylor series?", "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 Taylor series 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 Taylor series and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a Taylor series, 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 Taylor series, 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 Taylor series 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 Taylor series is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a Taylor series, 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 Taylor series, 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 Taylor series 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 } } } }