{ "model": { "rank": 1520, "code": "thing-q7754", "model_id": "vr.tr.mathematical-analysis", "name": "mathematical analysis", "purpose": "Let an agent explain concepts and results of mathematical analysis, support learning and problem solving, and relate analysis to calculus and applications.", "family": "Thing Registry", "category": "Information and virtual systems", "status": "research-draft", "kind": "thing", "plane": "INF", "domain": "INF.KNW", "industry": "", "version": "", "url": "/models/thing/q7754/", "tier": 2, "score": 141, "payload": { "layer": "wikidata", "aliases": [ "p-adic analysis", "fixed point theory", "calculus", "numerical calculus", "microlocal analysis", "Calculus on Euclidean space", "fractional calculus", "differential calculus", "integral calculus", "infinitesimal calculus", "Malliavin calculus", "multiverse analysis", "statistical analysis", "summability theory", "nonstandard analysis", "global analysis", "variational analysis", "non-classical analysis", "complex analysis", "differentiability class", "calculus of variations", "convex analysis", "error analysis", "constructive analysis", "smooth infinitesimal analysis", "algebraic analysis", "Clifford analysis", "computable analysis", "quantum calculus", "quaternionic analysis", "asymptotic analysis", "theorycraft", "real analysis", "differential calculus over commutative algebras", "visual calculus", "non-standard calculus", "constructive non-standard analysis", "Second variation", "error analysis in numerical analysis", "forward error analysis" ], "aliasCount": 42, "merged": 42, "knownIn": 141, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q7754", "url": "https://www.wikidata.org/wiki/Q7754", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-11T19:59:16Z", "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-Q7754", "registryId": "vr.tr.mathematical-analysis", "name": "mathematical analysis", "version": "0.2.0-wave.2", "entryKind": "thing", "family": "Thing Registry", "domain": [ "INF.KNW" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q7754/", "model": { "registry_id": "vr.tr.mathematical-analysis", "name": "mathematical analysis", "purpose": "Let an agent explain concepts and results of mathematical analysis, support learning and problem solving, and relate analysis to calculus and applications.", "definition": "The branch of mathematics dealing with limits, continuity, differentiation, integration, infinite series and related theory, including real and complex analysis, functional analysis, measure theory, numerical and p-adic analysis and fixed point theory; analysis provides the rigorous foundation of calculus and underpins physics, engineering and probability.", "what_it_is_for": "Rigorous study of continuous change and approximation.", "affordances": [ "explain definitions and theorems", "solve and check analysis problems", "relate analysis to calculus and applications", "guide study of the subject" ], "distinguishing_features": [ "Rigorous foundations of calculus", "Limits and continuity", "Many branches", "Proof-based" ], "appearance": "Not physical; definitions, proofs and formulas.", "visual_identification": [ "Limits, epsilon-delta arguments and proofs", "Real, complex and functional branches", "Calculus is the computational face of analysis" ], "physical_properties": [], "families_and_kinds": [ "real analysis", "complex analysis", "functional analysis and operator theory", "measure theory and integration", "numerical, harmonic and p-adic analysis" ], "related_models": [ { "relation": "is a kind of", "target": "pure mathematics", "why": "category" }, { "relation": "includes", "target": "integral", "why": "concept" }, { "relation": "includes", "target": "limit", "why": "concept" }, { "relation": "is related to", "target": "mathematical model", "why": "applications" } ], "identifiers": [], "standards_and_regulation": [ "ISO 80000-2 notation", "No regulation" ], "failure_modes_and_hazards": [ "Confusing intuition with proof", "Misapplying theorems outside their hypotheses", "Notation confusion" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "concepts", "name": "Concepts", "description": "Core ideas.", "rationale": "Rigour.", "layers": [ { "id": "define", "name": "Define", "description": "Definitions.", "findings": [ { "id": "define-finding", "name": "Define", "description": "Definitions.", "questions": [ { "text": "What is the precise definition of this concept, such as limit, continuity or convergence?", "kind": "definition" }, { "text": "How does it differ from the intuitive calculus notion?", "kind": "definition" } ] } ] }, { "id": "theorems", "name": "Theorems", "description": "Key results.", "findings": [ { "id": "theorems-finding", "name": "Theorems", "description": "Theorems.", "questions": [ { "text": "What does this theorem state, and what are its hypotheses?", "kind": "definition" }, { "text": "What are the standard counterexamples?", "kind": "provenance" } ] } ] } ] }, { "id": "solve", "name": "Solve", "description": "Problems and proofs.", "rationale": "Technique.", "layers": [ { "id": "prove", "name": "Prove", "description": "Writing proofs.", "findings": [ { "id": "prove-finding", "name": "Prove", "description": "Proofs.", "questions": [ { "text": "How can this statement be proved, and which techniques apply?", "kind": "action" }, { "text": "Is the argument rigorous at each step?", "kind": "boundary" } ] } ] }, { "id": "compute", "name": "Compute", "description": "Computation.", "findings": [ { "id": "compute-finding", "name": "Compute", "description": "Computation.", "questions": [ { "text": "How is this limit, series or integral evaluated?", "kind": "action" }, { "text": "Which convergence tests apply?", "kind": "definition" } ] } ] } ] }, { "id": "branches", "name": "Branches", "description": "Areas of analysis.", "rationale": "A broad field.", "layers": [ { "id": "which", "name": "Which", "description": "Which branch.", "findings": [ { "id": "which-finding", "name": "Which", "description": "Branch.", "questions": [ { "text": "Which branch of analysis does this topic belong to?", "kind": "definition" }, { "text": "How do the branches connect?", "kind": "definition" } ] } ] }, { "id": "applied", "name": "Applied", "description": "Applications.", "findings": [ { "id": "applied-finding", "name": "Applied", "description": "Applications.", "questions": [ { "text": "How is analysis applied in physics, engineering, probability or numerical computation?", "kind": "provenance" }, { "text": "Which results are used?", "kind": "provenance" } ] } ] } ] }, { "id": "learn", "name": "Learn", "description": "Studying analysis.", "rationale": "Resources.", "layers": [ { "id": "path", "name": "Path", "description": "Learning path.", "findings": [ { "id": "path-finding", "name": "Path", "description": "Learning path.", "questions": [ { "text": "Which textbooks and sequence suit this learner?", "kind": "action" }, { "text": "Which prerequisites are needed?", "kind": "provenance" } ] } ] }, { "id": "history", "name": "History", "description": "History.", "findings": [ { "id": "history-finding", "name": "History", "description": "History.", "questions": [ { "text": "How did analysis develop from calculus to rigorous foundations, according to historians?", "kind": "provenance" }, { "text": "Which mathematicians were key?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Should each branch be a separate entry?", "How should textbooks be linked?", "How should problem sets be linked?" ], "statistics": { "bundles": 4, "layers": 8, "findings": 8, "questions": 16 } }, "draft": { "generator": "vr.draft.v3", "status": "draft-generated", "researched": false, "archetype": "discipline or field of knowledge", "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 mathematical analysis, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain concepts and results of mathematical analysis, support learning and problem solving, and relate analysis to calculus and applications.", "characteristics": { "substance": "information", "origin": "conceptual", "agency": "inert" }, "whatYouCanDoWithIt": [ "read and interpreted" ], "distinguishingFeatures": [ "Names folded into this entry, which a task may need to split apart again: p-adic analysis, fixed point theory, calculus, numerical calculus, microlocal analysis, Calculus on Euclidean space, fractional calculus, differential calculus, integral calculus, infinitesimal calculus, Malliavin calculus, multiverse analysis.", "42 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 141 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 mathematical analysis, and on what evidence are they told apart?" ], "whatItIsMadeOf": "content that has to be carried by something else", "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": [ "read it and act on what it says" ], "howItIsRecognised": [], "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": [ "p-adic analysis", "fixed point theory", "calculus", "numerical calculus", "microlocal analysis", "Calculus on Euclidean space", "fractional calculus", "differential calculus", "integral calculus", "infinitesimal calculus", "Malliavin calculus", "multiverse analysis" ] } ], "standing": "Described in 141 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 42 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 mathematical analysis from another, and a mathematical analysis 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 mathematical analysis, 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 mathematical analysis, 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 mathematical analysis 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 mathematical analysis, 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 mathematical analysis, 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 mathematical analysis 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 mathematical analysis 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 mathematical analysis, 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 mathematical analysis, 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 mathematical analysis 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 mathematical analysis from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a mathematical analysis, 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 mathematical analysis, 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 mathematical analysis 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 mathematical analysis 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 mathematical analysis between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a mathematical analysis, 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 mathematical analysis, 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 mathematical analysis 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 mathematical analysis, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a mathematical analysis 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 mathematical analysis, 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 mathematical analysis, 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 mathematical analysis is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] }, { "id": "content-and-access", "name": "Content, encoding and access", "description": "What a mathematical analysis says, how it is encoded and who may read it.", "rationale": "An informational thing carries content that can be copied, versioned and withheld, none of which its physical carrier explains.", "layers": [ { "id": "content-and-encoding", "name": "Content and encoding", "description": "The content itself, its format and its language.", "findings": [ { "id": "content-and-format", "name": "Content, format and language", "description": "What a mathematical analysis contains and in what form it is held.", "questions": [ { "id": "content-and-format-q01", "text": "What identifies and describes the content of a mathematical analysis, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "content-and-format-q02", "text": "Who or what asserted this about the content of a mathematical analysis, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "content-and-format-q03", "text": "What may an agent decide or do once the content of a mathematical analysis is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] }, { "id": "access-and-rights", "name": "Access, rights and retention", "description": "Who may read, copy or change it, and for how long it is kept.", "findings": [ { "id": "access-rules", "name": "Access rules and retention", "description": "The permissions attached to a mathematical analysis and the period it survives.", "questions": [ { "id": "access-rules-q01", "text": "What identifies and describes access to a mathematical analysis, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "access-rules-q02", "text": "Who or what asserted this about access to a mathematical analysis, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "access-rules-q03", "text": "What may an agent decide or do once access to a mathematical analysis is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] }, { "id": "subject-and-method", "name": "Subject matter and method", "description": "What mathematical analysis studies and how it establishes anything.", "rationale": "A field is identified by its questions and its methods, and those are what distinguish it from the fields next to it.", "layers": [ { "id": "subject", "name": "Subject matter", "description": "The questions it takes as its own.", "findings": [ { "id": "subject-record", "name": "Questions and objects of study", "description": "What it is about, stated so a neighbouring field can be told apart.", "questions": [ { "id": "subject-record-q01", "text": "What questions and objects does mathematical analysis take as its own?", "kind": "definition" }, { "id": "subject-record-q02", "text": "Which questions does it share with a neighbouring field, and who claims them?", "kind": "boundary" } ] } ] }, { "id": "method", "name": "Method and evidence", "description": "How claims are established and what counts as evidence.", "findings": [ { "id": "method-record", "name": "Methods and standards of evidence", "description": "The methods used and what they are taken to establish.", "questions": [ { "id": "method-record-q01", "text": "By what methods does mathematical analysis establish claims, and what counts as sufficient evidence?", "kind": "provenance" }, { "id": "method-record-q02", "text": "What kind of claim can this field not settle, and where should an agent look instead?", "kind": "action" } ] } ] } ] }, { "id": "institutions-and-classification", "name": "Institutions and classification", "description": "Where mathematical analysis is practised and how catalogues place it.", "rationale": "The institutional footprint is the evidence that a field exists as a field rather than as a topic.", "layers": [ { "id": "institutions", "name": "Institutional markers", "description": "Societies, journals, degrees and departments.", "findings": [ { "id": "institution-record", "name": "Bodies and venues", "description": "Where the field organises itself.", "questions": [ { "id": "institution-record-q01", "text": "Which societies, journals or degrees mark mathematical analysis as an established field?", "kind": "provenance" }, { "id": "institution-record-q02", "text": "What would show that it is emerging or dissolving rather than established?", "kind": "boundary" } ] } ] }, { "id": "classification", "name": "Classification schemes", "description": "Where library and research classifications put it.", "findings": [ { "id": "classification-record", "name": "Codes and their disagreements", "description": "The classification codes that place it, and where they differ.", "questions": [ { "id": "classification-record-q01", "text": "Which classification schemes place mathematical analysis, under what codes?", "kind": "definition" }, { "id": "classification-record-q02", "text": "Where do those schemes disagree about its scope?", "kind": "boundary" } ] } ] } ] }, { "id": "provenance-and-evidence", "name": "Provenance, evidence and time", "description": "Where every claim about a mathematical analysis 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 mathematical analysis and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a mathematical analysis, 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 mathematical analysis, 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 mathematical analysis 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 mathematical analysis is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a mathematical analysis, 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 mathematical analysis, 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 mathematical analysis is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] } ] }, "statistics": { "bundles": 6, "layers": 12, "findings": 14, "questions": 38 } } } }