{ "model": { "rank": 411, "code": "thing-q395", "model_id": "vr.tr.mathematics", "name": "mathematics", "purpose": "Let an agent treat mathematics as a discipline with fields, proofs and conventions, and state mathematical claims with their assumptions.", "family": "Thing Registry", "category": "Information and virtual systems", "status": "research-draft", "kind": "thing", "plane": "INF", "domain": "INF.KNW", "industry": "", "version": "", "url": "/models/thing/q395/", "tier": 2, "score": 339, "payload": { "layer": "wikidata", "aliases": [ "systems science", "informal mathematics", "mathematical geography", "ecosystemology", "gnomonics", "combinatorial topology", "mathematical programming", "Māori mathematics", "computational mathematics", "calendrical mathematics", "number theory", "Mathematics-Economics", "mathematical linguistics", "mathematics in medieval Islam", "Indian mathematics", "graph theory", "Synthetic mathematics", "Introduction to advanced algebra: Concepts and application", "K-theory", "mathematical physics", "Japanese mathematics", "analytical mechanics", "ethnomathematics", "mathematical thinking", "modular arithmetic", "elementary mathematics", "business mathematics", "mathematics of paper folding", "applied mathematics", "Rabdology", "gambling mathematics", "topology", "advanced mathematics", "Burchnall–Chaundy theory", "classical mathematics", "Computable topology", "Greek mathematics", "probability theory", "postmodern mathematics", "lottery mathematics" ], "aliasCount": 176, "merged": 176, "knownIn": 339, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": "vr.tr.mathematics", "source": { "dataset": "wikidata", "item": "Q395", "url": "https://www.wikidata.org/wiki/Q395", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-11T05:15:23Z", "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-Q395", "registryId": "vr.tr.mathematics", "name": "mathematics", "version": "0.2.0-wave.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "INF.KNW" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q395/", "model": { "registry_id": "vr.tr.mathematics", "name": "mathematics", "purpose": "Let an agent treat mathematics as a discipline with fields, proofs and conventions, and state mathematical claims with their assumptions.", "definition": "The formal science of quantity, structure, space and change, which proves results from axioms by logical deduction and is used throughout science and engineering.", "what_it_is_for": "Reasoning precisely, modelling the world and computing.", "affordances": [ "prove theorems", "model and compute", "teach and learn it", "verify proofs, including by computer" ], "distinguishing_features": [ "Truth by proof from axioms", "Pure and applied branches", "Conventions and notation vary", "Results are cumulative and rarely overturned, unlike empirical science" ], "appearance": "Symbols, equations, proofs, diagrams and code.", "visual_identification": [ "Notation and proofs", "Field labels in the Mathematics Subject Classification", "Applied fields such as mathematical programming" ], "physical_properties": [], "families_and_kinds": [ "algebra", "analysis", "geometry and topology", "number theory", "probability and statistics", "discrete mathematics", "applied mathematics and optimisation" ], "related_models": [ { "relation": "has part", "target": "integer, sequence, series", "why": "objects of study" }, { "relation": "is used in", "target": "science and engineering", "why": "applications" }, { "relation": "is a kind of", "target": "formal science", "why": "discipline" }, { "relation": "is confused with", "target": "arithmetic", "why": "a small part" } ], "identifiers": [ { "scheme": "MSC 2020 code", "value_or_pattern": "two digits, letter, two digits", "note": "Mathematics Subject Classification" } ], "standards_and_regulation": [ "ISO 80000-2 mathematical signs and symbols" ], "failure_modes_and_hazards": [ "Unstated assumptions", "Errors in unverified proofs", "Misapplied models" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "fields", "name": "Fields", "description": "Branches.", "rationale": "The field locates a result.", "layers": [ { "id": "branch", "name": "Branch", "description": "MSC classification.", "findings": [ { "id": "branch-finding", "name": "Branch", "description": "The branch.", "questions": [ { "text": "Which branch of mathematics is this?", "kind": "definition" }, { "text": "Which MSC code applies?", "kind": "provenance" } ] } ] }, { "id": "objects", "name": "Objects", "description": "What is studied.", "findings": [ { "id": "objects-finding", "name": "Objects", "description": "Mathematical objects.", "questions": [ { "text": "Which objects does it concern?", "kind": "definition" }, { "text": "How are they defined?", "kind": "definition" } ] } ] } ] }, { "id": "claims", "name": "Claims", "description": "Theorems and conjectures.", "rationale": "Status of a claim is crucial.", "layers": [ { "id": "status", "name": "Status", "description": "Proven or conjectured.", "findings": [ { "id": "status-finding", "name": "Status", "description": "Proof status.", "questions": [ { "text": "Is this result proven, and where?", "kind": "provenance" }, { "text": "Is it a conjecture?", "kind": "boundary" } ] } ] }, { "id": "assumptions", "name": "Assumptions", "description": "Axioms and hypotheses.", "findings": [ { "id": "assumptions-finding", "name": "Assumptions", "description": "Assumptions required.", "questions": [ { "text": "Which assumptions does the result need?", "kind": "definition" }, { "text": "What fails without them?", "kind": "boundary" } ] } ] } ] }, { "id": "applications", "name": "Applications", "description": "Using mathematics.", "rationale": "Models are only as good as their fit.", "layers": [ { "id": "models", "name": "Models", "description": "Mathematical models.", "findings": [ { "id": "models-finding", "name": "Model", "description": "The model used.", "questions": [ { "text": "Which mathematical model is used, and why?", "kind": "definition" }, { "text": "How well does it fit the data?", "kind": "measurement" } ] } ] }, { "id": "computation", "name": "Computation", "description": "Numerics.", "findings": [ { "id": "computation-finding", "name": "Computation", "description": "Numerical methods.", "questions": [ { "text": "Which numerical methods are used?", "kind": "definition" }, { "text": "What are their error bounds?", "kind": "measurement" } ] } ] } ] }, { "id": "learning", "name": "Learning", "description": "Teaching mathematics.", "rationale": "Learning mathematics needs clear explanation.", "layers": [ { "id": "explanation", "name": "Explanation", "description": "Clear reasoning.", "findings": [ { "id": "explanation-finding", "name": "Explanation", "description": "How to explain.", "questions": [ { "text": "How can this be explained step by step?", "kind": "action" }, { "text": "What misconceptions are common?", "kind": "boundary" } ] } ] }, { "id": "verification", "name": "Verification", "description": "Checking work.", "findings": [ { "id": "verification-finding", "name": "Verification", "description": "How to check.", "questions": [ { "text": "How can the result be checked?", "kind": "action" }, { "text": "Should a proof assistant be used?", "kind": "definition" } ] } ] } ] } ] }, "openQuestions": [ "Should fields be separate entries by MSC?", "How should agents distinguish proven results from conjectures?", "The registry entry has merged aliases such as ecosystemology; should they be split off?" ], "statistics": { "bundles": 4, "layers": 8, "findings": 8, "questions": 16 } }, "draft": { "generator": "vr.draft.v3", "status": "draft-generated", "researched": false, "archetype": "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 mathematics, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent treat mathematics as a discipline with fields, proofs and conventions, and state mathematical claims with their assumptions.", "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: systems science, informal mathematics, mathematical geography, ecosystemology, gnomonics, combinatorial topology, mathematical programming, Māori mathematics, computational mathematics, calendrical mathematics, number theory, Mathematics-Economics.", "176 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 339 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 mathematics, 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": [ "systems science", "informal mathematics", "mathematical geography", "ecosystemology", "gnomonics", "combinatorial topology", "mathematical programming", "Māori mathematics", "computational mathematics", "calendrical mathematics", "number theory", "Mathematics-Economics" ] } ], "standing": "Described in 339 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 176 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 mathematics from another, and a mathematics 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 mathematics, 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 mathematics, 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 mathematics 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 mathematics, 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 mathematics, 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 mathematics 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 mathematics 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 mathematics, 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 mathematics, 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 mathematics 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 mathematics from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a mathematics, 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 mathematics, 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 mathematics 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 mathematics 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 mathematics between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a mathematics, 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 mathematics, 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 mathematics 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 mathematics, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a mathematics 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 mathematics, 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 mathematics, 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 mathematics 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 mathematics 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 mathematics contains and in what form it is held.", "questions": [ { "id": "content-and-format-q01", "text": "What identifies and describes the content of a mathematics, 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 mathematics, 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 mathematics 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 mathematics and the period it survives.", "questions": [ { "id": "access-rules-q01", "text": "What identifies and describes access to a mathematics, 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 mathematics, 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 mathematics 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 mathematics 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 mathematics 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 mathematics 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 mathematics 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 mathematics 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 mathematics, 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 mathematics 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 mathematics and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a mathematics, 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 mathematics, 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 mathematics 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 mathematics is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a mathematics, 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 mathematics, 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 mathematics 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 } } } }