{ "model": { "rank": 15332, "code": "thing-q1140046", "model_id": "vr.tr.mathematical-notation", "name": "mathematical notation", "purpose": "Let an agent explain mathematical notation and its main conventions, relay standards and history from mathematical references, describe regional and field variations such as decimal separators, and distinguish notation from the mathematical concepts it expresses and from typesetting systems.", "family": "Thing Registry", "category": "Information and virtual systems", "status": "research-draft", "kind": "thing", "plane": "INF", "domain": "INF.MED", "industry": "", "version": "", "url": "/models/thing/q1140046/", "tier": 2, "score": 34, "payload": { "layer": "wikidata", "aliases": [ "type ascription", "radix character", "thousands separator", "function notation", "existential graph", "sigma notation", "sequence notation", "interval notation", "Voigt notation", "Conway triangle notation", "Feynman slash notation", "notation for differentiation", "set-builder notation", "actuarial notation", "common operator notation", "De Bruijn index", "De Bruijn notation", "string diagram", "Landau notation", "٬", "Lagrange's notation" ], "aliasCount": 21, "merged": 21, "knownIn": 34, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q1140046", "url": "https://www.wikidata.org/wiki/Q1140046", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-13T05:36:56Z", "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-Q1140046", "registryId": "vr.tr.mathematical-notation", "name": "mathematical notation", "version": "0.2.0-wave.3", "entryKind": "thing", "family": "Thing Registry", "domain": [ "INF.MED" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q1140046/", "model": { "registry_id": "vr.tr.mathematical-notation", "name": "mathematical notation", "purpose": "Let an agent explain mathematical notation and its main conventions, relay standards and history from mathematical references, describe regional and field variations such as decimal separators, and distinguish notation from the mathematical concepts it expresses and from typesetting systems.", "definition": "The system of symbols and conventions used to write mathematical expressions, including numerals and radix characters such as the decimal point and thousands separators, operator and function notation such as f(x), summation or sigma notation, set, logic and type notations such as type ascription, and diagrammatic systems such as Peirce s existential graphs, developed over centuries and standardised in part by ISO 80000-2; notation varies across countries and fields and shapes how mathematics is taught and communicated.", "what_it_is_for": "Writing mathematics.", "affordances": [ "explain conventions", "relay standards and history", "describe variations", "distinguish from concepts and typesetting" ], "distinguishing_features": [ "Symbolic conventions", "Historical layering", "Regional variation", "Partial standardisation" ], "appearance": "Symbols, letters and layouts on a page or screen.", "visual_identification": [ "Symbols and conventions for mathematics", "Radix characters, thousands separators, function notation, sigma notation, type ascription, existential graphs", "The concepts are what notation expresses; LaTeX is a typesetting tool; programming syntax is related but distinct" ], "physical_properties": [ { "quantity": "ISO standard", "typical_range": "ISO 80000-2", "unit": "note", "note": "quantities and units, mathematics" }, { "quantity": "decimal separator", "typical_range": "point or comma", "unit": "note", "note": "varies by country" }, { "quantity": "equals sign introduced", "typical_range": "1557", "unit": "year", "note": "Robert Recorde" } ], "families_and_kinds": [ "numeral notation including radix characters and digit grouping", "operator and function notation", "summation, product and integral notation", "set, logic and type notation including type ascription", "diagrammatic notations such as existential graphs and commutative diagrams", "field-specific notations in physics, statistics and computing" ], "related_models": [ { "relation": "is a kind of", "target": "notation", "why": "in registry terms" }, { "relation": "is a kind of", "target": "mathematical convention", "why": "in registry terms" }, { "relation": "is standardised by", "target": "ISO 80000-2", "why": "in part" }, { "relation": "is typeset with", "target": "LaTeX", "why": "and other systems" } ], "identifiers": [], "standards_and_regulation": [ "ISO 80000-2 mathematical signs and symbols", "Unicode mathematical symbols", "National conventions for decimal and thousands separators" ], "failure_modes_and_hazards": [ "Ambiguity between conventions such as decimal comma and point", "Confusing notation with the underlying concept", "Inconsistent notation across sources" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "understand", "name": "Understand", "description": "What mathematical notation is.", "rationale": "Definition.", "layers": [ { "id": "definition", "name": "Definition", "description": "Definition.", "findings": [ { "id": "definition-finding", "name": "Definition", "description": "Definition.", "questions": [ { "text": "What is mathematical notation, and how does it differ from the concepts it expresses and from typesetting?", "kind": "definition" }, { "text": "Is the question about notation in general, a specific symbol or a typesetting tool?", "kind": "boundary" } ] } ] }, { "id": "kinds", "name": "Kinds", "description": "Kinds.", "findings": [ { "id": "kinds-finding", "name": "Kinds", "description": "Kinds.", "questions": [ { "text": "What are numeral, operator, function, sigma, set, logic and type notations, and what are existential graphs?", "kind": "definition" }, { "text": "Which entry fits the specific notation?", "kind": "action" } ] } ] } ] }, { "id": "use", "name": "Use", "description": "Using notation.", "rationale": "Practice.", "layers": [ { "id": "conventions", "name": "Conventions", "description": "Conventions.", "findings": [ { "id": "conventions-finding", "name": "Conventions", "description": "Conventions.", "questions": [ { "text": "What conventions govern precedence, grouping, variables and function notation?", "kind": "provenance" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] }, { "id": "variation", "name": "Variation", "description": "Regional variation.", "findings": [ { "id": "variation-finding", "name": "Variation", "description": "Variation.", "questions": [ { "text": "How do radix characters, thousands separators and other conventions vary across countries and fields?", "kind": "provenance" }, { "text": "Which sources are cited?", "kind": "provenance" } ] } ] } ] }, { "id": "standards", "name": "Standards", "description": "Standards and tools.", "rationale": "Regulation.", "layers": [ { "id": "iso", "name": "ISO", "description": "ISO 80000-2 and Unicode.", "findings": [ { "id": "iso-finding", "name": "ISO", "description": "ISO.", "questions": [ { "text": "What do ISO 80000-2 and Unicode specify for mathematical symbols?", "kind": "provenance" }, { "text": "Which entry fits ISO 80000-2?", "kind": "action" } ] } ] }, { "id": "typesetting", "name": "Typesetting", "description": "Typesetting.", "findings": [ { "id": "typesetting-finding", "name": "Typesetting", "description": "Typesetting.", "questions": [ { "text": "How are LaTeX, MathML and other systems used to typeset notation?", "kind": "provenance" }, { "text": "Which entry fits LaTeX?", "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 notation develop from Diophantus and Arabic algebra to Leibniz, Euler and modern symbols?", "kind": "provenance" }, { "text": "Which entry fits the history of mathematical notation?", "kind": "action" } ] } ] }, { "id": "teaching", "name": "Teaching", "description": "Teaching.", "findings": [ { "id": "teaching-finding", "name": "Teaching", "description": "Teaching.", "questions": [ { "text": "How does notation affect learning, and what debates exist about notation in education?", "kind": "provenance" }, { "text": "Which entry fits mathematics education?", "kind": "action" } ] } ] } ] } ] }, "openQuestions": [ "Should sigma notation and decimal separator be separate primary entries?", "How should standards be linked?", "The registry entry has merged aliases naming specific notations; 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": "work, medium or creative form", "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 notation, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain mathematical notation and its main conventions, relay standards and history from mathematical references, describe regional and field variations such as decimal separators, and distinguish notation from the mathematical concepts it expresses and from typesetting systems.", "characteristics": { "substance": "information", "origin": "conceptual", "agency": "inert" }, "whatYouCanDoWithIt": [ "read and interpreted", "observed and measured" ], "distinguishingFeatures": [ "Names folded into this entry, which a task may need to split apart again: type ascription, radix character, thousands separator, function notation, existential graph, sigma notation, sequence notation, interval notation, Voigt notation, Conway triangle notation, Feynman slash notation, notation for differentiation.", "21 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 34 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 notation, 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", "observe it, measure it, record its state" ], "howItIsRecognised": [ "What is seen is a copy or a performance, not the work. Recognising the work means recognising the content through whatever is carrying it." ], "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": [ "type ascription", "radix character", "thousands separator", "function notation", "existential graph", "sigma notation", "sequence notation", "interval notation", "Voigt notation", "Conway triangle notation", "Feynman slash notation", "notation for differentiation" ] } ], "standing": "Described in 34 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 21 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 notation from another, and a mathematical notation 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 notation, 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 notation, 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 notation 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 notation, 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 notation, 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 notation 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 notation 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 notation, 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 notation, 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 notation 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 notation from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a mathematical notation, 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 notation, 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 notation 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 notation 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 notation between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a mathematical notation, 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 notation, 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 notation 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 notation, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a mathematical notation 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 notation, 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 notation, 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 notation 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 notation 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 notation contains and in what form it is held.", "questions": [ { "id": "content-and-format-q01", "text": "What identifies and describes the content of a mathematical notation, 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 notation, 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 notation 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 notation and the period it survives.", "questions": [ { "id": "access-rules-q01", "text": "What identifies and describes access to a mathematical notation, 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 notation, 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 notation is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] }, { "id": "work-and-manifestation", "name": "Work, version and copy", "description": "Which level of mathematical notation a statement is about.", "rationale": "The work, the edition, the file and the copy in hand are four things; rights and content attach to different ones.", "layers": [ { "id": "levels", "name": "Levels of the thing", "description": "Work, expression, manifestation and item, in plain terms.", "findings": [ { "id": "level-rules", "name": "What belongs at each level", "description": "Which facts hold for the work and which only for one copy.", "questions": [ { "id": "level-rules-q01", "text": "For mathematical notation, which facts belong to the work itself, which to a version, and which to a single copy?", "kind": "boundary" }, { "id": "level-rules-q02", "text": "What identifier exists at each level, and which one is being cited?", "kind": "definition" } ] } ] }, { "id": "versions", "name": "Versions, editions and variants", "description": "How versions differ and which is canonical to whom.", "findings": [ { "id": "version-record", "name": "Versions and canonicity", "description": "Differences that matter and who calls one authoritative.", "questions": [ { "id": "version-record-q01", "text": "Which versions or editions of mathematical notation exist, and how do they differ substantively?", "kind": "definition" }, { "id": "version-record-q02", "text": "Who treats which version as authoritative, and for what purpose?", "kind": "provenance" } ] } ] } ] }, { "id": "authorship-and-rights", "name": "Authorship, rights and permitted use", "description": "Who made mathematical notation and what may be done with it.", "rationale": "Rights are jurisdictional, time-limited and attached to a level, and an agent that ignores that will copy what it may not.", "layers": [ { "id": "authorship", "name": "Authorship and contribution", "description": "Who contributed what, and in what capacity.", "findings": [ { "id": "contribution-record", "name": "Contributors and roles", "description": "The people and bodies behind it, with their roles.", "questions": [ { "id": "contribution-record-q01", "text": "Who authored or contributed to mathematical notation, in what roles, and how is that attested?", "kind": "provenance" }, { "id": "contribution-record-q02", "text": "Where authorship is disputed or anonymous, what is recorded instead?", "kind": "boundary" } ] } ] }, { "id": "rights", "name": "Rights and permissions", "description": "Which rights subsist, where, until when, and what they permit.", "findings": [ { "id": "rights-record", "name": "Rights, term and permitted acts", "description": "The regime in force and what it allows.", "questions": [ { "id": "rights-record-q01", "text": "What rights subsist in mathematical notation, in which jurisdictions, and until when?", "kind": "definition" }, { "id": "rights-record-q02", "text": "Which acts are permitted without further permission, and which must an agent refuse?", "kind": "action" } ] } ] } ] }, { "id": "provenance-and-evidence", "name": "Provenance, evidence and time", "description": "Where every claim about a mathematical notation 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 notation and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a mathematical notation, 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 notation, 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 notation 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 notation is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a mathematical notation, 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 notation, 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 notation 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 } } } }