{ "model": { "rank": 3923, "code": "thing-q976981", "model_id": "vr.tr.formula", "name": "formula", "purpose": "Let an agent explain what formulas are across mathematics, logic, science and chemistry, distinguish kinds such as equations, inequations and logical formulas, relay notation standards, and help read, write and check formulas.", "family": "Thing Registry", "category": "Information and virtual systems", "status": "research-draft", "kind": "thing", "plane": "INF", "domain": "INF.MED", "industry": "", "version": "", "url": "/models/thing/q976981/", "tier": 2, "score": 80, "payload": { "layer": "wikidata", "aliases": [ "system of equations", "logical formula", "inequation", "non-autonomous system", "overdetermined system", "underdetermined system", "system of polynomial equations", "autonomous system", "system of differential equations", "Harrop formula", "quadratic inequality", "cubic inequality", "concentration inequality", "age-predicted maximal heart rate equation", "quadrature rule", "superformula", "Binomial Formula", "readability test", "interpolation formula", "Delambre analogies", "Napier's analogies", "asymptotic formula", "reflection formula", "formula for generating Pythagorean triples", "midparent", "system of quadratic equations", "Efron–Stein inequality", "Lexile" ], "aliasCount": 28, "merged": 28, "knownIn": 80, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": "vr.tr.formula-2", "source": { "dataset": "wikidata", "item": "Q976981", "url": "https://www.wikidata.org/wiki/Q976981", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-12T22:02:07Z", "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-Q976981", "registryId": "vr.tr.formula", "name": "formula", "version": "0.2.0-wave.3", "entryKind": "thing", "family": "Thing Registry", "domain": [ "INF.MED" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q976981/", "model": { "registry_id": "vr.tr.formula", "name": "formula", "purpose": "Let an agent explain what formulas are across mathematics, logic, science and chemistry, distinguish kinds such as equations, inequations and logical formulas, relay notation standards, and help read, write and check formulas.", "definition": "A concise expression of a mathematical, logical, scientific or chemical relationship in symbols, such as an equation, inequation, logical formula, system of equations or chemical formula, that states a fact, a rule or a computation; formulas are governed by the syntax of their notation, can be evaluated or solved, and range from everyday computations to systems of equations that may be determined, overdetermined or underdetermined.", "what_it_is_for": "Expressing relationships and rules compactly in symbols.", "affordances": [ "explain kinds of formula", "help read and write formulas", "relay notation standards", "distinguish from related notions" ], "distinguishing_features": [ "Symbolic and compact", "Governed by notation syntax", "Can be evaluated or solved", "Cross-disciplinary" ], "appearance": "Not a physical object; a line of symbols such as an equation on a page or screen.", "visual_identification": [ "Symbolic expression of a relationship or rule", "Equations, inequations, logical and chemical formulas", "An expression alone states no relationship; an algorithm is a procedure" ], "physical_properties": [], "families_and_kinds": [ "equations and systems of equations", "inequations and inequalities", "logical formulas, well-formed formulas", "scientific formulas such as physical laws", "chemical and molecular formulas", "spreadsheet and programming formulas", "systems classed as determined, overdetermined or underdetermined, autonomous or non-autonomous" ], "related_models": [ { "relation": "is a kind of", "target": "mathematical expression", "why": "stating a relationship" }, { "relation": "is a kind of", "target": "mathematical notation", "why": "in registry terms" }, { "relation": "includes", "target": "equation", "why": "the main kind" }, { "relation": "is related to", "target": "chemical formula", "why": "in chemistry" } ], "identifiers": [], "standards_and_regulation": [ "ISO 80000-2 mathematical signs and symbols", "IUPAC rules for chemical formulas", "Notation conventions of each field" ], "failure_modes_and_hazards": [ "Ambiguous notation", "Confusing formula with expression or algorithm", "Errors in transcription" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "concept", "name": "Concept", "description": "What a formula is.", "rationale": "Definition.", "layers": [ { "id": "definition", "name": "Definition", "description": "Definition and kinds.", "findings": [ { "id": "definition-finding", "name": "Definition", "description": "Definition.", "questions": [ { "text": "What is a formula, and what kinds exist across fields?", "kind": "definition" }, { "text": "Is the object a formula, an expression, an algorithm or a function?", "kind": "boundary" } ] } ] }, { "id": "systems", "name": "Systems", "description": "Systems of equations.", "findings": [ { "id": "systems-finding", "name": "Systems", "description": "Systems.", "questions": [ { "text": "What are determined, overdetermined and underdetermined systems, and autonomous versus non-autonomous systems?", "kind": "definition" }, { "text": "Which entry fits system of equations?", "kind": "action" } ] } ] } ] }, { "id": "use", "name": "Use", "description": "Reading and writing.", "rationale": "Practice.", "layers": [ { "id": "reading", "name": "Reading", "description": "Reading formulas.", "findings": [ { "id": "reading-finding", "name": "Reading", "description": "Reading.", "questions": [ { "text": "How is a given formula read, and what do its symbols mean?", "kind": "action" }, { "text": "What does the formula yield for the values in question?", "kind": "measurement" } ] } ] }, { "id": "writing", "name": "Writing", "description": "Writing and typesetting.", "findings": [ { "id": "writing-finding", "name": "Writing", "description": "Writing.", "questions": [ { "text": "How are formulas written and typeset, including in LaTeX and MathML?", "kind": "provenance" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] } ] }, { "id": "fields", "name": "Fields", "description": "Formulas by field.", "rationale": "Application.", "layers": [ { "id": "logic", "name": "Logic", "description": "Logical formulas.", "findings": [ { "id": "logic-finding", "name": "Logic", "description": "Logic.", "questions": [ { "text": "What are well-formed formulas in logic, and how are they interpreted?", "kind": "provenance" }, { "text": "Which entry fits formal logic?", "kind": "action" } ] } ] }, { "id": "science", "name": "Science", "description": "Scientific and chemical formulas.", "findings": [ { "id": "science-finding", "name": "Science", "description": "Science.", "questions": [ { "text": "How do physical laws and chemical formulas express relationships and composition?", "kind": "provenance" }, { "text": "Which entry fits chemical formula?", "kind": "action" } ] } ] } ] }, { "id": "context", "name": "Context", "description": "History and teaching.", "rationale": "Context.", "layers": [ { "id": "history", "name": "History", "description": "History of notation.", "findings": [ { "id": "history-finding", "name": "History", "description": "History.", "questions": [ { "text": "How did symbolic formulas develop from rhetorical algebra to modern notation?", "kind": "provenance" }, { "text": "Which entry fits the history of mathematical notation?", "kind": "action" } ] } ] }, { "id": "teach", "name": "Teach", "description": "Teaching.", "findings": [ { "id": "teach-finding", "name": "Teach", "description": "Teaching.", "questions": [ { "text": "How are formulas taught, and which misconceptions arise?", "kind": "provenance" }, { "text": "Which entry fits mathematics education?", "kind": "action" } ] } ] } ] } ] }, "openQuestions": [ "Should equation and chemical formula be the primary linked entries?", "How should notation standards be linked?", "The registry entry has merged aliases naming kinds of systems of equations; 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 formula, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain what formulas are across mathematics, logic, science and chemistry, distinguish kinds such as equations, inequations and logical formulas, relay notation standards, and help read, write and check formulas.", "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: system of equations, logical formula, inequation, non-autonomous system, overdetermined system, underdetermined system, system of polynomial equations, autonomous system, system of differential equations, Harrop formula, quadratic inequality, cubic inequality.", "28 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 80 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 formula, 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": [ "system of equations", "logical formula", "inequation", "non-autonomous system", "overdetermined system", "underdetermined system", "system of polynomial equations", "autonomous system", "system of differential equations", "Harrop formula", "quadratic inequality", "cubic inequality" ] } ], "standing": "Described in 80 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 28 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 formula from another, and a formula 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 formula, 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 formula, 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 formula 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 formula, 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 formula, 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 formula 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 formula 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 formula, 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 formula, 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 formula 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 formula from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a formula, 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 formula, 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 formula 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 formula 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 formula between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a formula, 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 formula, 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 formula 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 formula, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a formula 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 formula, 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 formula, 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 formula 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 formula 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 formula contains and in what form it is held.", "questions": [ { "id": "content-and-format-q01", "text": "What identifies and describes the content of a formula, 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 formula, 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 formula 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 formula and the period it survives.", "questions": [ { "id": "access-rules-q01", "text": "What identifies and describes access to a formula, 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 formula, 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 formula 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 formula 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 formula, 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 formula 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 formula 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 formula, 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 formula, 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 formula 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 formula and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a formula, 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 formula, 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 formula 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 formula is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a formula, 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 formula, 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 formula 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 } } } }