{ "model": { "rank": 1430, "code": "thing-q11345", "model_id": "vr.tr.equation", "name": "equation", "purpose": "Let an agent explain equations by type, solution method and application, help learners solve them step by step, and avoid personal financial advice when equations model investments.", "family": "Thing Registry", "category": "Information and virtual systems", "status": "research-draft", "kind": "thing", "plane": "INF", "domain": "INF.MED", "industry": "", "version": "", "url": "/models/thing/q11345/", "tier": 2, "score": 147, "payload": { "layer": "wikidata", "aliases": [ "payoff at maturity of covered call", "payoff at maturity of covered put", "payoff at maturity of protective put", "payoff at maturity of protective call", "differential equation", "difference equation", "Hill's spherical vortex", "linear differential equation", "Heun's differential equation", "nonlinear differential equation", "separable differentiable equation", "neural differential equation", "1-D Saint Venant equation", "stochastic differential equation", "Haselgrove's equations", "delay differential equation", "equations of motion", "homogeneous differential equation", "partial differential equation", "functional differential equation", "second order linear differential equation", "Kolmogorov equations", "nonhomogeneous differential equation", "ordinary differential equation", "algebraic differential equation", "Stuart–Landau equation", "second order differential equation", "matrix differential equation", "master equation", "universal differential equation", "rate equation", "matrix difference equation", "quantum KZ equations", "rational difference equation", "Mark–Houwink equation", "chemical equation", "balance equation", "homogeneous linear differential equation", "inhomogeneous linear differential equation", "Cauchy–Euler equation" ], "aliasCount": 196, "merged": 198, "knownIn": 147, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": "vr.tr.equation-act", "source": { "dataset": "wikidata", "item": "Q11345", "url": "https://www.wikidata.org/wiki/Q11345", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-11T13:11:21Z", "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-Q11345", "registryId": "vr.tr.equation", "name": "equation", "version": "0.2.0-wave.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "INF.MED" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q11345/", "model": { "registry_id": "vr.tr.equation", "name": "equation", "purpose": "Let an agent explain equations by type, solution method and application, help learners solve them step by step, and avoid personal financial advice when equations model investments.", "definition": "A mathematical statement that two expressions are equal, usually containing unknowns to be solved for, such as linear, quadratic, polynomial, differential and difference equations, used throughout science, engineering, economics and finance.", "what_it_is_for": "Modelling relationships and finding unknown values.", "affordances": [ "classify an equation", "solve equations step by step", "check solutions", "interpret equations in applications" ], "distinguishing_features": [ "States equality", "Has unknowns or parameters", "May have none, one or many solutions", "Used to model systems" ], "appearance": "Not physical; expressions with an equals sign.", "visual_identification": [ "An equals sign between expressions", "Unknowns such as x or y", "Inequalities use signs such as less than" ], "physical_properties": [], "families_and_kinds": [ "linear equations", "quadratic and polynomial equations", "systems of equations", "differential equations", "difference equations" ], "related_models": [ { "relation": "is a kind of", "target": "formula", "why": "category" }, { "relation": "includes", "target": "polynomial equation", "why": "kind" }, { "relation": "is solved by", "target": "algebra", "why": "method" }, { "relation": "is related to", "target": "theorem", "why": "mathematical statement" } ], "identifiers": [], "standards_and_regulation": [ "ISO 80000-2 mathematical signs and symbols" ], "failure_modes_and_hazards": [ "Dividing by zero or losing solutions", "Extraneous roots", "Treating model equations as guaranteed outcomes" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "classify", "name": "Classify", "description": "Type.", "rationale": "Type determines method.", "layers": [ { "id": "type", "name": "Type", "description": "Equation type.", "findings": [ { "id": "type-finding", "name": "Type", "description": "Equation type.", "questions": [ { "text": "Is this equation linear, quadratic, differential or another type?", "kind": "definition" }, { "text": "What are the unknowns?", "kind": "definition" } ] } ] }, { "id": "solutions", "name": "Solutions", "description": "Number of solutions.", "findings": [ { "id": "solutions-finding", "name": "Solutions", "description": "Solutions.", "questions": [ { "text": "How many solutions can this equation have?", "kind": "measurement" }, { "text": "Over which number set?", "kind": "boundary" } ] } ] } ] }, { "id": "solve", "name": "Solve", "description": "Methods.", "rationale": "Steps must be valid.", "layers": [ { "id": "steps", "name": "Steps", "description": "Step by step.", "findings": [ { "id": "steps-finding", "name": "Steps", "description": "Solving.", "questions": [ { "text": "What are the steps to solve this equation?", "kind": "action" }, { "text": "Is each step reversible?", "kind": "boundary" } ] } ] }, { "id": "check", "name": "Check", "description": "Verification.", "findings": [ { "id": "check-finding", "name": "Check", "description": "Checking.", "questions": [ { "text": "Does the solution satisfy the original equation?", "kind": "boundary" }, { "text": "Are there extraneous roots?", "kind": "boundary" } ] } ] } ] }, { "id": "applications", "name": "Applications", "description": "Models.", "rationale": "Equations model the world.", "layers": [ { "id": "science", "name": "Science", "description": "Physical models.", "findings": [ { "id": "science-finding", "name": "Science", "description": "Scientific models.", "questions": [ { "text": "What does this equation describe in physics or engineering?", "kind": "definition" }, { "text": "What assumptions does it make?", "kind": "boundary" } ] } ] }, { "id": "finance", "name": "Finance", "description": "Financial formulas.", "findings": [ { "id": "finance-finding", "name": "Finance", "description": "Financial formulas.", "questions": [ { "text": "What does this payoff or interest formula calculate, in general terms?", "kind": "definition" }, { "text": "Is the user seeking personal investment advice?", "kind": "boundary" } ] } ] } ] }, { "id": "learning", "name": "Learning", "description": "Teaching.", "rationale": "Practice builds skill.", "layers": [ { "id": "explain", "name": "Explain", "description": "Explaining.", "findings": [ { "id": "explain-finding", "name": "Explain", "description": "Explanation.", "questions": [ { "text": "How can this type of equation be explained to a beginner?", "kind": "action" }, { "text": "Which misconceptions are common?", "kind": "provenance" } ] } ] }, { "id": "tools", "name": "Tools", "description": "Software.", "findings": [ { "id": "tools-finding", "name": "Tools", "description": "Tools.", "questions": [ { "text": "Which tools can solve or graph equations?", "kind": "provenance" }, { "text": "How should results be checked?", "kind": "boundary" } ] } ] } ] } ] }, "openQuestions": [ "Should equation types be separate entries?", "How should famous equations be linked?", "How should financial formulas be framed?" ], "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 equation, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain equations by type, solution method and application, help learners solve them step by step, and avoid personal financial advice when equations model investments.", "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: payoff at maturity of covered call, payoff at maturity of covered put, payoff at maturity of protective put, payoff at maturity of protective call, differential equation, difference equation, Hill's spherical vortex, linear differential equation, Heun's differential equation, nonlinear differential equation, separable differentiable equation, neural differential equation.", "198 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 147 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 equation, 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": [ "payoff at maturity of covered call", "payoff at maturity of covered put", "payoff at maturity of protective put", "payoff at maturity of protective call", "differential equation", "difference equation", "Hill's spherical vortex", "linear differential equation", "Heun's differential equation", "nonlinear differential equation", "separable differentiable equation", "neural differential equation" ] } ], "standing": "Described in 147 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 198 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 equation from another, and a equation 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 equation, 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 equation, 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 equation 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 equation, 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 equation, 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 equation 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 equation 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 equation, 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 equation, 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 equation 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 equation from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a equation, 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 equation, 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 equation 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 equation 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 equation between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a equation, 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 equation, 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 equation 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 equation, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a equation 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 equation, 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 equation, 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 equation 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 equation 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 equation contains and in what form it is held.", "questions": [ { "id": "content-and-format-q01", "text": "What identifies and describes the content of a equation, 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 equation, 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 equation 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 equation and the period it survives.", "questions": [ { "id": "access-rules-q01", "text": "What identifies and describes access to a equation, 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 equation, 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 equation 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 equation 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 equation, 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 equation 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 equation 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 equation, 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 equation, 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 equation 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 equation and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a equation, 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 equation, 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 equation 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 equation is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a equation, 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 equation, 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 equation 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 } } } }