{ "model": { "rank": 2489, "code": "thing-q29175", "model_id": "vr.tr.derivative", "name": "derivative", "purpose": "Let an agent explain derivatives and compute them, apply derivatives to rates, optimisation and physics, interpret spectral quantities as derivatives, and separate the financial sense.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q29175/", "tier": 2, "score": 104, "payload": { "layer": "wikidata", "aliases": [ "spectral radiance with respect to frequency", "spectral irradiance with respect to frequency", "spectral radiant flux", "spectral radiant exitance with respect to frequency", "spectral linear absorption coefficient", "spectral fluence rate", "spectral photon exitance", "spectral photon flux", "spectral photon irradiance", "spectral quantity", "spectral radiant exitance with respect to wavelength", "spectral luminous intensity in terms of frequency", "spectral luminous intensity in terms of wavenumber", "spectral luminous intensity in terms of wavelength", "time derivative", "๐‘›th derivative", "Implicit derivatives", "partial derivative", "image derivatives", "covariant derivative", "first derivative", "higher-order derivative", "directional derivative", "total derivative", "parametric derivative", "logarithmic derivative", "Gateaux derivative" ], "aliasCount": 27, "merged": 28, "knownIn": 104, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": "vr.tr.derivative-substance", "source": { "dataset": "wikidata", "item": "Q29175", "url": "https://www.wikidata.org/wiki/Q29175", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-11T22:57:41Z", "providers": [ "Claude" ], "breadth": "written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify", "pass": 2, "wave": 2, "engine": "claude" }, "metaModel": { "id": "THING-Q29175", "registryId": "vr.tr.derivative", "name": "derivative", "version": "0.2.0-wave.2", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q29175/", "model": { "registry_id": "vr.tr.derivative", "name": "derivative", "purpose": "Let an agent explain derivatives and compute them, apply derivatives to rates, optimisation and physics, interpret spectral quantities as derivatives, and separate the financial sense.", "definition": "In calculus, the rate at which a function changes with respect to its variable, defined as the limit of the difference quotient and interpreted as the slope of the tangent or the instantaneous rate of change, with rules for computing derivatives of sums, products, quotients and compositions, and extensions to partial, directional and higher derivatives; in physics and engineering, spectral quantities such as spectral radiance are derivatives with respect to frequency or wavelength.", "what_it_is_for": "Rates of change of functions.", "affordances": [ "explain and compute derivatives", "apply to rates and optimisation", "interpret spectral derivatives", "separate other senses" ], "distinguishing_features": [ "Limit definition", "Local rate of change", "Rules of differentiation", "Generalisable" ], "appearance": "Not physical; slopes of curves and formulas.", "visual_identification": [ "Rate of change of a function", "Slope of the tangent", "A financial derivative is a contract, not a rate" ], "physical_properties": [], "families_and_kinds": [ "ordinary derivatives", "partial and directional derivatives", "higher-order derivatives", "spectral derivatives such as spectral radiance", "derivatives in vector calculus" ], "related_models": [ { "relation": "is a kind of", "target": "function", "why": "category" }, { "relation": "is a kind of", "target": "rate of change", "why": "category" }, { "relation": "is related to", "target": "sum", "why": "Riemann sums and integrals" }, { "relation": "is related to", "target": "acceleration", "why": "derivative of velocity" } ], "identifiers": [], "standards_and_regulation": [ "Mathematical notation conventions", "Radiometric quantity definitions for spectral derivatives" ], "failure_modes_and_hazards": [ "Confusing derivative with difference or with financial derivatives", "Differentiation rule errors", "Misinterpreting spectral quantities per frequency versus per wavelength" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "define", "name": "Define", "description": "What a derivative is.", "rationale": "Concepts.", "layers": [ { "id": "definition", "name": "Definition", "description": "Limit definition.", "findings": [ { "id": "definition-finding", "name": "Definition", "description": "Definition.", "questions": [ { "text": "How is the derivative defined as a limit, and how is it interpreted as slope and rate of change?", "kind": "definition" }, { "text": "Is the calculus sense, a financial derivative or a chemical derivative meant?", "kind": "boundary" } ] } ] }, { "id": "rules", "name": "Rules", "description": "Differentiation rules.", "findings": [ { "id": "rules-finding", "name": "Rules", "description": "Rules.", "questions": [ { "text": "What are the rules for derivatives of sums, products, quotients and compositions?", "kind": "definition" }, { "text": "What is the derivative of this function?", "kind": "action" } ] } ] } ] }, { "id": "apply", "name": "Apply", "description": "Using derivatives.", "rationale": "Applications.", "layers": [ { "id": "rates", "name": "Rates", "description": "Rates and optimisation.", "findings": [ { "id": "rates-finding", "name": "Rates", "description": "Rates.", "questions": [ { "text": "How are derivatives used to find rates of change, extrema and related rates in this problem?", "kind": "action" }, { "text": "How is a function analysed using its derivatives?", "kind": "action" } ] } ] }, { "id": "physics", "name": "Physics", "description": "Derivatives in science.", "findings": [ { "id": "physics-finding", "name": "Physics", "description": "Science.", "questions": [ { "text": "How do velocity, acceleration and other physical quantities arise as derivatives?", "kind": "definition" }, { "text": "What are spectral quantities such as spectral radiance with respect to frequency, and why do they differ per wavelength?", "kind": "definition" } ] } ] } ] }, { "id": "extend", "name": "Extend", "description": "Beyond one variable.", "rationale": "Advanced.", "layers": [ { "id": "partial", "name": "Partial", "description": "Partial and directional derivatives.", "findings": [ { "id": "partial-finding", "name": "Partial", "description": "Partial derivatives.", "questions": [ { "text": "What are partial, directional and total derivatives, and how are gradients used?", "kind": "definition" }, { "text": "How are they computed for this function?", "kind": "action" } ] } ] }, { "id": "numeric", "name": "Numeric", "description": "Numerical differentiation.", "findings": [ { "id": "numeric-finding", "name": "Numeric", "description": "Numerical.", "questions": [ { "text": "How are derivatives approximated numerically and computed by automatic differentiation?", "kind": "definition" }, { "text": "What errors arise?", "kind": "boundary" } ] } ] } ] }, { "id": "learn", "name": "Learn", "description": "Teaching and history.", "rationale": "Education.", "layers": [ { "id": "teach", "name": "Teach", "description": "Teaching derivatives.", "findings": [ { "id": "teach-finding", "name": "Teach", "description": "Teaching.", "questions": [ { "text": "How can derivatives be taught with graphs and motion examples?", "kind": "action" }, { "text": "Which misconceptions arise?", "kind": "provenance" } ] } ] }, { "id": "history", "name": "History", "description": "History.", "findings": [ { "id": "history-finding", "name": "History", "description": "History.", "questions": [ { "text": "How did Newton, Leibniz and later mathematicians develop the derivative?", "kind": "provenance" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Should differentiation rules be a separate entry?", "How should calculus resources be linked?", "How should radiometric definitions be linked?" ], "statistics": { "bundles": 4, "layers": 8, "findings": 8, "questions": 16 } }, "draft": { "generator": "vr.draft.v3", "status": "draft-generated", "researched": false, "archetype": "abstract concept", "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 derivative, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain derivatives and compute them, apply derivatives to rates, optimisation and physics, interpret spectral quantities as derivatives, and separate the financial sense.", "characteristics": { "substance": "abstract", "origin": "conceptual", "agency": "inert" }, "whatYouCanDoWithIt": [ "observed and measured" ], "distinguishingFeatures": [ "Names folded into this entry, which a task may need to split apart again: spectral radiance with respect to frequency, spectral irradiance with respect to frequency, spectral radiant flux, spectral radiant exitance with respect to frequency, spectral linear absorption coefficient, spectral fluence rate, spectral photon exitance, spectral photon flux, spectral photon irradiance, spectral quantity, spectral radiant exitance with respect to wavelength, spectral luminous intensity in terms of frequency.", "28 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 104 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 derivative, and on what evidence are they told apart?" ], "whatItIsMadeOf": "an abstraction with no physical instance", "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": [ "observe it, measure it, record its state" ], "howItIsRecognised": [ "Nothing to see. What is recognised is an instance of it, and which instances count is exactly what is argued about." ], "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": [ "spectral radiance with respect to frequency", "spectral irradiance with respect to frequency", "spectral radiant flux", "spectral radiant exitance with respect to frequency", "spectral linear absorption coefficient", "spectral fluence rate", "spectral photon exitance", "spectral photon flux", "spectral photon irradiance", "spectral quantity", "spectral radiant exitance with respect to wavelength", "spectral luminous intensity in terms of frequency" ] } ], "standing": "Described in 104 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 derivative from another, and a derivative 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 derivative, 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 derivative, 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 derivative 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 derivative, 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 derivative, 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 derivative 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 derivative 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 derivative, 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 derivative, 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 derivative 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 derivative from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a derivative, 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 derivative, 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 derivative 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 derivative 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 derivative between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a derivative, 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 derivative, 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 derivative 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 derivative, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a derivative 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 derivative, 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 derivative, 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 derivative is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] }, { "id": "definitions-in-contest", "name": "Definitions and who holds them", "description": "What derivative is taken to mean, and by whom.", "rationale": "When a field disagrees about a concept, the disagreement is the content. A model that picks one definition silently destroys the information.", "layers": [ { "id": "competing-definitions", "name": "Competing definitions", "description": "The main readings and the traditions behind them.", "findings": [ { "id": "definition-map", "name": "Definitions and their holders", "description": "Each definition with the school or body that holds it.", "questions": [ { "id": "definition-map-q01", "text": "Which definitions of derivative are in use, and which tradition or body holds each?", "kind": "definition" }, { "id": "definition-map-q02", "text": "What turns on the difference between them in practice?", "kind": "boundary" } ] } ] }, { "id": "operationalisation", "name": "Operationalisation", "description": "How it is measured or applied when it has to be.", "findings": [ { "id": "operational-record", "name": "Measures and proxies", "description": "Instruments and indicators used to stand in for it.", "questions": [ { "id": "operational-record-q01", "text": "How is derivative operationalised or measured in practice, and by what instrument?", "kind": "measurement" }, { "id": "operational-record-q02", "text": "What does that operationalisation leave out, and when does that matter?", "kind": "boundary" } ] } ] } ] }, { "id": "instances-and-use", "name": "Instances, use and consequence", "description": "What counts as an instance of derivative and what follows from calling something that.", "rationale": "Applying a concept is an act with consequences, so a model must say what the label licenses and what it does not.", "layers": [ { "id": "instances", "name": "What counts as an instance", "description": "Clear cases, borderline cases and non-cases.", "findings": [ { "id": "instance-tests", "name": "Tests for an instance", "description": "What would settle whether something falls under it.", "questions": [ { "id": "instance-tests-q01", "text": "What would settle whether something is an instance of derivative?", "kind": "boundary" }, { "id": "instance-tests-q02", "text": "Which borderline cases are argued about, and on what grounds?", "kind": "definition" } ] } ] }, { "id": "consequence", "name": "Consequence of application", "description": "Rights, duties or decisions that follow from the label.", "findings": [ { "id": "consequence-record", "name": "What the label licenses", "description": "What an agent may do once something is classified this way.", "questions": [ { "id": "consequence-record-q01", "text": "What follows practically once something is treated as derivative?", "kind": "action" }, { "id": "consequence-record-q02", "text": "What must an agent not infer from the label alone?", "kind": "action" } ] } ] } ] }, { "id": "provenance-and-evidence", "name": "Provenance, evidence and time", "description": "Where every claim about a derivative 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 derivative and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a derivative, 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 derivative, 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 derivative 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 derivative is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a derivative, 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 derivative, 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 derivative is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] } ] }, "statistics": { "bundles": 5, "layers": 10, "findings": 12, "questions": 32 } } } }