{ "model": { "rank": 5563, "code": "thing-q173582", "model_id": "vr.tr.gradient", "name": "gradient", "purpose": "Let an agent explain the gradient as a mathematical operator and as a rate of spatial change, support calculations and interpretation, describe its uses in physics, optimisation and data science, and support learning.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q173582/", "tier": 2, "score": 66, "payload": { "layer": "wikidata", "aliases": [ "spatial gradient", "magnetic field gradient", "elevational gradient", "longitudinal gradient", "latitudinal gradient", "habitat gradient", "ecological gradient", "abundance gradient", "color gradient", "four-gradient", "ombré" ], "aliasCount": 11, "merged": 11, "knownIn": 66, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q173582", "url": "https://www.wikidata.org/wiki/Q173582", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-12T05:41:24Z", "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-Q173582", "registryId": "vr.tr.gradient", "name": "gradient", "version": "0.2.0-wave.2", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q173582/", "model": { "registry_id": "vr.tr.gradient", "name": "gradient", "purpose": "Let an agent explain the gradient as a mathematical operator and as a rate of spatial change, support calculations and interpretation, describe its uses in physics, optimisation and data science, and support learning.", "definition": "In mathematics, the vector operator that assigns to a scalar function of several variables the vector of its partial derivatives, pointing in the direction of steepest increase with magnitude equal to the rate of change, and, by extension, the rate of change of a quantity with distance in physics and geography, as in temperature, pressure, concentration, magnetic field and elevational gradients; the gradient is central to calculus, physics, optimisation and machine learning.", "what_it_is_for": "Vector of partial derivatives and rate of spatial change.", "affordances": [ "explain the operator", "support calculations", "describe uses", "support learning" ], "distinguishing_features": [ "Direction of steepest ascent", "Vector-valued", "Coordinate-independent", "Wide application" ], "appearance": "Not physical; a mathematical object.", "visual_identification": [ "Vector of partial derivatives pointing uphill", "Mathematical operator and physical rate of change", "Divergence and curl are other vector operators; slope is the one-dimensional case" ], "physical_properties": [], "families_and_kinds": [ "gradient of scalar fields", "gradients in physics such as pressure and temperature", "ecological and geographic gradients", "gradient in optimisation and gradient descent", "generalisations on manifolds" ], "related_models": [ { "relation": "is a kind of", "target": "differential operator", "why": "category" }, { "relation": "is a kind of", "target": "vector operator", "why": "category" }, { "relation": "is related to", "target": "determinant", "why": "another concept of multivariable mathematics" }, { "relation": "is related to", "target": "fluid mechanics", "why": "pressure gradients driving flow" } ], "identifiers": [], "standards_and_regulation": [ "Mathematical notation conventions", "Curriculum standards for calculus", "No regulation of the concept" ], "failure_modes_and_hazards": [ "Confusing gradient with slope or derivative", "Coordinate errors", "Confusing mathematical and everyday senses" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "understand", "name": "Understand", "description": "What the gradient is.", "rationale": "Mathematics.", "layers": [ { "id": "concept", "name": "Concept", "description": "Definition and meaning.", "findings": [ { "id": "concept-finding", "name": "Concept", "description": "Concept.", "questions": [ { "text": "What is the gradient of a scalar function, and why does it point in the direction of steepest increase?", "kind": "definition" }, { "text": "Is the mathematical or a physical sense meant?", "kind": "boundary" } ] } ] }, { "id": "relations", "name": "Relations", "description": "Related operators.", "findings": [ { "id": "relations-finding", "name": "Relations", "description": "Relations.", "questions": [ { "text": "How does the gradient relate to the directional derivative, divergence, curl and the Laplacian?", "kind": "definition" }, { "text": "Which entry fits vector calculus?", "kind": "action" } ] } ] } ] }, { "id": "calculate", "name": "Calculate", "description": "Calculation.", "rationale": "Practice.", "layers": [ { "id": "compute", "name": "Compute", "description": "Computing gradients.", "findings": [ { "id": "compute-finding", "name": "Compute", "description": "Computation.", "questions": [ { "text": "How is the gradient of this function computed in Cartesian and other coordinates?", "kind": "action" }, { "text": "Which entry fits partial derivatives?", "kind": "action" } ] } ] }, { "id": "interpret", "name": "Interpret", "description": "Interpreting.", "findings": [ { "id": "interpret-finding", "name": "Interpret", "description": "Interpretation.", "questions": [ { "text": "How should a gradient be interpreted geometrically and physically?", "kind": "action" }, { "text": "Which entry fits level sets?", "kind": "action" } ] } ] } ] }, { "id": "apply", "name": "Apply", "description": "Applications.", "rationale": "Applications.", "layers": [ { "id": "physics", "name": "Physics", "description": "Physics and geography.", "findings": [ { "id": "physics-finding", "name": "Physics", "description": "Physics.", "questions": [ { "text": "How do pressure, temperature, concentration and field gradients drive physical processes, and how are geographic gradients used?", "kind": "provenance" }, { "text": "Which entry fits a specific gradient?", "kind": "action" } ] } ] }, { "id": "optimisation", "name": "Optimisation", "description": "Optimisation and learning.", "findings": [ { "id": "optimisation-finding", "name": "Optimisation", "description": "Optimisation.", "questions": [ { "text": "How is the gradient used in gradient descent and machine learning?", "kind": "provenance" }, { "text": "Which entry fits gradient descent?", "kind": "action" } ] } ] } ] }, { "id": "learn", "name": "Learn", "description": "History and teaching.", "rationale": "Education.", "layers": [ { "id": "history", "name": "History", "description": "History.", "findings": [ { "id": "history-finding", "name": "History", "description": "History.", "questions": [ { "text": "How did the gradient and vector calculus develop historically?", "kind": "provenance" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] }, { "id": "teach", "name": "Teach", "description": "Teaching.", "findings": [ { "id": "teach-finding", "name": "Teach", "description": "Teaching.", "questions": [ { "text": "How can the gradient be taught with visualisations?", "kind": "action" }, { "text": "Which misconceptions arise?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Should gradient descent be a separate entry?", "How should textbooks be linked?", "How should physics applications 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 gradient, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain the gradient as a mathematical operator and as a rate of spatial change, support calculations and interpretation, describe its uses in physics, optimisation and data science, and support learning.", "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: spatial gradient, magnetic field gradient, elevational gradient, longitudinal gradient, latitudinal gradient, habitat gradient, ecological gradient, abundance gradient, color gradient, four-gradient, ombré.", "11 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 66 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 gradient, 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": [ "spatial gradient", "magnetic field gradient", "elevational gradient", "longitudinal gradient", "latitudinal gradient", "habitat gradient", "ecological gradient", "abundance gradient", "color gradient", "four-gradient", "ombré" ] } ], "standing": "Described in 66 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 11 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 gradient from another, and a gradient 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 gradient, 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 gradient, 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 gradient 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 gradient, 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 gradient, 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 gradient 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 gradient 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 gradient, 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 gradient, 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 gradient 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 gradient from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a gradient, 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 gradient, 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 gradient 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 gradient 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 gradient between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a gradient, 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 gradient, 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 gradient 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 gradient, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a gradient 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 gradient, 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 gradient, 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 gradient 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 gradient 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 gradient 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 gradient 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 gradient 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 gradient?", "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 gradient?", "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 gradient 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 gradient and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a gradient, 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 gradient, 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 gradient 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 gradient is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a gradient, 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 gradient, 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 gradient 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 } } } }