{ "model": { "rank": 10354, "code": "thing-q193460", "model_id": "vr.tr.scalar-field", "name": "scalar field", "purpose": "Let an agent explain scalar fields, relay definition, examples, mathematical treatment and physics uses from mathematics and physics sources, describe the named examples, and distinguish scalar fields from vector and tensor fields, scalar quantities at a point and scalar potentials as a subtype.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q193460/", "tier": 2, "score": 45, "payload": { "layer": "wikidata", "aliases": [ "electric potential (electrodynamics)", "scalar potential", "velocity potential", "temperature field", "pressuron", "Higgs field", "baric field", "galileon", "graviscalar" ], "aliasCount": 9, "merged": 9, "knownIn": 45, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q193460", "url": "https://www.wikidata.org/wiki/Q193460", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-14T02:27:14Z", "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": 4, "engine": "claude" }, "metaModel": { "id": "THING-Q193460", "registryId": "vr.tr.scalar-field", "name": "scalar field", "version": "0.2.0-wave.4", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q193460/", "model": { "registry_id": "vr.tr.scalar-field", "name": "scalar field", "purpose": "Let an agent explain scalar fields, relay definition, examples, mathematical treatment and physics uses from mathematics and physics sources, describe the named examples, and distinguish scalar fields from vector and tensor fields, scalar quantities at a point and scalar potentials as a subtype.", "definition": "In mathematics and physics, a scalar field assigns a single number, a scalar, to every point in space or spacetime, such as temperature, pressure or electric potential at each location, in contrast with a vector field that assigns a vector; examples the registry aliases name include the temperature field, the electric scalar potential, the velocity potential in fluid flow, and, in physics, the Higgs field and the hypothetical pressuron. Scalar fields are described by functions and studied with gradients, level sets and partial differential equations, and in particle physics quantum scalar fields correspond to spin-zero particles.", "what_it_is_for": "Assigning a scalar value to each point in space.", "affordances": [ "explain the concept", "relay examples", "relay mathematical and physics treatment", "distinguish related fields" ], "distinguishing_features": [ "One value per point", "Described by functions", "Gradient and level sets", "Spin-zero in physics" ], "appearance": "Not a physical object; visualised as contour or heat maps of values over space.", "visual_identification": [ "A scalar value assigned to every point", "Electric potential, scalar potential, velocity potential, temperature field, pressuron, Higgs field", "Vector fields assign vectors; tensor fields assign tensors; a scalar quantity is a single value; scalar potentials are a subtype" ], "physical_properties": [ { "quantity": "assigns", "typical_range": "one number per point", "unit": "note", "note": "" }, { "quantity": "Higgs field", "typical_range": "a fundamental scalar field", "unit": "note", "note": "" }, { "quantity": "registry parents", "typical_range": "scalar function, field", "unit": "note", "note": "" } ], "families_and_kinds": [ "temperature and pressure fields", "scalar potentials", "quantum scalar fields" ], "related_models": [ { "relation": "is a kind of", "target": "field (physics)", "why": "in registry terms" }, { "relation": "is contrasted with", "target": "vector field", "why": "" }, { "relation": "is contrasted with", "target": "tensor field", "why": "" }, { "relation": "includes", "target": "Higgs field", "why": "" } ], "identifiers": [], "standards_and_regulation": [ "Not applicable" ], "failure_modes_and_hazards": [ "Confusing scalar and vector fields", "Confusing a field with a value at a point", "Oversimplified physics" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "understand", "name": "Understand", "description": "What a scalar field is.", "rationale": "Science.", "layers": [ { "id": "definition", "name": "Definition", "description": "Definition.", "findings": [ { "id": "definition-finding", "name": "Definition", "description": "Definition.", "questions": [ { "text": "What is a scalar field, and how does it differ from vector and tensor fields, a scalar quantity and a scalar potential?", "kind": "definition" }, { "text": "Is the question about mathematics, classical physics or quantum field theory?", "kind": "boundary" } ] } ] }, { "id": "examples", "name": "Examples", "description": "Named examples.", "findings": [ { "id": "examples-finding", "name": "Examples", "description": "Examples.", "questions": [ { "text": "What are temperature fields, electric and velocity potentials, the Higgs field and the pressuron?", "kind": "definition" }, { "text": "Which entry fits the specific field?", "kind": "action" } ] } ] } ] }, { "id": "mathematics", "name": "Mathematics", "description": "Mathematics.", "rationale": "Science.", "layers": [ { "id": "gradient", "name": "Gradient", "description": "Gradients and level sets.", "findings": [ { "id": "gradient-finding", "name": "Gradient", "description": "Gradient.", "questions": [ { "text": "How do gradients and level sets describe scalar fields?", "kind": "provenance" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] }, { "id": "pdes", "name": "PDEs", "description": "Partial differential equations.", "findings": [ { "id": "pdes-finding", "name": "PDEs", "description": "PDEs.", "questions": [ { "text": "How are scalar fields governed by equations such as Laplace and heat equations?", "kind": "provenance" }, { "text": "Which sources are cited?", "kind": "provenance" } ] } ] } ] }, { "id": "physics", "name": "Physics", "description": "Physics.", "rationale": "Science.", "layers": [ { "id": "potentials", "name": "Potentials", "description": "Scalar potentials.", "findings": [ { "id": "potentials-finding", "name": "Potentials", "description": "Potentials.", "questions": [ { "text": "How do electric and velocity potentials act as scalar fields?", "kind": "provenance" }, { "text": "Which entry fits electric potential?", "kind": "action" } ] } ] }, { "id": "quantum", "name": "Quantum", "description": "Quantum scalar fields.", "findings": [ { "id": "quantum-finding", "name": "Quantum", "description": "Quantum.", "questions": [ { "text": "How do quantum scalar fields relate to spin-zero particles such as the Higgs boson?", "kind": "provenance" }, { "text": "Is the information accurate?", "kind": "boundary" } ] } ] } ] }, { "id": "context", "name": "Context", "description": "Visualisation.", "rationale": "Science.", "layers": [ { "id": "visualisation", "name": "Visualisation", "description": "Visualising fields.", "findings": [ { "id": "visualisation-finding", "name": "Visualisation", "description": "Visualisation.", "questions": [ { "text": "How are scalar fields shown with contour and heat maps?", "kind": "provenance" }, { "text": "Which entry fits contour line?", "kind": "action" } ] } ] }, { "id": "vector", "name": "Vector fields", "description": "Vector fields.", "findings": [ { "id": "vector-finding", "name": "Vector fields", "description": "Vector fields.", "questions": [ { "text": "How do scalar and vector fields relate through the gradient?", "kind": "provenance" }, { "text": "Is the presentation neutral and attributed?", "kind": "boundary" } ] } ] } ] } ] }, "openQuestions": [ "Should the Higgs field be a separate entry?", "How should scalar potentials be linked?", "How should quantum field examples be documented?" ], "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 scalar field, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain scalar fields, relay definition, examples, mathematical treatment and physics uses from mathematics and physics sources, describe the named examples, and distinguish scalar fields from vector and tensor fields, scalar quantities at a point and scalar potentials as a subtype.", "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: electric potential (electrodynamics), scalar potential, velocity potential, temperature field, pressuron, Higgs field, baric field, galileon, graviscalar.", "9 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 45 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 scalar field, 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": [ "electric potential (electrodynamics)", "scalar potential", "velocity potential", "temperature field", "pressuron", "Higgs field", "baric field", "galileon", "graviscalar" ] } ], "standing": "Described in 45 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 9 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 scalar field from another, and a scalar field 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 scalar field, 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 scalar field, 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 scalar field 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 scalar field, 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 scalar field, 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 scalar field 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 scalar field 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 scalar field, 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 scalar field, 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 scalar field 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 scalar field from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a scalar field, 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 scalar field, 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 scalar field 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 scalar field 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 scalar field between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a scalar field, 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 scalar field, 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 scalar field 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 scalar field, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a scalar field 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 scalar field, 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 scalar field, 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 scalar field 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 scalar field 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 scalar field 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 scalar field 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 scalar field 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 scalar field?", "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 scalar field?", "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 scalar field 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 scalar field and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a scalar field, 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 scalar field, 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 scalar field 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 scalar field is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a scalar field, 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 scalar field, 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 scalar field 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 } } } }