{ "model": { "rank": 8737, "code": "thing-q208476", "model_id": "vr.tr.solid-angle", "name": "solid angle", "purpose": "Let an agent explain solid angle, relay definitions, units, calculations and uses from physics, metrology and graphics sources, describe the named related concepts and flag loosely filed aliases, and distinguish solid angle from plane angle, field of view as a linear angle, luminous intensity and square degrees used in astronomy.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q208476/", "tier": 2, "score": 50, "payload": { "layer": "wikidata", "aliases": [ "field of view", "field of regard", "trihedron", "camera field of view", "field of view in video games", "viewing frustum", "line of sight", "field of sight" ], "aliasCount": 8, "merged": 8, "knownIn": 50, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q208476", "url": "https://www.wikidata.org/wiki/Q208476", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-13T23:45:34Z", "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-Q208476", "registryId": "vr.tr.solid-angle", "name": "solid angle", "version": "0.2.0-wave.4", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q208476/", "model": { "registry_id": "vr.tr.solid-angle", "name": "solid angle", "purpose": "Let an agent explain solid angle, relay definitions, units, calculations and uses from physics, metrology and graphics sources, describe the named related concepts and flag loosely filed aliases, and distinguish solid angle from plane angle, field of view as a linear angle, luminous intensity and square degrees used in astronomy.", "definition": "A measure of the field of view from a point, the three-dimensional analogue of a plane angle, equal to the area of the projection of an object onto a unit sphere around the observer, measured in steradians, with a full sphere subtending 4 pi steradians, about 12.57, used in radiometry, photometry, antenna theory and astronomy; related concepts the registry aliases name include field of view, field of regard, camera field of view and field of view in video games, which are often given as plane angles, viewing frustums in computer graphics, and trihedra, figures formed by three planes meeting at a point, which appear loosely filed.", "what_it_is_for": "Measuring angular extent in three dimensions.", "affordances": [ "explain definition and units", "relay calculations", "describe related field-of-view concepts", "flag loosely filed aliases" ], "distinguishing_features": [ "Dimensionless SI derived quantity", "Measured on unit sphere", "Radiometry use", "Field-of-view link" ], "appearance": "Not a physical object; visualised as a cone from a point to a surface.", "visual_identification": [ "Three-dimensional angular extent", "Field of view, field of regard, trihedron, camera field of view, field of view in video games, viewing frustum", "Plane angles are two-dimensional; field of view is often in degrees; luminous intensity is candela per steradian; square degrees are an astronomy unit" ], "physical_properties": [ { "quantity": "SI unit", "typical_range": "steradian", "unit": "unit", "note": "sr" }, { "quantity": "full sphere", "typical_range": "4 pi", "unit": "sr", "note": "about 12.566" }, { "quantity": "square degrees in a sphere", "typical_range": "about 41,253", "unit": "deg2", "note": "" } ], "families_and_kinds": [ "solid angles of cones and polygons", "fields of view", "viewing frustums", "square degree measures" ], "related_models": [ { "relation": "is a kind of", "target": "physical quantity", "why": "in registry terms, dimensionless" }, { "relation": "is measured in", "target": "steradian", "why": "" }, { "relation": "is related to", "target": "field of view", "why": "" }, { "relation": "is contrasted with", "target": "angle", "why": "plane angle" } ], "identifiers": [], "standards_and_regulation": [ "SI Brochure", "ISO 80000-3" ], "failure_modes_and_hazards": [ "Confusing solid and plane angles", "Mixing square degrees and steradians", "Loosely filed geometry aliases" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "understand", "name": "Understand", "description": "What a solid angle is.", "rationale": "Definition.", "layers": [ { "id": "definition", "name": "Definition", "description": "Definition.", "findings": [ { "id": "definition-finding", "name": "Definition", "description": "Definition.", "questions": [ { "text": "What is a solid angle, and how does it differ from plane angles, field of view in degrees, luminous intensity and square degrees?", "kind": "definition" }, { "text": "Is the question about physics, astronomy, cameras or games?", "kind": "boundary" } ] } ] }, { "id": "concepts", "name": "Concepts", "description": "Named concepts.", "findings": [ { "id": "concepts-finding", "name": "Concepts", "description": "Concepts.", "questions": [ { "text": "What are field of view, field of regard, viewing frustums and trihedra, and how do they relate?", "kind": "definition" }, { "text": "Which entry fits the specific concept?", "kind": "action" } ] } ] } ] }, { "id": "mathematics", "name": "Mathematics", "description": "Calculation.", "rationale": "Science.", "layers": [ { "id": "steradian", "name": "Steradian", "description": "Steradian.", "findings": [ { "id": "steradian-finding", "name": "Steradian", "description": "Steradian.", "questions": [ { "text": "How is the steradian defined, and why does a sphere have 4 pi steradians?", "kind": "measurement" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] }, { "id": "cones", "name": "Cones", "description": "Cone formula.", "findings": [ { "id": "cones-finding", "name": "Cones", "description": "Cones.", "questions": [ { "text": "How is the solid angle of a cone with a given half-angle calculated?", "kind": "measurement" }, { "text": "Which sources are cited?", "kind": "provenance" } ] } ] } ] }, { "id": "applications", "name": "Applications", "description": "Applications.", "rationale": "Science.", "layers": [ { "id": "radiometry", "name": "Radiometry", "description": "Radiometry and photometry.", "findings": [ { "id": "radiometry-finding", "name": "Radiometry", "description": "Radiometry.", "questions": [ { "text": "How do radiance and luminous intensity use steradians?", "kind": "provenance" }, { "text": "Which entry fits candela?", "kind": "action" } ] } ] }, { "id": "astronomy", "name": "Astronomy", "description": "Sky surveys.", "findings": [ { "id": "astronomy-finding", "name": "Astronomy", "description": "Astronomy.", "questions": [ { "text": "How do astronomers express survey areas in square degrees?", "kind": "measurement" }, { "text": "Which entry fits square degree?", "kind": "action" } ] } ] } ] }, { "id": "context", "name": "Context", "description": "Imaging and games.", "rationale": "Context.", "layers": [ { "id": "cameras", "name": "Cameras", "description": "Camera field of view.", "findings": [ { "id": "cameras-finding", "name": "Cameras", "description": "Cameras.", "questions": [ { "text": "How do focal length and sensor size determine camera field of view?", "kind": "measurement" }, { "text": "Which entry fits angle of view?", "kind": "action" } ] } ] }, { "id": "frustum", "name": "Frustum", "description": "Viewing frustum.", "findings": [ { "id": "frustum-finding", "name": "Frustum", "description": "Frustum.", "questions": [ { "text": "What is a viewing frustum in 3D graphics, and how does game FOV work?", "kind": "provenance" }, { "text": "Which entry fits viewing frustum?", "kind": "action" } ] } ] } ] } ] }, "openQuestions": [ "The registry alias trihedron should be moved to geometry entries", "Should field of view be a separate entry?", "How should radiometry references 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 solid angle, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain solid angle, relay definitions, units, calculations and uses from physics, metrology and graphics sources, describe the named related concepts and flag loosely filed aliases, and distinguish solid angle from plane angle, field of view as a linear angle, luminous intensity and square degrees used in astronomy.", "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: field of view, field of regard, trihedron, camera field of view, field of view in video games, viewing frustum, line of sight, field of sight.", "8 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 50 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 solid angle, 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": [ "field of view", "field of regard", "trihedron", "camera field of view", "field of view in video games", "viewing frustum", "line of sight", "field of sight" ] } ], "standing": "Described in 50 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 8 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 solid angle from another, and a solid angle 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 solid angle, 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 solid angle, 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 solid angle 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 solid angle, 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 solid angle, 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 solid angle 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 solid angle 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 solid angle, 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 solid angle, 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 solid angle 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 solid angle from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a solid angle, 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 solid angle, 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 solid angle 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 solid angle 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 solid angle between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a solid angle, 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 solid angle, 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 solid angle 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 solid angle, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a solid angle 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 solid angle, 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 solid angle, 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 solid angle 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 solid angle 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 solid angle 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 solid angle 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 solid angle 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 solid angle?", "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 solid angle?", "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 solid angle 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 solid angle and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a solid angle, 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 solid angle, 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 solid angle 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 solid angle is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a solid angle, 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 solid angle, 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 solid angle 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 } } } }