{ "model": { "rank": 1287, "code": "thing-q17278", "model_id": "vr.tr.circle", "name": "circle", "purpose": "Let an agent explain circles by definition, formulas, theorems and applications, and separate geographic and other senses.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q17278/", "tier": 2, "score": 159, "payload": { "layer": "wikidata", "aliases": [ "parallel marker", "circle of latitude", "tropic", "color wheel", "spinning pinwheel", "unit circle", "triangle circles", "circumscribed circle", "Hart circle", "Rrakota", "Droz-Farny circle", "Soddy circle", "Carlyle circle", "Circle of equal altitude", "Mixtilinear Circle", "Color wheel theory of love", "magic circle", "Archimedes' twin circles", "circle of antisimilitude", "Archimedean circle", "director circle", "GEOS circle", "concentric circles", "Johnson circles", "fairy ring", "Spherical circle", "circumscribed circle for triangle", "Schoch circles", "Woo circles" ], "aliasCount": 29, "merged": 29, "knownIn": 159, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": "vr.tr.circle-artifact", "source": { "dataset": "wikidata", "item": "Q17278", "url": "https://www.wikidata.org/wiki/Q17278", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-11T14:24:29Z", "providers": [ "Claude" ], "breadth": "written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify", "pass": 2, "wave": 1, "engine": "claude" }, "metaModel": { "id": "THING-Q17278", "registryId": "vr.tr.circle", "name": "circle", "version": "0.2.0-wave.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q17278/", "model": { "registry_id": "vr.tr.circle", "name": "circle", "purpose": "Let an agent explain circles by definition, formulas, theorems and applications, and separate geographic and other senses.", "definition": "The set of all points in a plane at a fixed distance, the radius, from a centre point; its circumference is 2 pi r and its area pi r squared, and the unit circle underlies trigonometry; the word also names circles of latitude and circular shapes such as colour wheels.", "what_it_is_for": "Geometry, trigonometry, engineering and design.", "affordances": [ "calculate circumference, area and arc length", "use the unit circle in trigonometry", "explain circle theorems", "separate other senses of circle" ], "distinguishing_features": [ "Constant distance from centre", "Special conic section", "Defines pi", "Symmetric in every direction" ], "appearance": "A round closed curve, as in wheels, coins and drawings.", "visual_identification": [ "Constant radius from a centre", "Symbol pi in formulas", "Ellipses have two foci" ], "physical_properties": [ { "quantity": "circumference", "typical_range": "2 pi r", "unit": "", "note": "formula" }, { "quantity": "area", "typical_range": "pi r squared", "unit": "", "note": "formula" } ], "families_and_kinds": [ "unit circle", "great and small circles", "circles of latitude", "inscribed and circumscribed circles", "circle packing" ], "related_models": [ { "relation": "is a kind of", "target": "conic section", "why": "category" }, { "relation": "is related to", "target": "angular measure", "why": "angles" }, { "relation": "is used in", "target": "trigonometry", "why": "field" }, { "relation": "is related to", "target": "orbit", "why": "circular orbits" } ], "identifiers": [], "standards_and_regulation": [ "No specific regulation" ], "failure_modes_and_hazards": [ "Confusing radius and diameter", "Rounding pi too early" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "measure", "name": "Measure", "description": "Formulas.", "rationale": "Formulas are exact.", "layers": [ { "id": "formulas", "name": "Formulas", "description": "Circumference and area.", "findings": [ { "id": "formulas-finding", "name": "Formulas", "description": "Formulas.", "questions": [ { "text": "What are the circumference and area for this radius?", "kind": "measurement" }, { "text": "How precise should pi be?", "kind": "boundary" } ] } ] }, { "id": "arcs", "name": "Arcs", "description": "Arcs and sectors.", "findings": [ { "id": "arcs-finding", "name": "Arcs", "description": "Arcs and sectors.", "questions": [ { "text": "What are the arc length and sector area for this angle?", "kind": "measurement" }, { "text": "Is the angle in radians?", "kind": "boundary" } ] } ] } ] }, { "id": "theory", "name": "Theory", "description": "Theorems.", "rationale": "Circles have rich theory.", "layers": [ { "id": "theorems", "name": "Theorems", "description": "Circle theorems.", "findings": [ { "id": "theorems-finding", "name": "Theorems", "description": "Circle theorems.", "questions": [ { "text": "Which circle theorem applies here, such as the inscribed angle theorem?", "kind": "definition" }, { "text": "How is it proved?", "kind": "definition" } ] } ] }, { "id": "unit", "name": "Unit circle", "description": "Trigonometry.", "findings": [ { "id": "unit-finding", "name": "Unit circle", "description": "Unit circle.", "questions": [ { "text": "How does the unit circle define sine and cosine?", "kind": "definition" }, { "text": "What are the values at key angles?", "kind": "measurement" } ] } ] } ] }, { "id": "applications", "name": "Applications", "description": "Uses.", "rationale": "Circles are everywhere.", "layers": [ { "id": "engineering", "name": "Engineering", "description": "Design.", "findings": [ { "id": "engineering-finding", "name": "Engineering", "description": "Engineering.", "questions": [ { "text": "How are circles used in wheels, gears and pipes?", "kind": "definition" }, { "text": "Which tolerances apply?", "kind": "provenance" } ] } ] }, { "id": "geography", "name": "Geography", "description": "Circles of latitude.", "findings": [ { "id": "geography-finding", "name": "Geography", "description": "Circles of latitude.", "questions": [ { "text": "What are circles of latitude and the tropics?", "kind": "definition" }, { "text": "Where are they located?", "kind": "provenance" } ] } ] } ] }, { "id": "senses", "name": "Senses", "description": "Disambiguation.", "rationale": "Circle has other senses.", "layers": [ { "id": "social", "name": "Social", "description": "Social circles.", "findings": [ { "id": "social-finding", "name": "Social", "description": "Social sense.", "questions": [ { "text": "Is a social circle or group meant?", "kind": "boundary" }, { "text": "Which entry fits?", "kind": "action" } ] } ] }, { "id": "design", "name": "Design", "description": "Colour wheels and icons.", "findings": [ { "id": "design-finding", "name": "Design", "description": "Design sense.", "questions": [ { "text": "Is a colour wheel or a loading icon meant?", "kind": "boundary" }, { "text": "Which entry fits?", "kind": "action" } ] } ] } ] } ] }, "openQuestions": [ "Should circle theorems be separate entries?", "How should geographic circles be linked?", "How should other senses be split off?" ], "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 circle, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain circles by definition, formulas, theorems and applications, and separate geographic and other senses.", "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: parallel marker, circle of latitude, tropic, color wheel, spinning pinwheel, unit circle, triangle circles, circumscribed circle, Hart circle, Rrakota, Droz-Farny circle, Soddy circle.", "29 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 159 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 circle, 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": [ "parallel marker", "circle of latitude", "tropic", "color wheel", "spinning pinwheel", "unit circle", "triangle circles", "circumscribed circle", "Hart circle", "Rrakota", "Droz-Farny circle", "Soddy circle" ] } ], "standing": "Described in 159 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 29 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 circle from another, and a circle 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 circle, 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 circle, 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 circle 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 circle, 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 circle, 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 circle 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 circle 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 circle, 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 circle, 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 circle 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 circle from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a circle, 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 circle, 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 circle 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 circle 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 circle between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a circle, 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 circle, 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 circle 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 circle, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a circle 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 circle, 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 circle, 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 circle 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 circle 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 circle 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 circle 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 circle 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 circle?", "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 circle?", "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 circle 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 circle and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a circle, 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 circle, 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 circle 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 circle is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a circle, 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 circle, 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 circle 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 } } } }