{ "model": { "rank": 1132, "code": "thing-q19821", "model_id": "vr.tr.triangle", "name": "triangle", "purpose": "Let an agent explain triangle types and properties, solve triangle problems, apply triangles in construction and trigonometry, and describe symbolic uses with attribution.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q19821/", "tier": 2, "score": 179, "payload": { "layer": "wikidata", "aliases": [ "pink triangle", "Orthologic triangles", "central triangle", "non-equilateral triangle", "circumscribed triangle", "derived triangle", "oblique triangle", "Karpman drama triangle", "acute or obtuse triangle", "inscribed triangle", "desmic mate", "triangle character", "integer triangle", "isosceles triangle", "non-equilateral isosceles triangle", "golden triangle", "Calabi triangle" ], "aliasCount": 17, "merged": 17, "knownIn": 179, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": "vr.tr.triangle-2", "source": { "dataset": "wikidata", "item": "Q19821", "url": "https://www.wikidata.org/wiki/Q19821", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-11T20:18:40Z", "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-Q19821", "registryId": "vr.tr.triangle", "name": "triangle", "version": "0.2.0-wave.2", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q19821/", "model": { "registry_id": "vr.tr.triangle", "name": "triangle", "purpose": "Let an agent explain triangle types and properties, solve triangle problems, apply triangles in construction and trigonometry, and describe symbolic uses with attribution.", "definition": "A polygon with three edges and three vertices, the simplest polygon and a two-dimensional simplex, classified by sides as equilateral, isosceles or scalene and by angles as acute, right or obtuse, with properties such as the angle sum of 180 degrees in Euclidean geometry and many special centres and derived triangles; the triangle is fundamental in geometry, trigonometry, engineering and symbolism.", "what_it_is_for": "Geometry, measurement and structure.", "affordances": [ "classify triangles", "solve for sides, angles and area", "explain centres and theorems", "describe applications and symbolism" ], "distinguishing_features": [ "Simplest polygon", "Rigid shape", "Classified by sides and angles", "Basis of trigonometry" ], "appearance": "A three-sided figure.", "visual_identification": [ "Three sides and three vertices", "Angle sum of 180 degrees in the plane", "A quadrilateral has four sides" ], "physical_properties": [], "families_and_kinds": [ "equilateral, isosceles and scalene triangles", "acute, right and obtuse triangles", "special triangles such as 30-60-90", "derived triangles and triangle centres", "spherical and hyperbolic triangles" ], "related_models": [ { "relation": "is a kind of", "target": "polygon", "why": "category" }, { "relation": "is a kind of", "target": "simplex", "why": "category" }, { "relation": "is used in", "target": "truss", "why": "triangulated structures" }, { "relation": "is related to", "target": "line segment", "why": "edges" } ], "identifiers": [], "standards_and_regulation": [ "ISO 80000-2 notation", "No regulation" ], "failure_modes_and_hazards": [ "Applying Euclidean rules to curved surfaces", "Ambiguous case errors in solving triangles", "Misattributing symbolic meanings" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "classify", "name": "Classify", "description": "Types of triangle.", "rationale": "Sides and angles.", "layers": [ { "id": "type", "name": "Type", "description": "Which type.", "findings": [ { "id": "type-finding", "name": "Type", "description": "Type.", "questions": [ { "text": "What type of triangle is this by sides and angles?", "kind": "definition" }, { "text": "Is it a special triangle with known ratios?", "kind": "definition" } ] } ] }, { "id": "exists", "name": "Exists", "description": "Can it exist.", "findings": [ { "id": "exists-finding", "name": "Exists", "description": "Existence.", "questions": [ { "text": "Can a triangle with these sides or angles exist, by the triangle inequality and angle sum?", "kind": "boundary" }, { "text": "Is it unique?", "kind": "boundary" } ] } ] } ] }, { "id": "solve", "name": "Solve", "description": "Calculations.", "rationale": "Trigonometry.", "layers": [ { "id": "measure", "name": "Measure", "description": "Sides, angles and area.", "findings": [ { "id": "measure-finding", "name": "Measure", "description": "Measurement.", "questions": [ { "text": "What are the unknown sides, angles and area of this triangle?", "kind": "measurement" }, { "text": "Which rule applies, such as sine or cosine rule?", "kind": "definition" } ] } ] }, { "id": "centres", "name": "Centres", "description": "Triangle centres.", "findings": [ { "id": "centres-finding", "name": "Centres", "description": "Centres.", "questions": [ { "text": "Where are the centroid, circumcentre, incentre and orthocentre of this triangle?", "kind": "measurement" }, { "text": "Which theorems relate them?", "kind": "definition" } ] } ] } ] }, { "id": "apply", "name": "Apply", "description": "Applications.", "rationale": "Rigidity and measurement.", "layers": [ { "id": "structures", "name": "Structures", "description": "Triangles in engineering.", "findings": [ { "id": "structures-finding", "name": "Structures", "description": "Engineering.", "questions": [ { "text": "Why are triangles used in trusses and frames?", "kind": "definition" }, { "text": "How is triangulation used in surveying and graphics?", "kind": "definition" } ] } ] }, { "id": "geometries", "name": "Geometries", "description": "Non-Euclidean triangles.", "findings": [ { "id": "geometries-finding", "name": "Geometries", "description": "Non-Euclidean.", "questions": [ { "text": "How do spherical and hyperbolic triangles differ from Euclidean ones?", "kind": "definition" }, { "text": "When does this matter in practice?", "kind": "boundary" } ] } ] } ] }, { "id": "culture", "name": "Culture", "description": "Symbolism and teaching.", "rationale": "Attribution.", "layers": [ { "id": "symbols", "name": "Symbols", "description": "Symbolic triangles.", "findings": [ { "id": "symbols-finding", "name": "Symbols", "description": "Symbolism.", "questions": [ { "text": "What do triangle symbols mean in this context, such as warning signs, religious symbols or the pink triangle in LGBTQ history, as described by the communities and historians concerned?", "kind": "provenance" }, { "text": "Are meanings attributed rather than assumed?", "kind": "boundary" } ] } ] }, { "id": "teach", "name": "Teach", "description": "Teaching triangles.", "findings": [ { "id": "teach-finding", "name": "Teach", "description": "Teaching.", "questions": [ { "text": "How can triangle properties be taught with constructions and proofs?", "kind": "action" }, { "text": "Which misconceptions arise?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Should trigonometry be a separate entry?", "How should geometry resources be linked?", "How should symbolic uses be attributed?" ], "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 triangle, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain triangle types and properties, solve triangle problems, apply triangles in construction and trigonometry, and describe symbolic uses with attribution.", "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: pink triangle, Orthologic triangles, central triangle, non-equilateral triangle, circumscribed triangle, derived triangle, oblique triangle, Karpman drama triangle, acute or obtuse triangle, inscribed triangle, desmic mate, triangle character.", "17 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 179 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 triangle, 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": [ "pink triangle", "Orthologic triangles", "central triangle", "non-equilateral triangle", "circumscribed triangle", "derived triangle", "oblique triangle", "Karpman drama triangle", "acute or obtuse triangle", "inscribed triangle", "desmic mate", "triangle character" ] } ], "standing": "Described in 179 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 17 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 triangle from another, and a triangle 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 triangle, 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 triangle, 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 triangle 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 triangle, 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 triangle, 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 triangle 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 triangle 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 triangle, 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 triangle, 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 triangle 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 triangle from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a triangle, 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 triangle, 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 triangle 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 triangle 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 triangle between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a triangle, 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 triangle, 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 triangle 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 triangle, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a triangle 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 triangle, 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 triangle, 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 triangle 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 triangle 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 triangle 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 triangle 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 triangle 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 triangle?", "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 triangle?", "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 triangle 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 triangle and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a triangle, 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 triangle, 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 triangle 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 triangle is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a triangle, 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 triangle, 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 triangle 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 } } } }