{ "model": { "rank": 2553, "code": "thing-q46303", "model_id": "vr.tr.trapezoid", "name": "trapezoid", "purpose": "Let an agent explain trapezoids and their definitions and properties, compute area and other measures, distinguish inclusive and exclusive definitions and British usage, and support geometry learning.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q46303/", "tier": 2, "score": 103, "payload": { "layer": "wikidata", "aliases": [ "proper trapezoid", "isosceles trapezoid", "right trapezoid with exactly one pair of parallel sides", "isosceles trapezoid with exactly one pair of parallel sides", "bicentric trapezoid", "midsquare trapezoid", "tangential trapezoid", "right trapezoid", "irregular trapezium", "right tangential trapezoid" ], "aliasCount": 10, "merged": 10, "knownIn": 103, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q46303", "url": "https://www.wikidata.org/wiki/Q46303", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-12T00:11:07Z", "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-Q46303", "registryId": "vr.tr.trapezoid", "name": "trapezoid", "version": "0.2.0-wave.2", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q46303/", "model": { "registry_id": "vr.tr.trapezoid", "name": "trapezoid", "purpose": "Let an agent explain trapezoids and their definitions and properties, compute area and other measures, distinguish inclusive and exclusive definitions and British usage, and support geometry learning.", "definition": "A quadrilateral with at least one pair of parallel sides, called a trapezium in British usage, with special cases such as the isosceles trapezoid with equal legs, the right trapezoid with a right angle, and under the inclusive definition parallelograms as well, and with properties such as the midsegment and area formula based on the parallel sides and height; trapezoids appear in geometry education, architecture and engineering.", "what_it_is_for": "Quadrilaterals with parallel sides.", "affordances": [ "explain definitions and properties", "compute area and measures", "clarify terminology", "support learning" ], "distinguishing_features": [ "Parallel bases", "Legs and height", "Midsegment property", "Terminology variation" ], "appearance": "A four-sided figure with two parallel sides.", "visual_identification": [ "One pair of parallel sides", "Special cases isosceles and right", "A parallelogram has two pairs; British trapezium and trapezoid are swapped" ], "physical_properties": [], "families_and_kinds": [ "general trapezoids", "isosceles trapezoids", "right trapezoids", "bicentric and other special trapezoids", "parallelograms under the inclusive definition" ], "related_models": [ { "relation": "is a kind of", "target": "convex quadrilateral", "why": "category" }, { "relation": "is related to", "target": "triangle", "why": "related polygons" }, { "relation": "is related to", "target": "curvature", "why": "another geometric entry" }, { "relation": "is related to", "target": "difference", "why": "contrasting definitions" } ], "identifiers": [], "standards_and_regulation": [ "Mathematical definitions in curricula", "Terminology conventions by country" ], "failure_modes_and_hazards": [ "Confusing trapezoid and trapezium across dialects", "Applying the exclusive definition inconsistently", "Area formula errors" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "define", "name": "Define", "description": "What a trapezoid is.", "rationale": "Geometry.", "layers": [ { "id": "definition", "name": "Definition", "description": "Definitions.", "findings": [ { "id": "definition-finding", "name": "Definition", "description": "Definitions.", "questions": [ { "text": "What is a trapezoid, how do inclusive and exclusive definitions differ, and how does British trapezium usage differ?", "kind": "definition" }, { "text": "Which definition applies in this curriculum?", "kind": "boundary" } ] } ] }, { "id": "special", "name": "Special", "description": "Special cases.", "findings": [ { "id": "special-finding", "name": "Special", "description": "Special cases.", "questions": [ { "text": "What are isosceles, right, bicentric and midsquare trapezoids, and what properties do they have?", "kind": "definition" }, { "text": "Which entry fits a specific case?", "kind": "action" } ] } ] } ] }, { "id": "compute", "name": "Compute", "description": "Calculations.", "rationale": "Practice.", "layers": [ { "id": "area", "name": "Area", "description": "Area and perimeter.", "findings": [ { "id": "area-finding", "name": "Area", "description": "Area.", "questions": [ { "text": "How are the area, perimeter, midsegment and diagonals of a trapezoid computed?", "kind": "action" }, { "text": "How is the height found when not given?", "kind": "action" } ] } ] }, { "id": "prove", "name": "Prove", "description": "Proofs.", "findings": [ { "id": "prove-finding", "name": "Prove", "description": "Proofs.", "questions": [ { "text": "How are trapezoid properties proved, such as the midsegment theorem?", "kind": "action" }, { "text": "Which entry fits Euclidean geometry?", "kind": "action" } ] } ] } ] }, { "id": "apply", "name": "Apply", "description": "Applications.", "rationale": "Context.", "layers": [ { "id": "applications", "name": "Applications", "description": "Trapezoids in practice.", "findings": [ { "id": "applications-finding", "name": "Applications", "description": "Applications.", "questions": [ { "text": "Where do trapezoids appear in architecture, engineering and numerical integration such as the trapezoidal rule?", "kind": "provenance" }, { "text": "Which entry fits the trapezoidal rule?", "kind": "action" } ] } ] }, { "id": "generalise", "name": "Generalise", "description": "Generalisations.", "findings": [ { "id": "generalise-finding", "name": "Generalise", "description": "Generalisations.", "questions": [ { "text": "How do trapezoids generalise in higher dimensions and non-Euclidean geometry?", "kind": "definition" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] } ] }, { "id": "learn", "name": "Learn", "description": "Teaching and history.", "rationale": "Education.", "layers": [ { "id": "teach", "name": "Teach", "description": "Teaching trapezoids.", "findings": [ { "id": "teach-finding", "name": "Teach", "description": "Teaching.", "questions": [ { "text": "How can trapezoids be taught with constructions and classification exercises?", "kind": "action" }, { "text": "Which misconceptions arise?", "kind": "provenance" } ] } ] }, { "id": "history", "name": "History", "description": "History of the terms.", "findings": [ { "id": "history-finding", "name": "History", "description": "History.", "questions": [ { "text": "How did the terms trapezoid and trapezium develop and diverge?", "kind": "provenance" }, { "text": "Which entry fits history of geometry?", "kind": "action" } ] } ] } ] } ] }, "openQuestions": [ "Should isosceles trapezoid be a separate entry?", "How should curriculum standards be linked?", "How should terminology 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 trapezoid, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain trapezoids and their definitions and properties, compute area and other measures, distinguish inclusive and exclusive definitions and British usage, and support geometry learning.", "characteristics": { "substance": "abstract", "origin": "conceptual", "agency": "inert" }, "whatYouCanDoWithIt": [ "observed and measured" ], "distinguishingFeatures": [ "Names folded into this entry, which a task may need to split apart again: proper trapezoid, isosceles trapezoid, right trapezoid with exactly one pair of parallel sides, isosceles trapezoid with exactly one pair of parallel sides, bicentric trapezoid, midsquare trapezoid, tangential trapezoid, right trapezoid, irregular trapezium, right tangential trapezoid.", "10 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 103 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 trapezoid, 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": [ "proper trapezoid", "isosceles trapezoid", "right trapezoid with exactly one pair of parallel sides", "isosceles trapezoid with exactly one pair of parallel sides", "bicentric trapezoid", "midsquare trapezoid", "tangential trapezoid", "right trapezoid", "irregular trapezium", "right tangential trapezoid" ] } ], "standing": "Described in 103 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 10 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 trapezoid from another, and a trapezoid 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 trapezoid, 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 trapezoid, 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 trapezoid 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 trapezoid, 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 trapezoid, 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 trapezoid 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 trapezoid 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 trapezoid, 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 trapezoid, 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 trapezoid 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 trapezoid from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a trapezoid, 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 trapezoid, 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 trapezoid 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 trapezoid 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 trapezoid between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a trapezoid, 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 trapezoid, 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 trapezoid 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 trapezoid, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a trapezoid 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 trapezoid, 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 trapezoid, 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 trapezoid 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 trapezoid 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 trapezoid 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 trapezoid 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 trapezoid 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 trapezoid?", "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 trapezoid?", "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 trapezoid 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 trapezoid and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a trapezoid, 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 trapezoid, 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 trapezoid 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 trapezoid is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a trapezoid, 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 trapezoid, 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 trapezoid 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 } } } }