{ "model": { "rank": 1811, "code": "thing-q209", "model_id": "vr.tr.rectangle", "name": "rectangle", "purpose": "Let an agent explain the rectangle and its properties, support calculations of area, perimeter and diagonals, describe uses in design, computing and construction, and support learning.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q209/", "tier": 2, "score": 126, "payload": { "layer": "wikidata", "aliases": [ "oblong", "minimum bounding rectangle", "subrectangular", "dynamic rectangle" ], "aliasCount": 4, "merged": 4, "knownIn": 126, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q209", "url": "https://www.wikidata.org/wiki/Q209", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-12T04:08:37Z", "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-Q209", "registryId": "vr.tr.rectangle", "name": "rectangle", "version": "0.2.0-wave.2", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q209/", "model": { "registry_id": "vr.tr.rectangle", "name": "rectangle", "purpose": "Let an agent explain the rectangle and its properties, support calculations of area, perimeter and diagonals, describe uses in design, computing and construction, and support learning.", "definition": "A quadrilateral with four right angles, whose opposite sides are equal and parallel and whose diagonals are equal and bisect each other, including the square as the special case with equal sides and the oblong with unequal sides, and used in concepts such as the minimum bounding rectangle in computing and dynamic rectangles in design; the rectangle is one of the most common shapes in construction, design, screens and mathematics.", "what_it_is_for": "Quadrilateral with four right angles.", "affordances": [ "explain properties", "support calculations", "describe uses", "support learning" ], "distinguishing_features": [ "Right angles", "Equal diagonals", "Simple formulas", "Ubiquitous shape" ], "appearance": "A four-sided shape with right angles.", "visual_identification": [ "Four right angles, opposite sides equal", "Square as special case", "A parallelogram lacks right angles; a rhombus has equal sides without right angles" ], "physical_properties": [], "families_and_kinds": [ "squares", "oblongs", "golden and other dynamic rectangles", "bounding rectangles in computing", "rectangles in tiling and packing" ], "related_models": [ { "relation": "is a kind of", "target": "convex cyclic quadrilateral", "why": "category" }, { "relation": "is a kind of", "target": "isosceles trapezoid", "why": "category" }, { "relation": "is related to", "target": "hypercube", "why": "the square as a two-dimensional hypercube" }, { "relation": "is related to", "target": "base", "why": "rectangular bases of solids" } ], "identifiers": [], "standards_and_regulation": [ "Mathematical conventions", "Paper and screen size standards based on rectangles", "No regulation" ], "failure_modes_and_hazards": [ "Confusing rectangle with parallelogram", "Assuming all rectangles are oblongs", "Aspect ratio confusion" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "understand", "name": "Understand", "description": "What a rectangle is.", "rationale": "Geometry.", "layers": [ { "id": "definition", "name": "Definition", "description": "Definition and properties.", "findings": [ { "id": "definition-finding", "name": "Definition", "description": "Definition.", "questions": [ { "text": "What defines a rectangle, and what properties of sides, angles and diagonals follow?", "kind": "definition" }, { "text": "Which entry fits quadrilaterals?", "kind": "action" } ] } ] }, { "id": "kinds", "name": "Kinds", "description": "Squares, oblongs and ratios.", "findings": [ { "id": "kinds-finding", "name": "Kinds", "description": "Kinds.", "questions": [ { "text": "How do squares, oblongs and dynamic rectangles such as the golden rectangle differ?", "kind": "definition" }, { "text": "Which entry fits the golden ratio?", "kind": "action" } ] } ] } ] }, { "id": "compute", "name": "Compute", "description": "Calculations.", "rationale": "Practice.", "layers": [ { "id": "calculate", "name": "Calculate", "description": "Area, perimeter and diagonals.", "findings": [ { "id": "calculate-finding", "name": "Calculate", "description": "Calculation.", "questions": [ { "text": "What are the area, perimeter and diagonal of this rectangle?", "kind": "action" }, { "text": "Which entry fits area?", "kind": "action" } ] } ] }, { "id": "coordinates", "name": "Coordinates", "description": "Coordinates and bounding boxes.", "findings": [ { "id": "coordinates-finding", "name": "Coordinates", "description": "Coordinates.", "questions": [ { "text": "How are rectangles represented in coordinates, and how are minimum bounding rectangles computed?", "kind": "action" }, { "text": "Which entry fits computational geometry?", "kind": "action" } ] } ] } ] }, { "id": "apply", "name": "Apply", "description": "Applications.", "rationale": "Context.", "layers": [ { "id": "design", "name": "Design", "description": "Design and construction.", "findings": [ { "id": "design-finding", "name": "Design", "description": "Design.", "questions": [ { "text": "How do rectangles and aspect ratios shape paper sizes, screens, buildings and layouts?", "kind": "provenance" }, { "text": "Which entry fits paper sizes?", "kind": "action" } ] } ] }, { "id": "tiling", "name": "Tiling", "description": "Tiling and packing.", "findings": [ { "id": "tiling-finding", "name": "Tiling", "description": "Tiling.", "questions": [ { "text": "How are rectangles used in tiling, packing and layout problems?", "kind": "provenance" }, { "text": "Which entry fits packing problems?", "kind": "action" } ] } ] } ] }, { "id": "learn", "name": "Learn", "description": "Teaching.", "rationale": "Education.", "layers": [ { "id": "teach", "name": "Teach", "description": "Teaching.", "findings": [ { "id": "teach-finding", "name": "Teach", "description": "Teaching.", "questions": [ { "text": "How can rectangles and their properties be taught to children?", "kind": "action" }, { "text": "Which misconceptions arise?", "kind": "provenance" } ] } ] }, { "id": "history", "name": "History", "description": "History.", "findings": [ { "id": "history-finding", "name": "History", "description": "History.", "questions": [ { "text": "How did rectangles feature in ancient geometry and measurement?", "kind": "provenance" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Should the square be a separate entry?", "How should geometry resources be linked?", "How should design ratio resources 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 rectangle, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain the rectangle and its properties, support calculations of area, perimeter and diagonals, describe uses in design, computing and construction, and support 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: oblong, minimum bounding rectangle, subrectangular, dynamic rectangle.", "4 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 126 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 rectangle, 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": [ "oblong", "minimum bounding rectangle", "subrectangular", "dynamic rectangle" ] } ], "standing": "Described in 126 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 4 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 rectangle from another, and a rectangle 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 rectangle, 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 rectangle, 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 rectangle 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 rectangle, 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 rectangle, 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 rectangle 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 rectangle 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 rectangle, 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 rectangle, 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 rectangle 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 rectangle from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a rectangle, 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 rectangle, 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 rectangle 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 rectangle 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 rectangle between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a rectangle, 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 rectangle, 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 rectangle 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 rectangle, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a rectangle 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 rectangle, 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 rectangle, 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 rectangle 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 rectangle 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 rectangle 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 rectangle 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 rectangle 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 rectangle?", "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 rectangle?", "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 rectangle 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 rectangle and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a rectangle, 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 rectangle, 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 rectangle 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 rectangle is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a rectangle, 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 rectangle, 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 rectangle 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 } } } }