{ "model": { "rank": 3156, "code": "thing-q48297", "model_id": "vr.tr.parabola", "name": "parabola", "purpose": "Let an agent explain the parabola, relay its definition, properties and applications from mathematics sources, and distinguish it from the other conic sections and from general plane curves.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q48297/", "tier": 2, "score": 90, "payload": { "layer": "wikidata", "aliases": [ "Kiepert parabola", "Artzt parabola" ], "aliasCount": 2, "merged": 2, "knownIn": 90, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q48297", "url": "https://www.wikidata.org/wiki/Q48297", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-14T03:25:52Z", "providers": [ "Claude" ], "breadth": "written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify", "pass": 2, "wave": 4, "engine": "claude" }, "metaModel": { "id": "THING-Q48297", "registryId": "vr.tr.parabola", "name": "parabola", "version": "0.2.0-wave.4", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q48297/", "model": { "registry_id": "vr.tr.parabola", "name": "parabola", "purpose": "Let an agent explain the parabola, relay its definition, properties and applications from mathematics sources, and distinguish it from the other conic sections and from general plane curves.", "definition": "A plane curve that is symmetric and U-shaped, defined as the set of points equidistant from a fixed point called the focus and a fixed line called the directrix; it is one of the conic sections, obtained by slicing a cone parallel to its side. The parabola appears in mathematics as the graph of a quadratic function and in physics as the path of a projectile under gravity and the shape of reflector dishes. The registry aliases name special constructions such as the Kiepert and Artzt parabolas from triangle geometry.", "what_it_is_for": "Describing a specific symmetric plane curve.", "affordances": [ "explain its definition", "relay its properties", "relay its applications", "distinguish it from other conics" ], "distinguishing_features": [ "Single open symmetric curve", "Focus and directrix definition", "Graph of a quadratic", "Reflective property" ], "appearance": "A smooth symmetric open curve shaped like an arch or the letter U, extending to infinity on both arms.", "visual_identification": [ "U-shaped symmetric open curve", "Kiepert parabola, Artzt parabola in triangle geometry", "An ellipse is closed; a hyperbola has two branches; a circle is closed and round" ], "physical_properties": [ { "quantity": "type", "typical_range": "conic section", "unit": "note", "note": "" }, { "quantity": "defined by", "typical_range": "focus and directrix", "unit": "note", "note": "" }, { "quantity": "registry parents", "typical_range": "plane curve, conic section", "unit": "note", "note": "" } ], "families_and_kinds": [ "graph of a quadratic", "Kiepert parabola", "Artzt parabola" ], "related_models": [ { "relation": "is a kind of", "target": "conic section", "why": "in registry terms" }, { "relation": "is contrasted with", "target": "ellipse", "why": "" }, { "relation": "is contrasted with", "target": "hyperbola", "why": "" }, { "relation": "is a kind of", "target": "plane curve", "why": "" } ], "identifiers": [], "standards_and_regulation": [ "Mathematical definition" ], "failure_modes_and_hazards": [ "Confusing with other conics", "Confusing the curve with its equation", "Overstating physical idealisation" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "understand", "name": "Understand", "description": "What a parabola is.", "rationale": "Definition.", "layers": [ { "id": "definition", "name": "Definition", "description": "Definition.", "findings": [ { "id": "definition-finding", "name": "Definition", "description": "Definition.", "questions": [ { "text": "What is a parabola, and how does it differ from an ellipse, hyperbola and circle?", "kind": "definition" }, { "text": "Is the question about a special construction such as the Kiepert parabola?", "kind": "boundary" } ] } ] }, { "id": "focus", "name": "Focus", "description": "Focus and directrix.", "findings": [ { "id": "focus-finding", "name": "Focus", "description": "Focus.", "questions": [ { "text": "How do the focus and directrix define a parabola?", "kind": "definition" }, { "text": "How is a parabola measured or parameterised?", "kind": "measurement" } ] } ] } ] }, { "id": "properties", "name": "Properties", "description": "Properties.", "rationale": "Sources.", "layers": [ { "id": "equation", "name": "Equation", "description": "Equation.", "findings": [ { "id": "equation-finding", "name": "Equation", "description": "Equation.", "questions": [ { "text": "How is a parabola written as the graph of a quadratic?", "kind": "provenance" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] }, { "id": "reflection", "name": "Reflection", "description": "Reflective property.", "findings": [ { "id": "reflection-finding", "name": "Reflection", "description": "Reflection.", "questions": [ { "text": "What is the reflective property of a parabola?", "kind": "provenance" }, { "text": "Which sources are cited?", "kind": "provenance" } ] } ] } ] }, { "id": "applications", "name": "Applications", "description": "Applications.", "rationale": "Sources.", "layers": [ { "id": "physics", "name": "Physics", "description": "Projectiles.", "findings": [ { "id": "physics-finding", "name": "Physics", "description": "Physics.", "questions": [ { "text": "Why does a projectile follow a parabola under gravity?", "kind": "provenance" }, { "text": "Is the model idealised?", "kind": "boundary" } ] } ] }, { "id": "engineering", "name": "Engineering", "description": "Reflectors.", "findings": [ { "id": "engineering-finding", "name": "Engineering", "description": "Engineering.", "questions": [ { "text": "How are parabolic shapes used in dishes and reflectors?", "kind": "provenance" }, { "text": "Which sources are cited?", "kind": "provenance" } ] } ] } ] }, { "id": "context", "name": "Context", "description": "Context.", "rationale": "Context.", "layers": [ { "id": "conics", "name": "Conics", "description": "Conic family.", "findings": [ { "id": "conics-finding", "name": "Conics", "description": "Conics.", "questions": [ { "text": "How does the parabola fit among the conic sections?", "kind": "provenance" }, { "text": "Which entry fits conic section?", "kind": "action" } ] } ] }, { "id": "geometry", "name": "Geometry", "description": "Triangle geometry.", "findings": [ { "id": "geometry-finding", "name": "Geometry", "description": "Geometry.", "questions": [ { "text": "What are the Kiepert and Artzt parabolas?", "kind": "provenance" }, { "text": "Which sources are cited?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Should special parabolas be separate entries?", "How should the conic-section family be linked?", "How should applications be scoped?" ], "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 parabola, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain the parabola, relay its definition, properties and applications from mathematics sources, and distinguish it from the other conic sections and from general plane curves.", "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: Kiepert parabola, Artzt parabola.", "2 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 90 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 parabola, 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": [ "Kiepert parabola", "Artzt parabola" ] } ], "standing": "Described in 90 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 2 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 parabola from another, and a parabola 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 parabola, 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 parabola, 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 parabola 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 parabola, 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 parabola, 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 parabola 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 parabola 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 parabola, 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 parabola, 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 parabola 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 parabola from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a parabola, 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 parabola, 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 parabola 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 parabola 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 parabola between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a parabola, 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 parabola, 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 parabola 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 parabola, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a parabola 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 parabola, 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 parabola, 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 parabola 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 parabola 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 parabola 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 parabola 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 parabola 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 parabola?", "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 parabola?", "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 parabola 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 parabola and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a parabola, 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 parabola, 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 parabola 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 parabola is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a parabola, 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 parabola, 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 parabola 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 } } } }