{ "model": { "rank": 3547, "code": "thing-q124255", "model_id": "vr.tr.conic-section", "name": "conic section", "purpose": "Let an agent explain conic sections by definition, equations, properties and applications for learners and practitioners.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q124255/", "tier": 2, "score": 84, "payload": { "layer": "wikidata", "aliases": [ "triangle conic", "Dupin indicatrix", "hyperbola", "Nine-point conic", "degenerate conic section", "non-degenerate conic section", "Kiepert conics", "Kiepert hyperbola", "circumconic", "Evans conic", "inconic", "Nine-point hyperbola", "Conjugate hyperbola", "Jerabek hyperbola", "Feuerbach hyperbola", "equilateral hyperbola" ], "aliasCount": 16, "merged": 16, "knownIn": 84, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q124255", "url": "https://www.wikidata.org/wiki/Q124255", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-11T14:24:29Z", "providers": [ "Claude" ], "breadth": "written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify", "pass": 2, "wave": 1, "engine": "claude" }, "metaModel": { "id": "THING-Q124255", "registryId": "vr.tr.conic-section", "name": "conic section", "version": "0.2.0-wave.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q124255/", "model": { "registry_id": "vr.tr.conic-section", "name": "conic section", "purpose": "Let an agent explain conic sections by definition, equations, properties and applications for learners and practitioners.", "definition": "A curve obtained by intersecting a cone with a plane, namely the circle, ellipse, parabola and hyperbola, plus degenerate cases such as a point or a pair of lines; conics are described by second-degree equations and classified by eccentricity, and they model planetary orbits, projectile paths and optical reflectors.", "what_it_is_for": "Geometry, algebra, astronomy and engineering.", "affordances": [ "identify a conic from its equation", "compute foci, directrices and eccentricity", "relate conics to orbits and reflectors", "explain degenerate conics" ], "distinguishing_features": [ "Plane sections of a cone", "Second-degree equations", "Classified by eccentricity", "Have foci and directrices" ], "appearance": "Not physical; curves drawn in the plane and seen in orbits and dish shapes.", "visual_identification": [ "Circles, ellipses, parabolas and hyperbolas", "Eccentricity values", "Cubic curves are higher degree" ], "physical_properties": [], "families_and_kinds": [ "circle", "ellipse", "parabola", "hyperbola", "degenerate conics" ], "related_models": [ { "relation": "is a kind of", "target": "algebraic curve", "why": "category" }, { "relation": "includes", "target": "circle", "why": "example" }, { "relation": "describes", "target": "orbit", "why": "application" }, { "relation": "is studied in", "target": "analytic geometry", "why": "field" } ], "identifiers": [], "standards_and_regulation": [ "No specific regulation" ], "failure_modes_and_hazards": [ "Misclassifying from incomplete equations", "Sign errors in rotated conics" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "classify", "name": "Classify", "description": "Which conic.", "rationale": "Equations reveal type.", "layers": [ { "id": "equation", "name": "Equation", "description": "From equations.", "findings": [ { "id": "equation-finding", "name": "Equation", "description": "Classification.", "questions": [ { "text": "Which conic does this second-degree equation describe?", "kind": "definition" }, { "text": "What does the discriminant indicate?", "kind": "definition" } ] } ] }, { "id": "eccentricity", "name": "Eccentricity", "description": "Eccentricity.", "findings": [ { "id": "eccentricity-finding", "name": "Eccentricity", "description": "Eccentricity.", "questions": [ { "text": "What is the eccentricity, and what does it say about the shape?", "kind": "measurement" }, { "text": "How is it computed?", "kind": "definition" } ] } ] } ] }, { "id": "properties", "name": "Properties", "description": "Foci and more.", "rationale": "Geometry has structure.", "layers": [ { "id": "foci", "name": "Foci", "description": "Foci and directrices.", "findings": [ { "id": "foci-finding", "name": "Foci", "description": "Foci and directrices.", "questions": [ { "text": "Where are the foci and directrices of this conic?", "kind": "measurement" }, { "text": "How is the reflective property explained?", "kind": "definition" } ] } ] }, { "id": "degenerate", "name": "Degenerate", "description": "Degenerate cases.", "findings": [ { "id": "degenerate-finding", "name": "Degenerate", "description": "Degenerate conics.", "questions": [ { "text": "When does a conic degenerate into a point or lines?", "kind": "definition" }, { "text": "How can this be recognised?", "kind": "definition" } ] } ] } ] }, { "id": "applications", "name": "Applications", "description": "Uses.", "rationale": "Conics describe the world.", "layers": [ { "id": "orbits", "name": "Orbits", "description": "Kepler orbits.", "findings": [ { "id": "orbits-finding", "name": "Orbits", "description": "Orbits.", "questions": [ { "text": "Why are gravitational orbits conic sections?", "kind": "definition" }, { "text": "Which conic fits an escape trajectory?", "kind": "definition" } ] } ] }, { "id": "optics", "name": "Optics", "description": "Reflectors.", "findings": [ { "id": "optics-finding", "name": "Optics", "description": "Reflectors.", "questions": [ { "text": "How do parabolic and elliptical reflectors use focal properties?", "kind": "definition" }, { "text": "Where are they used?", "kind": "provenance" } ] } ] } ] }, { "id": "learning", "name": "Learning", "description": "Teaching.", "rationale": "Visuals help.", "layers": [ { "id": "visual", "name": "Visual", "description": "Cone slicing.", "findings": [ { "id": "visual-finding", "name": "Visual", "description": "Visualisation.", "questions": [ { "text": "How can cone sections be demonstrated with models or software?", "kind": "action" }, { "text": "Which tools help?", "kind": "provenance" } ] } ] }, { "id": "history", "name": "History", "description": "Apollonius.", "findings": [ { "id": "history-finding", "name": "History", "description": "History.", "questions": [ { "text": "How did Apollonius and later mathematicians study conics, according to historians?", "kind": "provenance" }, { "text": "Which works are key?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Should each conic be a separate entry?", "How should projective treatments be linked?", "How should applications 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 conic section, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain conic sections by definition, equations, properties and applications for learners and practitioners.", "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: triangle conic, Dupin indicatrix, hyperbola, Nine-point conic, degenerate conic section, non-degenerate conic section, Kiepert conics, Kiepert hyperbola, circumconic, Evans conic, inconic, Nine-point hyperbola.", "16 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 84 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 conic section, 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": [ "triangle conic", "Dupin indicatrix", "hyperbola", "Nine-point conic", "degenerate conic section", "non-degenerate conic section", "Kiepert conics", "Kiepert hyperbola", "circumconic", "Evans conic", "inconic", "Nine-point hyperbola" ] } ], "standing": "Described in 84 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 16 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 conic section from another, and a conic section 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 conic section, 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 conic section, 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 conic section 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 conic section, 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 conic section, 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 conic section 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 conic section 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 conic section, 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 conic section, 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 conic section 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 conic section from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a conic section, 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 conic section, 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 conic section 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 conic section 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 conic section between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a conic section, 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 conic section, 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 conic section 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 conic section, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a conic section 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 conic section, 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 conic section, 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 conic section 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 conic section 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 conic section 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 conic section 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 conic section 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 conic section?", "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 conic section?", "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 conic section 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 conic section and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a conic section, 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 conic section, 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 conic section 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 conic section is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a conic section, 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 conic section, 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 conic section 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 } } } }