{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.parabola","code":"thing-q48297","url":"https://ver.cy/models/thing/q48297/","name":"parabola","alternateNames":["Kiepert parabola","Artzt parabola"],"kind":"thing","status":"published","version":"0.2.0-wave.4","language":"en","classifiers":{"family":"Thing Registry","category":"Cross-cutting context","entryKind":"thing","plane":"XCT","domain":["XCT.QLT"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"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.","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.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Single open symmetric curve","Focus and directrix definition","Graph of a quadratic","Reflective property"],"structure":{"bundles":[{"id":"understand","name":"Understand","description":"What a parabola is.","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.","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.","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.","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"}]}]}]}]},"agentConduct":{"may":["Explain the parabola, its focus and directrix and its equations.","Use parabolic models where they fit, such as projectile paths or reflectors.","Distinguish a parabola from other conic sections."],"mustNot":["Confuse a parabola with a catenary or other U-shaped curves in engineering.","Present a parabolic model as exact when air resistance or other factors matter.","Confuse the curve with one particular equation for it.","Use a parabolic fit to extrapolate trends in health or economics without stating its limits."],"requiresHuman":["Relying on a parabolic design in a structure or device where failure endangers people."]},"ethics":{"considerations":["Simple curve fits can mislead public decisions when extrapolated.","Students deserve clear, correct explanations."],"affectedParties":["Students","Engineers","People affected by modelled decisions"]},"owners":{"steward":"Nobody: a mathematical object held in common.","roles":[],"masterSystems":[]},"relations":[{"target":"Q1060874","type":"parent","note":"registry parent class"},{"target":"Q124255","type":"parent","note":"registry parent class"},{"target":"Q2064156","type":"parent","note":"registry parent class"},{"target":"Q211548","type":"parent","note":"registry parent class"},{"target":"Q25967482","type":"parent","note":"registry parent class"},{"target":"Q266237","type":"parent","note":"registry parent class"},{"target":"conic section","type":"related","note":"in registry terms"},{"target":"ellipse","type":"related"},{"target":"hyperbola","type":"related"},{"target":"plane curve","type":"related"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.parabola","Wikidata: Q48297 (https://www.wikidata.org/wiki/Q48297)"]},"properties":{"applicability":"not-applicable","items":["type: conic section note","defined by: focus and directrix note","registry parents: plane curve, conic section note"]},"recognition":{"applicability":"optional","items":["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","A smooth symmetric open curve shaped like an arch or the letter U, extending to infinity on both arms."]},"capabilities":{"applicability":"required","items":["explain its definition","relay its properties","relay its applications","distinguish it from other conics"]},"hazards":{"applicability":"required","items":["Confusing with other conics","Confusing the curve with its equation","Overstating physical idealisation"]},"interfaces":{"applicability":"required","items":["Mathematical definition"]},"context":{"applicability":"required","items":["Describing a specific symmetric plane curve.","graph of a quadratic","Kiepert parabola","Artzt parabola"]}},"sources":[{"title":"Wikidata item Q48297: parabola","url":"https://www.wikidata.org/wiki/Q48297","note":"identity and sense of the item"},{"title":"Wikipedia: Parabola","url":"https://en.wikipedia.org/wiki/Parabola","note":"general description of the item"}],"openQuestions":["Should special parabolas be separate entries?","How should the conic-section family be linked?","How should applications be scoped?"],"resources":{"spec":"/models/things/publications/thing-q48297/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q48297/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-14T03:25:52Z","builder":"tools/build_cards.py@1.0.0"},"completeness":{"sections":{"classifiers":"filled","whatItIs":"filled","purpose":"filled","distinguishingFeatures":"filled","structure":"filled","agentConduct":"filled","ethics":"filled","owners":"filled","relations":"filled","interaction.identity":"filled","interaction.properties":"not-applicable","interaction.recognition":"filled","interaction.capabilities":"filled","interaction.hazards":"filled","interaction.interfaces":"filled","interaction.context":"filled","sources":"filled"},"notes":{"_gate":"Published through the thing publication gate 1.0 on 2026-10-06T19:52:00+00:00: completeness 1.00; sense: Wikidata description; 2 live sources; review by codex: pass","interaction.properties":"Plane XCT: no invented physical properties."},"score":1.0}}