{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.dimension","code":"thing-q4440864","url":"https://ver.cy/models/thing/q4440864/","name":"dimension","alternateNames":["Krasnoselskii genus","Krull dimension","Weld size","Leg size","Throat thickness","Root opening","Groove angle","Weld width","Weld reinforcement","fractal dimension","Lebesgue covering dimension","critical dimension"],"kind":"thing","status":"research-draft","version":"0.2.0-wave.2","language":"en","classifiers":{"family":"Thing Registry","category":"Cross-cutting context","entryKind":"thing","plane":"XCT","domain":["XCT.QLT"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"A mathematical property of a space or object giving the number of independent coordinates needed to specify a point, generalised to notions such as the dimension of a vector space, topological and fractal dimensions, the Krull dimension of a ring and other algebraic and analytic dimensions; the word also denotes measured sizes such as length, width and height and, in engineering, specified sizes such as weld leg and throat dimensions.","purpose":"Let an agent explain mathematical dimension in its various senses, compute or identify the dimension of a given object, separate the measurement sense, and support learning across levels.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Degrees of freedom","Many generalisations","Integer or fractional","Also a size measure"],"structure":{"bundles":[{"id":"define","name":"Define","description":"What dimension means.","layers":[{"id":"senses","name":"Senses","description":"Which sense.","findings":[{"id":"senses-finding","name":"Senses","description":"Senses.","questions":[{"text":"Is the mathematical dimension of a space, a measured size, a physical dimension in unit analysis or an engineering specification meant?","kind":"boundary"},{"text":"Which entry fits?","kind":"action"}]}]},{"id":"basic","name":"Basic","description":"Dimension of a space.","findings":[{"id":"basic-finding","name":"Basic","description":"Basic notion.","questions":[{"text":"What is the dimension of a vector space or manifold, and why is it well defined?","kind":"definition"},{"text":"How is the dimension of this object computed?","kind":"action"}]}]}]},{"id":"generalise","name":"Generalise","description":"Beyond the basics.","layers":[{"id":"topological","name":"Topological","description":"Topological and fractal.","findings":[{"id":"topological-finding","name":"Topological","description":"Topological and fractal.","questions":[{"text":"What are topological, Hausdorff and box-counting dimensions, and how can dimension be fractional?","kind":"definition"},{"text":"What is the dimension of a given fractal?","kind":"action"}]}]},{"id":"algebraic","name":"Algebraic","description":"Algebraic dimensions.","findings":[{"id":"algebraic-finding","name":"Algebraic","description":"Algebraic.","questions":[{"text":"What is the Krull dimension of a ring, and how does it relate to geometric dimension?","kind":"definition"},{"text":"Which other algebraic dimensions exist?","kind":"definition"}]}]}]},{"id":"apply","name":"Apply","description":"Uses.","layers":[{"id":"physics","name":"Physics","description":"Dimensions in physics.","findings":[{"id":"physics-finding","name":"Physics","description":"Physics.","questions":[{"text":"How is dimension used in physics, from spacetime to higher-dimensional theories, with speculative parts attributed?","kind":"provenance"},{"text":"What is the curse of dimensionality in data?","kind":"definition"}]}]},{"id":"engineering","name":"Engineering","description":"Engineering sizes.","findings":[{"id":"engineering-finding","name":"Engineering","description":"Engineering.","questions":[{"text":"What do weld dimensions such as leg size, throat thickness and root opening mean, and which standards specify them?","kind":"provenance"},{"text":"How are dimensions shown on drawings?","kind":"provenance"}]}]}]},{"id":"learn","name":"Learn","description":"Teaching.","layers":[{"id":"teach","name":"Teach","description":"Teaching dimension.","findings":[{"id":"teach-finding","name":"Teach","description":"Teaching.","questions":[{"text":"How can dimension be taught from coordinates to fractals?","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 the concept of dimension develop, from Euclid to Cantor, Hausdorff and beyond?","kind":"provenance"},{"text":"Which references are standard?","kind":"provenance"}]}]}]}]},"agentConduct":{"may":["Explain which notion of dimension is meant and compute it where it is well defined.","Check that measured dimensions are stated with units and tolerances."],"mustNot":["Mix up different notions of dimension, such as fractal and topological, without saying so.","Report measured sizes without units or in the wrong units.","Change dimensions on a drawing or specification it is not authorized to edit.","Present a contested or open dimension result as proven."],"requiresHuman":["Approving dimension changes on parts or structures that people depend on for safety."]},"ethics":{"considerations":["Wrong dimensions in engineering can make parts fail or not fit, with safety consequences.","Mathematical claims should be stated precisely so learners are not misled."],"affectedParties":["Students and researchers","Engineers and manufacturers","Users of built things"]},"owners":{"steward":"Nobody owns the concept; the author of a drawing or specification answers for its dimensions.","roles":[],"masterSystems":[]},"relations":[{"target":"Q3924032","type":"parent","note":"registry parent class"},{"target":"mathematical property","type":"related","note":"category"},{"target":"ordered pair","type":"related","note":"coordinates"},{"target":"homomorphism","type":"related","note":"linear maps and rank"},{"target":"intensive quantity","type":"related","note":"dimensional analysis contrast"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.dimension","Wikidata: Q4440864 (https://www.wikidata.org/wiki/Q4440864)"]},"properties":{"applicability":"not-applicable","items":[]},"recognition":{"applicability":"optional","items":["Number of independent coordinates","Generalised in many ways","A measured length is the everyday sense","Not physical; a number attached to a space or a measurement of size."]},"capabilities":{"applicability":"required","items":["explain notions of dimension","determine the dimension of a space or object","separate measurement and engineering senses","support learning"]},"hazards":{"applicability":"required","items":["Confusing senses of dimension","Assuming dimension is always an integer","Misreading engineering dimensions"]},"interfaces":{"applicability":"required","items":["Mathematical conventions","Engineering drawing and welding standards for sizes"]},"context":{"applicability":"required","items":["Degrees of freedom and measured sizes.","dimension of vector spaces","topological dimension","fractal and Hausdorff dimension","algebraic dimensions such as Krull dimension","measured dimensions and engineering sizes"]}},"sources":[{"title":"Wikidata item Q4440864: dimension","url":"https://www.wikidata.org/wiki/Q4440864","note":"identity and sense of the item"},{"title":"Wikipedia: Dimension","url":"https://en.wikipedia.org/wiki/Dimension","note":"general description of the item"}],"openQuestions":["Should each notion of dimension be a separate entry?","How should engineering standards be linked?","How should physical dimension analysis be linked?"],"resources":{"spec":"/models/things/publications/thing-q4440864/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q4440864/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-11T21:59:31Z","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":{"interaction.properties":"Plane XCT: no invented physical properties."},"score":1.0}}