{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.transformation-q12202238","code":"thing-q12202238","url":"https://ver.cy/models/thing/q12202238/","name":"transformation","alternateNames":["dependency preserving decomposition","lossless decomposition","sequence transform","inverse fast Fourier transformation","sequence transformation","homography","centering","projective transformation","Operational transformation","discrete transform","data transformation","polynomial transformation"],"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":"In mathematics, a transformation is a function from a set to itself, assigning each element of that set exactly one element of the same set; particular transformations may have additional geometric or algebraic properties, and an inverse transform is a mathematical mapping distinct from an algorithm used to compute it.","purpose":"Let an agent explain transformations in mathematics, relay kinds and properties from mathematics sources, describe the named transformations, flag the database aliases, and distinguish transformations from functions generally, transforms as operators, decompositions in database theory and transformation in other senses such as biology or business.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Maps structures","Geometric and analytic kinds","Composable","Aliases include database terms"],"structure":{"bundles":[{"id":"understand","name":"Understand","description":"What a transformation is.","layers":[{"id":"definition","name":"Definition","description":"Definition.","findings":[{"id":"definition-finding","name":"Definition","description":"Definition.","questions":[{"text":"What is a transformation, and how does it differ from functions, transforms and database decompositions?","kind":"definition"},{"text":"Is the question about geometry, analysis, signal processing or databases?","kind":"boundary"}]}]},{"id":"named","name":"Named","description":"Named transformations.","findings":[{"id":"named-finding","name":"Named","description":"Named.","questions":[{"text":"What are homographies, sequence transformations, the inverse FFT and lossless and dependency preserving decompositions?","kind":"definition"},{"text":"Which entry fits the specific term?","kind":"action"}]}]}]},{"id":"geometry","name":"Geometry","description":"Geometric transformations.","layers":[{"id":"kinds","name":"Kinds","description":"Kinds.","findings":[{"id":"kinds-finding","name":"Kinds","description":"Kinds.","questions":[{"text":"How do translations, rotations, affine and projective transformations differ?","kind":"provenance"},{"text":"Which references are standard?","kind":"provenance"}]}]},{"id":"groups","name":"Groups","description":"Transformation groups.","findings":[{"id":"groups-finding","name":"Groups","description":"Groups.","questions":[{"text":"How did Klein s Erlangen program classify geometries by transformation groups?","kind":"provenance"},{"text":"Which sources are cited?","kind":"provenance"}]}]}]},{"id":"analysis","name":"Analysis","description":"Transforms and sequences.","layers":[{"id":"fourier","name":"Fourier","description":"Fourier.","findings":[{"id":"fourier-finding","name":"Fourier","description":"Fourier.","questions":[{"text":"How do the Fourier transform and FFT work in signal processing?","kind":"provenance"},{"text":"Which entry fits fast Fourier transform?","kind":"action"}]}]},{"id":"sequences","name":"Sequences","description":"Series acceleration.","findings":[{"id":"sequences-finding","name":"Sequences","description":"Sequences.","questions":[{"text":"How do sequence transformations such as Aitken s delta-squared accelerate convergence?","kind":"provenance"},{"text":"Which entry fits series acceleration?","kind":"action"}]}]}]},{"id":"context","name":"Context","description":"Other fields.","layers":[{"id":"databases","name":"Databases","description":"Decompositions.","findings":[{"id":"databases-finding","name":"Databases","description":"Databases.","questions":[{"text":"What are lossless and dependency preserving decompositions in database normalisation?","kind":"provenance"},{"text":"Which entry fits database normalization?","kind":"action"}]}]},{"id":"vision","name":"Vision","description":"Computer vision.","findings":[{"id":"vision-finding","name":"Vision","description":"Vision.","questions":[{"text":"How are homographies used in image stitching?","kind":"provenance"},{"text":"Which entry fits image stitching?","kind":"action"}]}]}]}]},"agentConduct":{"may":["Explain transformations in mathematics, such as geometric and projective ones, with examples.","Apply transformations to data the agent is authorized to process."],"mustNot":["Confuse a transformation with a transform such as the Fourier transform without saying so.","Apply transformations to data that silently distort it or lose information.","Mix senses from database theory or other fields with the mathematical one."],"requiresHuman":["Applying transformations to datasets that feed decisions about people."]},"ethics":{"considerations":["Transformed data can mislead if the transformation is hidden.","Clear mathematics teaching helps students across sciences."],"affectedParties":["Students","Users of transformed data","Analysts"]},"owners":{"steward":"Nobody owns the concept; it belongs to mathematics as shared knowledge.","roles":[],"masterSystems":[]},"relations":[{"target":"Q11348","type":"parent","note":"registry parent class"},{"target":"Q24034552","type":"parent","note":"registry parent class"},{"target":"function","type":"related","note":"in registry terms"},{"target":"homography","type":"related"},{"target":"Fourier transform","type":"related"},{"target":"database normalization","type":"related","note":"for misfiled aliases"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.transformation-q12202238","Wikidata: Q12202238 (https://www.wikidata.org/wiki/Q12202238)"]},"properties":{"applicability":"not-applicable","items":["fast Fourier transform: O(n log n) complexity","homography: 3x3 matrix up to scale in the plane note","registry parents: function, mathematical concept note"]},"recognition":{"applicability":"optional","items":["Mapping of a set or space","Homography, sequence transformation, inverse fast Fourier transformation, dependency preserving decomposition, lossless decomposition","Functions are the general concept; transforms are operators on functions; database decompositions split relations","Not a visible object; seen in diagrams of moved, scaled or distorted shapes."]},"capabilities":{"applicability":"required","items":["explain the concept","relay kinds and properties","describe named transformations","distinguish related senses"]},"hazards":{"applicability":"required","items":["Confusing transformation and transform","Registry aliases from database theory","Mixing mathematical and everyday senses"]},"interfaces":{"applicability":"required","items":["No regulation"]},"context":{"applicability":"required","items":["Not applicable; a mathematical concept.","geometric transformations such as isometries and homographies","linear transformations","integral transforms such as Fourier","sequence transformations","database decompositions as misfiled terms"]}},"sources":[{"title":"Wikidata item Q12202238: transformation","url":"https://www.wikidata.org/wiki/Q12202238","note":"identity and sense of the item"},{"title":"Wikipedia: Transformation (function)","url":"https://en.wikipedia.org/wiki/Transformation_%28function%29","note":"general description of the item"}],"openQuestions":["Should homography and sequence transformation be separate entries?","How should mathematics sources be linked?","The registry aliases dependency preserving decomposition and lossless decomposition should be moved to database normalization"],"resources":{"spec":"/models/things/publications/thing-q12202238/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q12202238/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-13T19:38:08Z","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 2026-10-08T18:54:35+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}}