{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.real-valued-function","code":"thing-q5189500","url":"https://ver.cy/models/thing/q5189500/","name":"real-valued function","alternateNames":["real-valued function on a real interval","real-valued function of a real variable","quasimorphism","quasiconvex function","harmonic index of a graph","radial basis function","integer-valued function","pseudo-absolute value","power curve","Entanglement measure","Lorentzian function","atomic function"],"kind":"thing","status":"published","version":"0.2.0-wave.3","language":"en","classifiers":{"family":"Thing Registry","category":"Cross-cutting context","entryKind":"thing","plane":"XCT","domain":["XCT.QLT"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"A function whose values are real numbers, most commonly a real-valued function of a real variable defined on an interval or subset of the real line, the central object of calculus and real analysis, but also functions from other domains to the reals such as quasimorphisms on groups, quasiconvex functions in optimisation, radial basis functions in approximation and graph invariants such as the harmonic index; real-valued functions are studied for continuity, differentiability, integrability and convexity.","purpose":"Let an agent define real-valued functions, relay their main properties and classes from analysis references, describe applications in optimisation and approximation, and distinguish them from complex-valued and vector-valued functions.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Real codomain","Order structure of values","Calculus properties","Many special classes"],"structure":{"bundles":[{"id":"define","name":"Define","description":"Definition.","layers":[{"id":"definition","name":"Definition","description":"Definition.","findings":[{"id":"definition-finding","name":"Definition","description":"Definition.","questions":[{"text":"What is a real-valued function, and how does the domain vary?","kind":"definition"},{"text":"Is the function real-valued, complex-valued or vector-valued?","kind":"boundary"}]}]},{"id":"properties","name":"Properties","description":"Properties.","findings":[{"id":"properties-finding","name":"Properties","description":"Properties.","questions":[{"text":"What are continuity, differentiability, integrability, monotonicity and convexity?","kind":"definition"},{"text":"Which entry fits the specific property?","kind":"action"}]}]}]},{"id":"classes","name":"Classes","description":"Special classes.","layers":[{"id":"optimisation","name":"Optimisation","description":"Convex and quasiconvex.","findings":[{"id":"optimisation-finding","name":"Optimisation","description":"Optimisation.","questions":[{"text":"What are convex and quasiconvex functions, and why do they matter in optimisation?","kind":"provenance"},{"text":"Which entry fits quasiconvex function?","kind":"action"}]}]},{"id":"other","name":"Other","description":"Radial basis and quasimorphisms.","findings":[{"id":"other-finding","name":"Other","description":"Other.","questions":[{"text":"What are radial basis functions and quasimorphisms, and where are they used?","kind":"provenance"},{"text":"Which references are standard?","kind":"provenance"}]}]}]},{"id":"apply","name":"Apply","description":"Applications.","layers":[{"id":"modelling","name":"Modelling","description":"Modelling.","findings":[{"id":"modelling-finding","name":"Modelling","description":"Modelling.","questions":[{"text":"How are real-valued functions used to model quantities in science and economics?","kind":"provenance"},{"text":"Which sources are cited?","kind":"provenance"}]}]},{"id":"approximation","name":"Approximation","description":"Approximation and computation.","findings":[{"id":"approximation-finding","name":"Approximation","description":"Approximation.","questions":[{"text":"How are real functions approximated and computed numerically?","kind":"provenance"},{"text":"Which entry fits numerical analysis?","kind":"action"}]}]}]},{"id":"context","name":"Context","description":"Foundations and history.","layers":[{"id":"foundations","name":"Foundations","description":"Foundations.","findings":[{"id":"foundations-finding","name":"Foundations","description":"Foundations.","questions":[{"text":"How does the construction of the real numbers underpin real-valued functions?","kind":"provenance"},{"text":"Which entry fits real number?","kind":"action"}]}]},{"id":"history","name":"History","description":"History.","findings":[{"id":"history-finding","name":"History","description":"History.","questions":[{"text":"How did the modern function concept develop from Euler to Dirichlet and Weierstrass?","kind":"provenance"},{"text":"Which entry fits the history of analysis?","kind":"action"}]}]}]}]},"agentConduct":{"may":["Define, evaluate, plot and analyze real-valued functions.","Check domains, continuity and limits in calculations it is asked to verify."],"mustNot":["Claim properties of a function, such as continuity or boundedness, without proof or check.","Report results from floating point evaluation as exact real values without noting rounding.","Present copied proofs or solutions as a student's own work for graded assessment."],"requiresHuman":["Using a model function to make decisions that affect people, such as pricing or risk scores."]},"ethics":{"considerations":["Functions used in models can encode unfair assumptions that look neutral because they are mathematical.","Academic honesty depends on agents not doing graded work for students."],"affectedParties":["Students and teachers","People scored by mathematical models"]},"owners":{"steward":"Nobody owns the concept; it belongs to shared mathematical knowledge.","roles":[],"masterSystems":[]},"relations":[{"target":"Q11893837","type":"parent","note":"registry parent class"},{"target":"scalar function","type":"related","note":"in registry terms"},{"target":"real analysis","type":"related","note":"the field"},{"target":"complex-valued function","type":"related","note":"with complex codomain"},{"target":"continuous function","type":"related","note":"as a major class"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.real-valued-function","Wikidata: Q5189500 (https://www.wikidata.org/wiki/Q5189500)"]},"properties":{"applicability":"not-applicable","items":[]},"recognition":{"applicability":"optional","items":["Function with real number values","Functions of a real variable, quasiconvex, radial basis, quasimorphisms","Complex-valued and vector-valued functions have other codomains","A graph in the plane for functions of one real variable."]},"capabilities":{"applicability":"required","items":["define and classify","relay properties","describe applications","distinguish from other function types"]},"hazards":{"applicability":"required","items":["Confusing domain and codomain conditions","Assuming continuity or differentiability","Conflating unrelated special classes"]},"interfaces":{"applicability":"required","items":["No regulation; mathematical conventions"]},"context":{"applicability":"required","items":["Not applicable; a mathematical object.","real-valued functions of a real variable on intervals","continuous, differentiable and integrable functions","convex and quasiconvex functions","radial basis functions","quasimorphisms on groups","real-valued graph invariants such as the harmonic index","real-valued functions on measure spaces"]}},"sources":[{"title":"Wikidata item Q5189500: real-valued function","url":"https://www.wikidata.org/wiki/Q5189500","note":"identity and sense of the item"},{"title":"Wikipedia: Real-valued function","url":"https://en.wikipedia.org/wiki/Real-valued_function","note":"general description of the item"}],"openQuestions":["Should function of a real variable be the primary linked entry?","How should analysis references be linked?","The registry entry has merged aliases naming unrelated special classes; should they be split off?"],"resources":{"spec":"/models/things/publications/thing-q5189500/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q5189500/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-13T01:23:35Z","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}}