{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.mathematics","code":"thing-q395","url":"https://ver.cy/models/thing/q395/","name":"mathematics","alternateNames":["systems science","informal mathematics","mathematical geography","ecosystemology","gnomonics","combinatorial topology","mathematical programming","Māori mathematics","computational mathematics","calendrical mathematics","number theory","Mathematics-Economics"],"kind":"thing","status":"published","version":"0.2.0-wave.1","language":"en","classifiers":{"family":"Thing Registry","category":"Information and virtual systems","entryKind":"thing","plane":"INF","domain":["INF.KNW"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"The formal science of quantity, structure, space and change, which proves results from axioms by logical deduction and is used throughout science and engineering.","purpose":"Let an agent treat mathematics as a discipline with fields, proofs and conventions, and state mathematical claims with their assumptions.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Truth by proof from axioms","Pure and applied branches","Conventions and notation vary","Results are cumulative and rarely overturned, unlike empirical science"],"structure":{"bundles":[{"id":"fields","name":"Fields","description":"Branches.","layers":[{"id":"branch","name":"Branch","description":"MSC classification.","findings":[{"id":"branch-finding","name":"Branch","description":"The branch.","questions":[{"text":"Which branch of mathematics is this?","kind":"definition"},{"text":"Which MSC code applies?","kind":"provenance"}]}]},{"id":"objects","name":"Objects","description":"What is studied.","findings":[{"id":"objects-finding","name":"Objects","description":"Mathematical objects.","questions":[{"text":"Which objects does it concern?","kind":"definition"},{"text":"How are they defined?","kind":"definition"}]}]}]},{"id":"claims","name":"Claims","description":"Theorems and conjectures.","layers":[{"id":"status","name":"Status","description":"Proven or conjectured.","findings":[{"id":"status-finding","name":"Status","description":"Proof status.","questions":[{"text":"Is this result proven, and where?","kind":"provenance"},{"text":"Is it a conjecture?","kind":"boundary"}]}]},{"id":"assumptions","name":"Assumptions","description":"Axioms and hypotheses.","findings":[{"id":"assumptions-finding","name":"Assumptions","description":"Assumptions required.","questions":[{"text":"Which assumptions does the result need?","kind":"definition"},{"text":"What fails without them?","kind":"boundary"}]}]}]},{"id":"applications","name":"Applications","description":"Using mathematics.","layers":[{"id":"models","name":"Models","description":"Mathematical models.","findings":[{"id":"models-finding","name":"Model","description":"The model used.","questions":[{"text":"Which mathematical model is used, and why?","kind":"definition"},{"text":"How well does it fit the data?","kind":"measurement"}]}]},{"id":"computation","name":"Computation","description":"Numerics.","findings":[{"id":"computation-finding","name":"Computation","description":"Numerical methods.","questions":[{"text":"Which numerical methods are used?","kind":"definition"},{"text":"What are their error bounds?","kind":"measurement"}]}]}]},{"id":"learning","name":"Learning","description":"Teaching mathematics.","layers":[{"id":"explanation","name":"Explanation","description":"Clear reasoning.","findings":[{"id":"explanation-finding","name":"Explanation","description":"How to explain.","questions":[{"text":"How can this be explained step by step?","kind":"action"},{"text":"What misconceptions are common?","kind":"boundary"}]}]},{"id":"verification","name":"Verification","description":"Checking work.","findings":[{"id":"verification-finding","name":"Verification","description":"How to check.","questions":[{"text":"How can the result be checked?","kind":"action"},{"text":"Should a proof assistant be used?","kind":"definition"}]}]}]}]},"agentConduct":{"may":["Prove results or cite proofs, stating assumptions.","Check calculations and flag unverified steps."],"mustNot":["Present an unverified proof as established.","Hide assumptions behind results.","Apply a model outside its valid range without saying so."],"requiresHuman":["Relying on a mathematical model in decisions about people's safety or rights."]},"ethics":{"considerations":["Mathematical models used in decisions can encode bias behind a show of objectivity."],"affectedParties":["Users of models","Students"]},"owners":{"steward":"Nobody owns mathematics; it is held in common.","roles":[],"masterSystems":[]},"relations":[{"target":"Q7991","type":"parent","note":"registry parent class"},{"target":"integer, sequence, series","type":"contains","note":"objects of study"},{"target":"science and engineering","type":"related","note":"applications"},{"target":"formal science","type":"related","note":"discipline"},{"target":"arithmetic","type":"related","note":"a small part"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.mathematics","Wikidata: Q395 (https://www.wikidata.org/wiki/Q395)","MSC 2020 code: two digits, letter, two digits Mathematics Subject Classification"]},"properties":{"applicability":"not-applicable","items":[]},"recognition":{"applicability":"optional","items":["Notation and proofs","Field labels in the Mathematics Subject Classification","Applied fields such as mathematical programming","Symbols, equations, proofs, diagrams and code."]},"capabilities":{"applicability":"required","items":["prove theorems","model and compute","teach and learn it","verify proofs, including by computer"]},"hazards":{"applicability":"required","items":["Unstated assumptions","Errors in unverified proofs","Misapplied models"]},"interfaces":{"applicability":"required","items":["ISO 80000-2 mathematical signs and symbols"]},"context":{"applicability":"required","items":["Reasoning precisely, modelling the world and computing.","algebra","analysis","geometry and topology","number theory","probability and statistics","discrete mathematics","applied mathematics and optimisation"]}},"sources":[{"title":"Wikidata item Q395: mathematics","url":"https://www.wikidata.org/wiki/Q395","note":"identity and sense of the item"},{"title":"Wikipedia: Mathematics","url":"https://en.wikipedia.org/wiki/Mathematics","note":"general description of the item"}],"openQuestions":["Should fields be separate entries by MSC?","How should agents distinguish proven results from conjectures?","The registry entry has merged aliases such as ecosystemology; should they be split off?"],"resources":{"spec":"/models/things/publications/thing-q395/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q395/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-11T05:15:23Z","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 2026-10-06T19:51:59+00:00: completeness 1.00; sense: Wikidata description; 2 live sources; review by codex: pass","interaction.properties":"Plane INF: no invented physical properties."},"score":1.0}}