{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.1-n-expansion","code":"thing-q951142","url":"https://ver.cy/models/thing/q951142/","name":"1/N expansion","alternateNames":[],"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.REL"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"A perturbative method in theoretical physics in which a theory with N components, colours or flavours is expanded in powers of 1/N, so that the limit of large N becomes tractable and corrections are organised by their order in 1/N; used in quantum chromodynamics, statistical mechanics, matrix models and the study of gauge and string dualities.","purpose":"Let an agent explain the 1/N expansion as a method, its main applications and limits, relay results with attribution to the literature, and route detailed calculations to specialist references.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Expansion parameter is the inverse number of components","Large N limit simplifies the theory","Organises Feynman diagrams by topology in gauge theories","Applies across field theory, statistical mechanics and matrix models"],"structure":{"bundles":[{"id":"idea","name":"Idea","description":"What the expansion is.","layers":[{"id":"definition","name":"Definition","description":"Definition.","findings":[{"id":"definition-finding","name":"Definition","description":"Definition.","questions":[{"text":"What is expanded in 1/N, and why does the large N limit simplify a theory?","kind":"definition"},{"text":"Is the question about the 1/N expansion or about ordinary perturbation theory?","kind":"boundary"}]}]},{"id":"organisation","name":"Organisation","description":"Diagram organisation.","findings":[{"id":"organisation-finding","name":"Organisation","description":"Organisation.","questions":[{"text":"How are diagrams organised by order in 1/N, including the planar limit in gauge theories?","kind":"definition"},{"text":"Which entry fits Feynman diagrams?","kind":"action"}]}]}]},{"id":"applications","name":"Applications","description":"Where it is used.","layers":[{"id":"field","name":"Field theory","description":"Gauge and vector models.","findings":[{"id":"field-finding","name":"Field","description":"Field.","questions":[{"text":"How is the expansion used in QCD and in O(N) models, with results attributed?","kind":"provenance"},{"text":"Which references are standard?","kind":"provenance"}]}]},{"id":"other","name":"Other","description":"Statistical mechanics and matrices.","findings":[{"id":"other-finding","name":"Other","description":"Other.","questions":[{"text":"How is it used in statistical mechanics, random matrices and holography?","kind":"provenance"},{"text":"Which entry fits a specific application?","kind":"action"}]}]}]},{"id":"limits","name":"Limits","description":"Validity and corrections.","layers":[{"id":"validity","name":"Validity","description":"When it works.","findings":[{"id":"validity-finding","name":"Validity","description":"Validity.","questions":[{"text":"When is the expansion reliable, and how large are corrections for physical N?","kind":"measurement"},{"text":"What is proven versus conjectured?","kind":"boundary"}]}]},{"id":"corrections","name":"Corrections","description":"Higher orders.","findings":[{"id":"corrections-finding","name":"Corrections","description":"Corrections.","questions":[{"text":"How are higher-order corrections computed and resummed?","kind":"provenance"},{"text":"Which entry fits resummation methods?","kind":"action"}]}]}]},{"id":"learn","name":"Learn","description":"History and teaching.","layers":[{"id":"history","name":"History","description":"History.","findings":[{"id":"history-finding","name":"History","description":"History.","questions":[{"text":"How did the method develop from Stanley and t Hooft onward?","kind":"provenance"},{"text":"Which entry fits a specific physicist?","kind":"action"}]}]},{"id":"teach","name":"Teach","description":"Teaching.","findings":[{"id":"teach-finding","name":"Teach","description":"Teaching.","questions":[{"text":"How is the expansion taught in graduate courses, and which texts are standard?","kind":"provenance"},{"text":"Which prerequisites are needed?","kind":"boundary"}]}]}]}]},"agentConduct":{"may":["Explain the 1/N expansion and where the large N limit simplifies a theory.","Report results from published work with their stated assumptions."],"mustNot":["Apply a large N result to small N without noting the size of corrections.","Confuse vector and matrix large N behaviour.","Present a conjectured duality or extrapolation as proven.","Attribute results to researchers who did not obtain them."],"requiresHuman":["Stating that a large N result holds for a physical theory with small N."]},"ethics":{"considerations":["Overstated results mislead students and other researchers.","Credit for results matters to researchers' careers."],"affectedParties":["Researchers and students","Readers of popular science"]},"owners":{"steward":"Nobody owns the method; it belongs to the physics community.","roles":[],"masterSystems":[]},"relations":[{"target":"Q3511310","type":"parent","note":"registry parent class"},{"target":"perturbative series","type":"related","note":"an expansion method"},{"target":"quantum chromodynamics","type":"related","note":"a main application"},{"target":"mean-field theory","type":"related","note":"often the leading order for vector models"},{"target":"AdS/CFT correspondence","type":"related","note":"large N is essential to the duality"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.1-n-expansion","Wikidata: Q951142 (https://www.wikidata.org/wiki/Q951142)"]},"properties":{"applicability":"not-applicable","items":[]},"recognition":{"applicability":"optional","items":["Expansion parameter 1/N with N the number of components or colours","Leading order often planar or mean-field","Ordinary coupling-constant perturbation theory is a different expansion","Not visible; a series in powers of 1/N in equations."]},"capabilities":{"applicability":"required","items":["explain the idea of large N limits","describe main applications in field theory and statistical mechanics","explain planar diagrams and topological organisation","point to standard references"]},"hazards":{"applicability":"required","items":["Applying large N results to small N without checking corrections","Confusing vector and matrix large N behaviour","Presenting conjectured dualities as proven"]},"interfaces":{"applicability":"required","items":["No regulation; conventions follow the physics literature"]},"context":{"applicability":"required","items":["Making strongly coupled or many-component theories calculable.","large N vector models such as the O(N) model","large N gauge theories and the planar limit","matrix models and random matrices","large N in condensed matter and spin models","holographic dualities at large N"]}},"sources":[{"title":"Wikidata item Q951142: 1/N expansion","url":"https://www.wikidata.org/wiki/Q951142","note":"identity and sense of the item"},{"title":"Wikipedia: 1/N expansion","url":"https://en.wikipedia.org/wiki/1/N_expansion","note":"general description of the item"}],"openQuestions":["Should vector and matrix large N be separate entries?","How should standard reviews be linked?","How should the status of conjectures be recorded?"],"resources":{"spec":"/models/things/publications/thing-q951142/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q951142/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-12T19:51:39Z","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 2026-10-06T19:52:03+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}}