{"paper":{"title":"Integrable discrete nets in Grassmannians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.SI"],"primary_cat":"math.DG","authors_text":"Alexander I. Bobenko, Vsevolod E. Adler, Yuri B. Suris","submitted_at":"2008-12-30T19:43:04Z","abstract_excerpt":"We consider discrete nets in Grassmannians $\\mathbb{G}^d_r$ which generalize Q-nets (maps $\\mathbb{Z}^N\\to\\mathbb{P}^d$ with planar elementary quadrilaterals) and Darboux nets ($\\mathbb{P}^d$-valued maps defined on the edges of $\\mathbb{Z}^N$ such that quadruples of points corresponding to elementary squares are all collinear). We give a geometric proof of integrability (multidimensional consistency) of these novel nets, and show that they are analytically described by the noncommutative discrete Darboux system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.5102","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}