{"paper":{"title":"Racah matrices and hidden integrability in evolution of knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.QA"],"primary_cat":"hep-th","authors_text":"A. Mironov, A. Morozov, An. Morozov, A. Sleptsov","submitted_at":"2016-05-16T19:44:44Z","abstract_excerpt":"We construct a general procedure to extract the exclusive Racah matrices S and \\bar S from the inclusive 3-strand mixing matrices by the evolution method and apply it to the first simple representations R =[1], [2], [3] and [2,2]. The matrices S and \\bar S relate respectively the maps (R\\otimes R)\\otimes \\bar R\\longrightarrow R with R\\otimes (R \\otimes \\bar R) \\longrightarrow R and (R\\otimes \\bar R) \\otimes R \\longrightarrow R with R\\otimes (\\bar R \\otimes R) \\longrightarrow R. They are building blocks for the colored HOMFLY polynomials of arbitrary arborescent (double fat) knots. Remarkably, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04881","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"}