{"paper":{"title":"Invariants of the Colored Braid Groupoid","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Illia E. Rohozhkin","submitted_at":"2026-06-18T16:52:40Z","abstract_excerpt":"In this paper, a braid is regarded as a dynamical system of points in the plane. The states of this dynamical system are given by Delaunay triangulations. This construction makes it possible to define an abstract groupoid $\\overset{{abc}}{\\mathcal{G}^{4}_{n+3}}$, which gives a representation of the colored braid groupoid $\\text{ColB}(n)$. We define homomorphisms ${f}_{n+3}:\\overset{{abc}}{\\mathcal{G}^{4}_{n+3}} \\rightarrow\\text{GL}_{2n+1}(\\mathbb{Q})$ and ${f}'_{n+3}:\\overset{{abc}}{\\mathcal{G}^{4}_{n+3}} \\rightarrow\\text{GL}_{2n+1}(\\mathbb{C})$, and describe an algorithm for computing the res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.20473","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.20473/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}