{"paper":{"title":"On Uniform Connectivity of Algebraic Matrix Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.OA"],"primary_cat":"math.NA","authors_text":"Fredy Vides","submitted_at":"2018-02-05T03:16:48Z","abstract_excerpt":"In this document we study the uniform local path connectivity of sets of $m$-tuples of pairwise commuting normal matrices with some additional constraints.\n  More specifically, given given $\\varepsilon>0$, a fixed metric $\\eth$ in ${M_n(\\mathbb{C})}^m$ induced by the operator norm $\\|\\cdot\\|$, any collection of $r$ non-constant multivariable polynomials $p_1(x_1,\\ldots,x_m),\\ldots,p_r(x_1,\\ldots,x_m)$ over $\\mathbb{C}$ with finite zero set $\\mathbf{Z}(p_1,\\ldots,p_r)\\subset \\mathbb{C}^m$, and any $m$-tuple $\\mathbf{X}=(X_1,\\ldots,X_m)$ in the set $\\mathbb{ZD}_n^m(p_1,\\ldots,p_r)\\subseteq M_n^m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01249","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/1802.01249/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"}