{"paper":{"title":"A simplex-based measure of symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.MG","authors_text":"Amir Yehudayoff, Egor Bakaev","submitted_at":"2026-07-04T10:50:29Z","abstract_excerpt":"For compact convex sets $L,K \\subset \\mathbb{R}^n$, denote by $\\lambda_K(L)$ the smallest size of a homothet of $K$ that contains $L$. We define a measure of symmetry based on the $n$-simplex $\\Delta = \\Delta^n \\subset \\mathbb{R}^n$ as the ratio \\[ \\rho_\\Delta(L):=\\frac{\\lambda_{-\\Delta}(L)}{\\lambda_{\\Delta}(L)}. \\] We study this measure and deduce the following results:\n  (1) The classical Minkowski measure of symmetry $m^*(L)$ can be defined as an affine-invariant version of $\\rho_\\Delta(L)$.\n  (2) We improve the stability analysis for the Minkowski measure of symmetry; if $m^*(L)\\ge n-\\vare"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.03815","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/2607.03815/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"}