{"paper":{"title":"Stochastically evolving ellipsoids with symmetries","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT","math.PR"],"primary_cat":"math.MG","authors_text":"Elisha B. Abuya, Nihar Gargava, Yufei Zhao","submitted_at":"2026-06-03T17:07:07Z","abstract_excerpt":"We prove that there is a universal constant $c > 0$ such that, along an infinite sequence of dimensions $N$, there are lattice sphere packings in $\\mathbb{R}^N$ of density at least $c N^2 \\log\\log N \\, 2^{-N}$, improving the previous best bound due to Klartag by a $\\log\\log N$ factor. The proof follows Klartag's stochastic ellipsoid evolution process, subject to the cyclotomic symmetries introduced by Venkatesh."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05105","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/2606.05105/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"}