{"paper":{"title":"A Sharp Reverse Minkowski Inequality for the Gaussian Mass of Integral Unimodular Lattices Through Rank $32$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MG"],"primary_cat":"math.NT","authors_text":"Scott Duke Kominers","submitted_at":"2026-05-31T16:55:52Z","abstract_excerpt":"The integer lattice $\\mathbb{Z}^n$ is conjectured to maximize the Gaussian mass $\\Theta_L(t)=\\sum_{x\\in L}e^{-t\\|x\\|^2}$ over the set of stable lattices in $\\mathbb{R}^n$, for every $t>0$. We prove this sharp inequality for every integral unimodular lattice $L$ of rank $n\\leq 32$, with equality only at $L\\cong\\mathbb{Z}^n$, and furthermore obtain the strict inequality for every even unimodular lattice of rank $40$. The proof does not use the classification of unimodular lattices in these ranks; rather, it parametrizes integral unimodular theta series as polynomials in the modular function $u=\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01347","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/2606.01347/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"}