{"paper":{"title":"Strict Periodic Extreme Lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.MG","authors_text":"Achill Sch\\\"urmann","submitted_at":"2012-11-23T16:04:22Z","abstract_excerpt":"A lattice is called periodic extreme if it cannot locally be modified to yield a better periodic sphere packing. It is called strict periodic extreme if its sphere packing density is an isolated local optimum among periodic point sets. In this note we show that a lattice is periodic extreme if and only if it is extreme, that is, locally optimal among lattices. Moreover, we show that a lattice is strict periodic extreme if and only if it is extreme and non-floating."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5534","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":""},"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"}