{"paper":{"title":"On Limits of Dense Packing of Equal Spheres in a Cube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CG","authors_text":"Milos Tatarevic","submitted_at":"2015-03-27T00:38:35Z","abstract_excerpt":"We examine packing of $n$ congruent spheres in a cube when $n$ is close but less than the number of spheres in a regular cubic close-packed (ccp) arrangement of $\\lceil p^{3}/2\\rceil$ spheres. For this family of packings, the previous best-known arrangements were usually derived from a ccp by omission of a certain number of spheres without changing the initial structure. In this paper, we show that better arrangements exist for all $n\\leq\\lceil p^{3}/2\\rceil-2$. We introduce an optimization method to reveal improvements of these packings, and present many new improvements for $n\\leq4629$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07933","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"}