{"paper":{"title":"Mesh ratios for best-packing and limits of minimal energy configurations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A. V. Bondarenko, D. P. Hardin, E. B. Saff","submitted_at":"2012-12-26T16:51:54Z","abstract_excerpt":"For $N$-point best-packing configurations $\\omega_N$ on a compact metric space $(A,\\rho)$, we obtain estimates for the mesh-separation ratio $\\gamma(\\omega_N,A)$, which is the quotient of the covering radius of $\\omega_N$ relative to $A$ and the minimum pairwise distance between points in $\\omega_N$. For best-packing configurations $\\omega_N$ that arise as limits of minimal Riesz $s$-energy configurations as $s\\to \\infty$, we prove that $\\gamma(\\omega_N,A)\\le 1$ and this bound can be attained even for the sphere. In the particular case when N=5 on $S^2$ with $\\rho$ the Euclidean metric, we pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6211","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"}