{"paper":{"title":"Polarization optimality of equally spaced points on the circle for discrete potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A. P. Kendall, D. P. Hardin, E. B. Saff","submitted_at":"2012-08-26T23:06:03Z","abstract_excerpt":"We prove a conjecture of Ambrus, Ball and Erd\\'{e}lyi that equally spaced points maximize the minimum of discrete potentials on the unit circle whenever the potential is of the form \\sum_{k=1}^n f(d(z,z_k)), where $f:[0,\\pi]\\to [0,\\infty]$ is non-increasing and strictly convex and $d(z,w)$ denotes the geodesic distance between $z$ and $w$ on the circle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5261","kind":"arxiv","version":3},"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"}