{"paper":{"title":"Exact value of Tammes problem for N=10","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Masaharu Tanemura, Teruhisa Sugimoto","submitted_at":"2015-09-06T04:54:15Z","abstract_excerpt":"Let $C_{i}$ ($\\,i=1,\\ldots ,N\\,$) be the $i$-th open spherical cap of angular radius $r$ and let $M_{i}$ be its center under the condition that none of the spherical caps contains the center of another one in its interior. We consider the upper bound, $r_{N} $, (not the lower bound !) of $r$ of the case in which the whole spherical surface of a unit sphere is completely covered with $N$ congruent open spherical caps under the condition, sequentially for $i=2,\\ldots ,N-1\\,$, that $M_{i}$ is set on the perimeter of $C_{i-1}$, and that each area of the set $(\\cup _{\\nu =1}^{i-1}C_{\\nu })\\cap C_{i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01768","kind":"arxiv","version":2},"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"}