{"paper":{"title":"Some remarks on the midrange crossing constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"\\'E. Czabarka, I. Singgih, L.A. Sz\\'ekely, Zhiyu Wang","submitted_at":"2019-06-30T11:28:54Z","abstract_excerpt":"We verify an upper bound of Pach and T\\'oth [Combinatorica 17(1997), 427-439, Discrete and Computational Geometry 36(2006), 527-552] on the midrange crossing constant. Details of their $\\frac{8}{9\\pi^2}$ upper bound have not been available. Our verification is different from their method and hinges on a result of Moon [J. Soc. Indust. Appl. Math. 13(1965), 506-510]. As Moon's result is optimal, we raise the question whether the midrange crossing constant is $\\frac{8}{9\\pi^2}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.00368","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"}