{"paper":{"title":"The Six Cylinders Problem: $\\mathbb{D}_{3}$-symmetry Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Oleg Ogievetsky, Senya Shlosman","submitted_at":"2018-05-24T18:04:25Z","abstract_excerpt":"Motivated by a question of W. Kuperberg, we study the 18-dimensional manifold of configurations of 6 non-intersecting infinite cylinders of radius $r,$ all touching the unit ball in $\\mathbb{R}^{3}.$ We find a configuration with \\[ r=\\frac{1}{8}\\left( 3+\\sqrt{33}\\right) \\approx1.093070331\\ .\\] We believe that this value is the maximal possible."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09833","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"}