{"paper":{"title":"Bounds on \\\"{U}bercrossing and Petal Numbers for Knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ashley Weber, Colin Adams, Daniel Irvine, Daniel Vitek, Jesse Freeman, Orsola Capovilla-Searle, Samantha Petti, Sicong Zhang","submitted_at":"2013-11-03T20:55:56Z","abstract_excerpt":"An $n$-crossing is a point in the projection of a knot where $n$ strands cross so that each strand bisects the crossing. An \\\"ubercrossing projection has a single $n$-crossing and a petal projection has a single $n$-crossing such that there are no loops nested within others. The \\\"ubercrossing number, $\\text{\\\"u}(K)$, is the smallest $n$ for which we can represent a knot $K$ with a single $n$-crossing. The petal number is the number of loops in the minimal petal projection. In this paper, we relate the \\\"{u}bercrossing number and petal number to well-known invariants such as crossing number, b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0526","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"}