{"paper":{"title":"Knot projections with a single multi-crossing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Alex Tong Lin, Benjamin DeMeo, Colin Adams, Farrah Yhee, Michael Landry, MurphyKate Montee, Saraswathi Venkatesh, Seojung Park, Thomas Crawford","submitted_at":"2012-08-28T18:46:52Z","abstract_excerpt":"Introduced recently, an n-crossing is a singular point in a projection of a link at which n strands cross such that each strand travels straight through the crossing. We introduce the notion of an \\\"ubercrossing projection, a knot projection with a single n-crossing. Such a projection is necessarily composed of a collection of loops emanating from the crossing. We prove the surprising fact that all knots have a special type of \\\"ubercrossing projection, which we call a petal projection, in which no loops contain any others. The rigidity of this form allows all the information about the knot to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5742","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"}