{"paper":{"title":"A Trichotomy for Rectangles Inscribed in Jordan Loops","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Richard Evan Schwartz","submitted_at":"2018-04-02T21:44:39Z","abstract_excerpt":"Let g be an arbitrary Jordan loop and let G denote the space of rectangles R which are inscribed in g in such a way that the cyclic order of the vertices of R is the same whether it is induced by R or by g. We prove that G contains a connected set S satisfying one of three properties: 1. S consists of rectangles of uniformly large area, including a square, and every point of g is the vertex of a rectangle in S. 2. S consists of rectangles having all possible aspect ratios, and all but at most 4 points of g are vertices of rectangles in S. 3. S contains rectangles of every sufficiently small di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00740","kind":"arxiv","version":4},"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"}