{"paper":{"title":"On the horseshoe conjecture for maximal distance minimizers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Danila Cherkashin, Yana Teplitskaya","submitted_at":"2015-11-03T18:42:30Z","abstract_excerpt":"We study the properties of sets $\\Sigma$ having the minimal length (one-dimensional Hausdorff measure) over the class of closed connected sets $\\Sigma \\subset \\mathbb{R}^2$ satisfying the inequality $\\mbox{max}_{y \\in M} \\mbox{dist}(y,\\Sigma) \\leq r$ for a given compact set $M \\subset \\mathbb{R}^2$ and some given $r > 0$. Such sets can be considered shortest possible pipelines arriving at a distance at most $r$ to every point of $M$ which in this case is considered as the set of customers of the pipeline.\n  We prove the conjecture of Miranda, Paolini and Stepanov about the set of minimizers fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01026","kind":"arxiv","version":3},"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"}