{"paper":{"title":"The curves not carried","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Saul Schleimer, Vaibhav Gadre","submitted_at":"2014-10-17T23:24:24Z","abstract_excerpt":"Suppose $\\tau$ is a train track on a surface $S$. Let $C(\\tau)$ be the set of isotopy classes of simple closed curves carried by $\\tau$. Masur and Minsky [2004] prove $C(\\tau)$ is quasi-convex inside the curve complex $C(S)$. We prove the complement, $C(S) - C(\\tau)$, is quasi-convex."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4886","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"}