{"paper":{"title":"Characterizing slopes for Legendrian knots","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"Chi Zhang, Youlin Li","submitted_at":"2026-08-06T14:22:26Z","abstract_excerpt":"We establish a criterion relating smooth and contact characterizing slopes under a uniqueness assumption. Let $L$ be a Legendrian representative of a knot $K\\subset S^3$ with standard contact structure, and assume that the isotopy class of $L$ is uniquely determined by its classical invariants: the Thurston--Bennequin invariant $tb(L)$ and the rotation number. Then, for any non-zero rational number $r$, if $r+tb(L)$ is a smooth characterizing slope for $K$, it becomes a contact characterizing slope for $L$. As applications, we study the characterizing slopes for Legendrian representatives of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.06079","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.06079/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}