{"paper":{"title":"Finite-sheeted Cauchy operator at rational corners","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Louis Shuo Wang","submitted_at":"2026-06-10T22:13:21Z","abstract_excerpt":"We study Cauchy singular integral operators on planar wedges whose opening angle is a rational multiple of $\\pi$. For $\\theta=p\\pi/q$, the covering $w=\\zeta^q$ yields an exact finite-sheeted factorization of the wedge Cauchy transform into $2q$ interval Cauchy transforms with explicit algebraic recombination coefficients. The factorization is formulated on weighted conormal H\\\"older spaces. We prove that the lifting operator preserves conormal order, lowers the H\\\"older exponent from $\\beta$ to $\\beta/q$, and has sharp $\\ell^1$ sheet norm $q$. Combining this operator factorization with a Melli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.12722","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/2606.12722/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"}