{"paper":{"title":"Non-Euclidean unification of isoperimetric profiles and grand Lebesgue-Sobolev scales","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alexander Zuevsky, Daniel Levin","submitted_at":"2026-06-08T18:48:08Z","abstract_excerpt":"Let $(X,d,\\mu)$ be a complete separable metric measure space satisfying a doubling condition and a $(1,1)$-Poincar\\'e inequality. We develop a rigorous framework unifying two lines of analysis: the isoperimetric-profile approach of Coulhon-Grigor'yan-Levin \\cite{CGL2003} and the grand/small Lebesgue-Sobolev scale introduced by Fiorenza-Formica-Gogatishvili \\cite{FFG2018}. An explicit profile-to-scale transform $\\PhiX$, defined via an inverse integral of $\\IX$, converts geometric data into grand Lebesgue parameters. Sharp, up to universal constants, embeddings $W^{1,1}(X) \\hookrightarrow \\mathc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10073","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/2606.10073/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"}