{"paper":{"title":"Approximation in Metric Sobolev Spaces: A General Framework","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.FA","authors_text":"Giacomo Enrico Sodini, Massimo Fornasier","submitted_at":"2026-06-22T12:57:53Z","abstract_excerpt":"In our recent work [FHS25], we introduced a numerical framework for approximating Sobolev functions on Wasserstein spaces from finite samples, leveraging structural properties established in [FSS23]. The present paper demonstrates that this methodology extends far beyond that specific setting. We identify a general class of metric measure spaces -- including weighted Riemannian manifolds and spaces of measures equipped with the Hellinger--Kantorovich distance -- for which the key hypotheses of Hilbertianity and the existence of a computable algebra of Lipschitz functions hold. Within this abst"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23282","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/2606.23282/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"}