{"paper":{"title":"Regularity thresholds for anomalous dissipation and related phenomena in passive scalars","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Camillo De Lellis, Daniel W. Boutros, Marco Bagnara, Svitlana Mayboroda","submitted_at":"2026-03-12T02:44:36Z","abstract_excerpt":"We prove the absence of anomalous dissipation for passive scalars driven by some random autonomous divergence-free vector fields in $\\mathbb T^d$. In dimension $d=2$ we just need continuity almost surely and a mild nondegeneracy condition on the randomness. In dimension $d\\geq 3$ we assume a special geometric structure and almost sure H\\\"older regularity with a H\\\"older exponent bigger than $\\frac{1}{8}$. No regularity is assumed on the passive scalar except for boundedness in the initial data. The proof relies on dimension-theoretic arguments, as opposed to commutator estimates. A consequence"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.11466","kind":"arxiv","version":3},"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/2603.11466/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"}