{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:QKP75USVVPJS4IAUCDXPK26PJT","short_pith_number":"pith:QKP75USV","schema_version":"1.0","canonical_sha256":"829ffed255abd32e201410eef56bcf4cc648b26bb1faf475eba3860db968304c","source":{"kind":"arxiv","id":"2107.12115","version":2},"attestation_state":"computed","paper":{"title":"Mixing for generic rough shear flows","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Lucio Galeati, Massimiliano Gubinelli","submitted_at":"2021-07-26T11:24:19Z","abstract_excerpt":"We study mixing and diffusion properties of passive scalars driven by $generic$ rough shear flows. Genericity is here understood in the sense of prevalence and (ir)regularity is measured in the Besov-Nikolskii scale $B^{\\alpha}_{1, \\infty}$, $\\alpha \\in (0, 1)$. We provide upper and lower bounds, showing that in general inviscid mixing in $H^{1/2}$ holds sharply with rate $r(t) \\sim t^{1/(2 \\alpha)}$, while enhanced dissipation holds with rate $r(\\nu) \\sim \\nu^{\\alpha / (\\alpha+2)}$. Our results in the inviscid mixing case rely on the concept of $\\rho$-irregularity, first introduced by Catelli"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2107.12115","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-07-26T11:24:19Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"7bf4111db0a9a94f8f2e8bb3b80b3e72cc55c71464d4075ff424af27164fdfef","abstract_canon_sha256":"acc32a9046c9801903138545d44b80b597128fdc62ac84c887353110b2f524d9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:22:56.441413Z","signature_b64":"dDa/uCwzHOSPknhdO9Q5huJ7AjJUH1D5qpIbggx594knXZN0SMMnEe4+l4crEdBxQBR2aaL1G6uezMvqPGq6DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"829ffed255abd32e201410eef56bcf4cc648b26bb1faf475eba3860db968304c","last_reissued_at":"2026-07-05T06:22:56.440912Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:22:56.440912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mixing for generic rough shear flows","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Lucio Galeati, Massimiliano Gubinelli","submitted_at":"2021-07-26T11:24:19Z","abstract_excerpt":"We study mixing and diffusion properties of passive scalars driven by $generic$ rough shear flows. Genericity is here understood in the sense of prevalence and (ir)regularity is measured in the Besov-Nikolskii scale $B^{\\alpha}_{1, \\infty}$, $\\alpha \\in (0, 1)$. We provide upper and lower bounds, showing that in general inviscid mixing in $H^{1/2}$ holds sharply with rate $r(t) \\sim t^{1/(2 \\alpha)}$, while enhanced dissipation holds with rate $r(\\nu) \\sim \\nu^{\\alpha / (\\alpha+2)}$. Our results in the inviscid mixing case rely on the concept of $\\rho$-irregularity, first introduced by Catelli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.12115","kind":"arxiv","version":2},"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/2107.12115/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2107.12115","created_at":"2026-07-05T06:22:56.440971+00:00"},{"alias_kind":"arxiv_version","alias_value":"2107.12115v2","created_at":"2026-07-05T06:22:56.440971+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.12115","created_at":"2026-07-05T06:22:56.440971+00:00"},{"alias_kind":"pith_short_12","alias_value":"QKP75USVVPJS","created_at":"2026-07-05T06:22:56.440971+00:00"},{"alias_kind":"pith_short_16","alias_value":"QKP75USVVPJS4IAU","created_at":"2026-07-05T06:22:56.440971+00:00"},{"alias_kind":"pith_short_8","alias_value":"QKP75USV","created_at":"2026-07-05T06:22:56.440971+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QKP75USVVPJS4IAUCDXPK26PJT","json":"https://pith.science/pith/QKP75USVVPJS4IAUCDXPK26PJT.json","graph_json":"https://pith.science/api/pith-number/QKP75USVVPJS4IAUCDXPK26PJT/graph.json","events_json":"https://pith.science/api/pith-number/QKP75USVVPJS4IAUCDXPK26PJT/events.json","paper":"https://pith.science/paper/QKP75USV"},"agent_actions":{"view_html":"https://pith.science/pith/QKP75USVVPJS4IAUCDXPK26PJT","download_json":"https://pith.science/pith/QKP75USVVPJS4IAUCDXPK26PJT.json","view_paper":"https://pith.science/paper/QKP75USV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2107.12115&json=true","fetch_graph":"https://pith.science/api/pith-number/QKP75USVVPJS4IAUCDXPK26PJT/graph.json","fetch_events":"https://pith.science/api/pith-number/QKP75USVVPJS4IAUCDXPK26PJT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QKP75USVVPJS4IAUCDXPK26PJT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QKP75USVVPJS4IAUCDXPK26PJT/action/storage_attestation","attest_author":"https://pith.science/pith/QKP75USVVPJS4IAUCDXPK26PJT/action/author_attestation","sign_citation":"https://pith.science/pith/QKP75USVVPJS4IAUCDXPK26PJT/action/citation_signature","submit_replication":"https://pith.science/pith/QKP75USVVPJS4IAUCDXPK26PJT/action/replication_record"}},"created_at":"2026-07-05T06:22:56.440971+00:00","updated_at":"2026-07-05T06:22:56.440971+00:00"}