{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:UNDJDT3WROE3AXLER2ACMG2PK2","short_pith_number":"pith:UNDJDT3W","schema_version":"1.0","canonical_sha256":"a34691cf768b89b05d648e80261b4f56b0c2528865bc0a9d3f06048992ea52b8","source":{"kind":"arxiv","id":"1911.01561","version":1},"attestation_state":"computed","paper":{"title":"Almost-sure enhanced dissipation and uniform-in-diffusivity exponential mixing for advection-diffusion by stochastic Navier-Stokes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.PR","physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"Alex Blumenthal, Jacob Bedrossian, Samuel Punshon-Smith","submitted_at":"2019-11-05T01:39:22Z","abstract_excerpt":"We study the mixing and dissipation properties of the advection-diffusion equation with diffusivity $0 < \\kappa \\ll 1$ and advection by a class of random velocity fields on $\\mathbb T^d$, $d=\\{2,3\\}$, including solutions of the 2D Navier-Stokes equations forced by sufficiently regular-in-space, non-degenerate white-in-time noise. We prove that the solution almost surely mixes exponentially fast uniformly in the diffusivity $\\kappa$. Namely, that there is a deterministic, exponential rate (independent of $\\kappa$) such that all mean-zero $H^1$ initial data decays exponentially fast in $H^{-1}$ "},"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":"1911.01561","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-11-05T01:39:22Z","cross_cats_sorted":["math.DS","math.PR","physics.flu-dyn"],"title_canon_sha256":"adca0d528fe9fedd7bccfaa65289f6af5d06f87a4bc5ff4d199b6c466c5dbec5","abstract_canon_sha256":"461109115c64b90bb02ab37242fc96ce0555dedeb942501de498461f623f4eec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:52:11.604400Z","signature_b64":"ZyF4N7lGJY1nE+I9uy/1m1T67CEGv6Hmq5ncdVZR56EimufM3R49Kj7edp978TS6KLX0jjTEd73LRv5e2b5cDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a34691cf768b89b05d648e80261b4f56b0c2528865bc0a9d3f06048992ea52b8","last_reissued_at":"2026-07-05T02:52:11.603977Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:52:11.603977Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Almost-sure enhanced dissipation and uniform-in-diffusivity exponential mixing for advection-diffusion by stochastic Navier-Stokes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.PR","physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"Alex Blumenthal, Jacob Bedrossian, Samuel Punshon-Smith","submitted_at":"2019-11-05T01:39:22Z","abstract_excerpt":"We study the mixing and dissipation properties of the advection-diffusion equation with diffusivity $0 < \\kappa \\ll 1$ and advection by a class of random velocity fields on $\\mathbb T^d$, $d=\\{2,3\\}$, including solutions of the 2D Navier-Stokes equations forced by sufficiently regular-in-space, non-degenerate white-in-time noise. We prove that the solution almost surely mixes exponentially fast uniformly in the diffusivity $\\kappa$. Namely, that there is a deterministic, exponential rate (independent of $\\kappa$) such that all mean-zero $H^1$ initial data decays exponentially fast in $H^{-1}$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.01561","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/1911.01561/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":"1911.01561","created_at":"2026-07-05T02:52:11.604033+00:00"},{"alias_kind":"arxiv_version","alias_value":"1911.01561v1","created_at":"2026-07-05T02:52:11.604033+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.01561","created_at":"2026-07-05T02:52:11.604033+00:00"},{"alias_kind":"pith_short_12","alias_value":"UNDJDT3WROE3","created_at":"2026-07-05T02:52:11.604033+00:00"},{"alias_kind":"pith_short_16","alias_value":"UNDJDT3WROE3AXLE","created_at":"2026-07-05T02:52:11.604033+00:00"},{"alias_kind":"pith_short_8","alias_value":"UNDJDT3W","created_at":"2026-07-05T02:52:11.604033+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.07329","citing_title":"Sampling and Optimization meet Enhanced Flows","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UNDJDT3WROE3AXLER2ACMG2PK2","json":"https://pith.science/pith/UNDJDT3WROE3AXLER2ACMG2PK2.json","graph_json":"https://pith.science/api/pith-number/UNDJDT3WROE3AXLER2ACMG2PK2/graph.json","events_json":"https://pith.science/api/pith-number/UNDJDT3WROE3AXLER2ACMG2PK2/events.json","paper":"https://pith.science/paper/UNDJDT3W"},"agent_actions":{"view_html":"https://pith.science/pith/UNDJDT3WROE3AXLER2ACMG2PK2","download_json":"https://pith.science/pith/UNDJDT3WROE3AXLER2ACMG2PK2.json","view_paper":"https://pith.science/paper/UNDJDT3W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1911.01561&json=true","fetch_graph":"https://pith.science/api/pith-number/UNDJDT3WROE3AXLER2ACMG2PK2/graph.json","fetch_events":"https://pith.science/api/pith-number/UNDJDT3WROE3AXLER2ACMG2PK2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UNDJDT3WROE3AXLER2ACMG2PK2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UNDJDT3WROE3AXLER2ACMG2PK2/action/storage_attestation","attest_author":"https://pith.science/pith/UNDJDT3WROE3AXLER2ACMG2PK2/action/author_attestation","sign_citation":"https://pith.science/pith/UNDJDT3WROE3AXLER2ACMG2PK2/action/citation_signature","submit_replication":"https://pith.science/pith/UNDJDT3WROE3AXLER2ACMG2PK2/action/replication_record"}},"created_at":"2026-07-05T02:52:11.604033+00:00","updated_at":"2026-07-05T02:52:11.604033+00:00"}