{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:GGHFWFDBWCREK4UTFXEMJLBKF3","short_pith_number":"pith:GGHFWFDB","schema_version":"1.0","canonical_sha256":"318e5b1461b0a24572932dc8c4ac2a2ef8d6b9285dfb24d90afe07a4cb060bba","source":{"kind":"arxiv","id":"2606.11055","version":1},"attestation_state":"computed","paper":{"title":"Exponential mixing and enhanced dissipation on the unit sphere with Rossby-Haurwitz flows","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS","physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"Augusto Del Zotto, Marc Nualart","submitted_at":"2026-06-09T16:19:03Z","abstract_excerpt":"We exhibit a family of smooth incompressible velocity fields on the two-dimensional unit sphere such that the time evolution of any mean-free initial data passively advected by any of them is mixed exponentially fast. In the presence of molecular diffusivity, we show that the solution to the associated advection-diffusion equation experiences enhanced dissipation with optimal decay rates. Each member of this family is an alternating combination of two Rossby-Haurwitz flows with random amplitudes and constitutes a spherical analogue to the sine shear-alternating example of Pierrehumbert."},"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":"2606.11055","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-09T16:19:03Z","cross_cats_sorted":["math.DS","physics.flu-dyn"],"title_canon_sha256":"d7d747c6e7d0e980d1526f0c7483fe1cad4549856bf724ef82da91ecab8f9d2e","abstract_canon_sha256":"62948c1863f0c3f78cc02ef686936962b8c8781adfd51d8bb0552cb0010f6f9d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-10T01:11:07.215967Z","signature_b64":"I7DmII06YRrDvSk0S0gDZjUQtHC7fY+o9iRLY5QplrRPThVs8aCM4YfSW/yr8v8jikTpUj8q1pLnSAEt9GPECw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"318e5b1461b0a24572932dc8c4ac2a2ef8d6b9285dfb24d90afe07a4cb060bba","last_reissued_at":"2026-06-10T01:11:07.215070Z","signature_status":"signed_v1","first_computed_at":"2026-06-10T01:11:07.215070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exponential mixing and enhanced dissipation on the unit sphere with Rossby-Haurwitz flows","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS","physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"Augusto Del Zotto, Marc Nualart","submitted_at":"2026-06-09T16:19:03Z","abstract_excerpt":"We exhibit a family of smooth incompressible velocity fields on the two-dimensional unit sphere such that the time evolution of any mean-free initial data passively advected by any of them is mixed exponentially fast. In the presence of molecular diffusivity, we show that the solution to the associated advection-diffusion equation experiences enhanced dissipation with optimal decay rates. Each member of this family is an alternating combination of two Rossby-Haurwitz flows with random amplitudes and constitutes a spherical analogue to the sine shear-alternating example of Pierrehumbert."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11055","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/2606.11055/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":"2606.11055","created_at":"2026-06-10T01:11:07.215223+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.11055v1","created_at":"2026-06-10T01:11:07.215223+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.11055","created_at":"2026-06-10T01:11:07.215223+00:00"},{"alias_kind":"pith_short_12","alias_value":"GGHFWFDBWCRE","created_at":"2026-06-10T01:11:07.215223+00:00"},{"alias_kind":"pith_short_16","alias_value":"GGHFWFDBWCREK4UT","created_at":"2026-06-10T01:11:07.215223+00:00"},{"alias_kind":"pith_short_8","alias_value":"GGHFWFDB","created_at":"2026-06-10T01:11:07.215223+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/GGHFWFDBWCREK4UTFXEMJLBKF3","json":"https://pith.science/pith/GGHFWFDBWCREK4UTFXEMJLBKF3.json","graph_json":"https://pith.science/api/pith-number/GGHFWFDBWCREK4UTFXEMJLBKF3/graph.json","events_json":"https://pith.science/api/pith-number/GGHFWFDBWCREK4UTFXEMJLBKF3/events.json","paper":"https://pith.science/paper/GGHFWFDB"},"agent_actions":{"view_html":"https://pith.science/pith/GGHFWFDBWCREK4UTFXEMJLBKF3","download_json":"https://pith.science/pith/GGHFWFDBWCREK4UTFXEMJLBKF3.json","view_paper":"https://pith.science/paper/GGHFWFDB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.11055&json=true","fetch_graph":"https://pith.science/api/pith-number/GGHFWFDBWCREK4UTFXEMJLBKF3/graph.json","fetch_events":"https://pith.science/api/pith-number/GGHFWFDBWCREK4UTFXEMJLBKF3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GGHFWFDBWCREK4UTFXEMJLBKF3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GGHFWFDBWCREK4UTFXEMJLBKF3/action/storage_attestation","attest_author":"https://pith.science/pith/GGHFWFDBWCREK4UTFXEMJLBKF3/action/author_attestation","sign_citation":"https://pith.science/pith/GGHFWFDBWCREK4UTFXEMJLBKF3/action/citation_signature","submit_replication":"https://pith.science/pith/GGHFWFDBWCREK4UTFXEMJLBKF3/action/replication_record"}},"created_at":"2026-06-10T01:11:07.215223+00:00","updated_at":"2026-06-10T01:11:07.215223+00:00"}