{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:CXEKDXU2FZO3QA4ZRAXMYXSSHJ","short_pith_number":"pith:CXEKDXU2","schema_version":"1.0","canonical_sha256":"15c8a1de9a2e5db80399882ecc5e523a50e8e8e0da9d63e2fb94dbe12f2885b3","source":{"kind":"arxiv","id":"1105.1101","version":1},"attestation_state":"computed","paper":{"title":"Using multiscale norms to quantify mixing and transport","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Jean-Luc Thiffeault","submitted_at":"2011-05-05T15:27:40Z","abstract_excerpt":"Mixing is relevant to many areas of science and engineering, including the pharmaceutical and food industries, oceanography, atmospheric sciences, and civil engineering. In all these situations one goal is to quantify and often then to improve the degree of homogenisation of a substance being stirred, referred to as a passive scalar or tracer. A classical measure of mixing is the variance of the concentration of the scalar, which can be related to the $L^2$ norm of the concentration field. Recently other norms have been used to quantify mixing, in particular the mix-norm as well as negative So"},"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":"1105.1101","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2011-05-05T15:27:40Z","cross_cats_sorted":[],"title_canon_sha256":"4f001db9095071a962f23f51d2e832106a24ca0533d2a73d26308b314bd20aa3","abstract_canon_sha256":"882dc1e876a066a4655745f0e7ef3af61c13358a36055a536b2717f98c681eb1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:35.371515Z","signature_b64":"VRDnOaSQ6z9Nfmvj8BhU/LizzMK4Fhto71FBkDlaOjxCpSpYHawczQU0GEKrN01lnFnCPSRqe6EIz3iPuUJ2CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15c8a1de9a2e5db80399882ecc5e523a50e8e8e0da9d63e2fb94dbe12f2885b3","last_reissued_at":"2026-05-18T03:12:35.370726Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:35.370726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Using multiscale norms to quantify mixing and transport","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Jean-Luc Thiffeault","submitted_at":"2011-05-05T15:27:40Z","abstract_excerpt":"Mixing is relevant to many areas of science and engineering, including the pharmaceutical and food industries, oceanography, atmospheric sciences, and civil engineering. In all these situations one goal is to quantify and often then to improve the degree of homogenisation of a substance being stirred, referred to as a passive scalar or tracer. A classical measure of mixing is the variance of the concentration of the scalar, which can be related to the $L^2$ norm of the concentration field. Recently other norms have been used to quantify mixing, in particular the mix-norm as well as negative So"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1101","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":""},"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":"1105.1101","created_at":"2026-05-18T03:12:35.370853+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.1101v1","created_at":"2026-05-18T03:12:35.370853+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1101","created_at":"2026-05-18T03:12:35.370853+00:00"},{"alias_kind":"pith_short_12","alias_value":"CXEKDXU2FZO3","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"CXEKDXU2FZO3QA4Z","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"CXEKDXU2","created_at":"2026-05-18T12:26:26.731475+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/CXEKDXU2FZO3QA4ZRAXMYXSSHJ","json":"https://pith.science/pith/CXEKDXU2FZO3QA4ZRAXMYXSSHJ.json","graph_json":"https://pith.science/api/pith-number/CXEKDXU2FZO3QA4ZRAXMYXSSHJ/graph.json","events_json":"https://pith.science/api/pith-number/CXEKDXU2FZO3QA4ZRAXMYXSSHJ/events.json","paper":"https://pith.science/paper/CXEKDXU2"},"agent_actions":{"view_html":"https://pith.science/pith/CXEKDXU2FZO3QA4ZRAXMYXSSHJ","download_json":"https://pith.science/pith/CXEKDXU2FZO3QA4ZRAXMYXSSHJ.json","view_paper":"https://pith.science/paper/CXEKDXU2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.1101&json=true","fetch_graph":"https://pith.science/api/pith-number/CXEKDXU2FZO3QA4ZRAXMYXSSHJ/graph.json","fetch_events":"https://pith.science/api/pith-number/CXEKDXU2FZO3QA4ZRAXMYXSSHJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CXEKDXU2FZO3QA4ZRAXMYXSSHJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CXEKDXU2FZO3QA4ZRAXMYXSSHJ/action/storage_attestation","attest_author":"https://pith.science/pith/CXEKDXU2FZO3QA4ZRAXMYXSSHJ/action/author_attestation","sign_citation":"https://pith.science/pith/CXEKDXU2FZO3QA4ZRAXMYXSSHJ/action/citation_signature","submit_replication":"https://pith.science/pith/CXEKDXU2FZO3QA4ZRAXMYXSSHJ/action/replication_record"}},"created_at":"2026-05-18T03:12:35.370853+00:00","updated_at":"2026-05-18T03:12:35.370853+00:00"}