{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:2NQODK7NEJYTU337BBFSTP5YXE","short_pith_number":"pith:2NQODK7N","schema_version":"1.0","canonical_sha256":"d360e1abed22713a6f7f084b29bfb8b91fcb7fc367742812c457525f425864a7","source":{"kind":"arxiv","id":"2310.02934","version":2},"attestation_state":"computed","paper":{"title":"Anomalous dissipation and Euler flows","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bian Wu, Jan Burczak, L\\'aszl\\'o Sz\\'ekelyhidi Jr.","submitted_at":"2023-10-04T16:11:11Z","abstract_excerpt":"We show anomalous dissipation of scalars advected by weak solutions to the incompressible Euler equations with $C^{(\\sfrac{1}{3})^-}$ regularity, for an arbitrary initial datum in $\\dot H^1 (\\T^3)$. This is the first rigorous derivation of zeroth law of scalar turbulence, where the scalar is advected by solution to an equation of hydrodynamics (unforced and deterministic). As a byproduct of our method, we provide a typicality statement for the drift, and recover certain desired properties of turbulence, including a lower bound on scalar variance commensurate with the Richardson pair dispersion"},"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":"2310.02934","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-10-04T16:11:11Z","cross_cats_sorted":[],"title_canon_sha256":"1d68defe2f9463482dca3c83c453d3fb8cd808b48bcc7d1e65f5c733ad8124e7","abstract_canon_sha256":"70a3372e0a06e7ecc2dfe85c14b31837669922346299eae7e329962eb9b834aa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:08:21.152577Z","signature_b64":"FnNanq5KePE3AyXsMNJD1D2X6wSKuXGantWj2Dj3xmAEcy3sHefz13lsol+8SfMFA9NOQcTXk6KXi9VXLGVdBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d360e1abed22713a6f7f084b29bfb8b91fcb7fc367742812c457525f425864a7","last_reissued_at":"2026-07-05T09:08:21.152033Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:08:21.152033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Anomalous dissipation and Euler flows","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bian Wu, Jan Burczak, L\\'aszl\\'o Sz\\'ekelyhidi Jr.","submitted_at":"2023-10-04T16:11:11Z","abstract_excerpt":"We show anomalous dissipation of scalars advected by weak solutions to the incompressible Euler equations with $C^{(\\sfrac{1}{3})^-}$ regularity, for an arbitrary initial datum in $\\dot H^1 (\\T^3)$. This is the first rigorous derivation of zeroth law of scalar turbulence, where the scalar is advected by solution to an equation of hydrodynamics (unforced and deterministic). As a byproduct of our method, we provide a typicality statement for the drift, and recover certain desired properties of turbulence, including a lower bound on scalar variance commensurate with the Richardson pair dispersion"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.02934","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/2310.02934/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":"2310.02934","created_at":"2026-07-05T09:08:21.152095+00:00"},{"alias_kind":"arxiv_version","alias_value":"2310.02934v2","created_at":"2026-07-05T09:08:21.152095+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.02934","created_at":"2026-07-05T09:08:21.152095+00:00"},{"alias_kind":"pith_short_12","alias_value":"2NQODK7NEJYT","created_at":"2026-07-05T09:08:21.152095+00:00"},{"alias_kind":"pith_short_16","alias_value":"2NQODK7NEJYTU337","created_at":"2026-07-05T09:08:21.152095+00:00"},{"alias_kind":"pith_short_8","alias_value":"2NQODK7N","created_at":"2026-07-05T09:08:21.152095+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":7,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.07096","citing_title":"Non-selection of Lagrangian trajectories in the zero-noise limit for a class of stochastic regularizations","ref_index":11,"is_internal_anchor":false},{"citing_arxiv_id":"2605.20451","citing_title":"Turbulent Dynamos on Bounded Domains and Their Generalization to the Geometric Transport Equation","ref_index":20,"is_internal_anchor":false},{"citing_arxiv_id":"2508.01440","citing_title":"Dissipation concentration in two-dimensional fluids","ref_index":9,"is_internal_anchor":false},{"citing_arxiv_id":"2604.23883","citing_title":"Sharp pathwise nonuniqueness for additive SDEs","ref_index":13,"is_internal_anchor":false},{"citing_arxiv_id":"2604.13912","citing_title":"Scalar anomalous dissipation and optimal regularity via iterated homogenization","ref_index":10,"is_internal_anchor":false},{"citing_arxiv_id":"2604.14100","citing_title":"The 2D Euler equations are well-posed for generic initial data in $L^2$","ref_index":4,"is_internal_anchor":false},{"citing_arxiv_id":"2605.02561","citing_title":"Quantitative homogenization of elliptic equations with infinitely many scales","ref_index":13,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2NQODK7NEJYTU337BBFSTP5YXE","json":"https://pith.science/pith/2NQODK7NEJYTU337BBFSTP5YXE.json","graph_json":"https://pith.science/api/pith-number/2NQODK7NEJYTU337BBFSTP5YXE/graph.json","events_json":"https://pith.science/api/pith-number/2NQODK7NEJYTU337BBFSTP5YXE/events.json","paper":"https://pith.science/paper/2NQODK7N"},"agent_actions":{"view_html":"https://pith.science/pith/2NQODK7NEJYTU337BBFSTP5YXE","download_json":"https://pith.science/pith/2NQODK7NEJYTU337BBFSTP5YXE.json","view_paper":"https://pith.science/paper/2NQODK7N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2310.02934&json=true","fetch_graph":"https://pith.science/api/pith-number/2NQODK7NEJYTU337BBFSTP5YXE/graph.json","fetch_events":"https://pith.science/api/pith-number/2NQODK7NEJYTU337BBFSTP5YXE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2NQODK7NEJYTU337BBFSTP5YXE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2NQODK7NEJYTU337BBFSTP5YXE/action/storage_attestation","attest_author":"https://pith.science/pith/2NQODK7NEJYTU337BBFSTP5YXE/action/author_attestation","sign_citation":"https://pith.science/pith/2NQODK7NEJYTU337BBFSTP5YXE/action/citation_signature","submit_replication":"https://pith.science/pith/2NQODK7NEJYTU337BBFSTP5YXE/action/replication_record"}},"created_at":"2026-07-05T09:08:21.152095+00:00","updated_at":"2026-07-05T09:08:21.152095+00:00"}