{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:ECDSEQRCR7F57RGZYJARWURFCO","short_pith_number":"pith:ECDSEQRC","schema_version":"1.0","canonical_sha256":"20872242228fcbdfc4d9c2411b522513abedd7256c19d3c97f67e1cf5fa25911","source":{"kind":"arxiv","id":"1901.09023","version":2},"attestation_state":"computed","paper":{"title":"Convex integration and phenomenologies in turbulence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tristan Buckmaster, Vlad Vicol","submitted_at":"2019-01-25T18:47:30Z","abstract_excerpt":"In this review article we discuss a number of recent results concerning wild weak solutions of the incompressible Euler and Navier-Stokes equations. These results build on the groundbreaking works of De Lellis and Sz\\'ekelyhidi Jr., who extended Nash's fundamental ideas on $C^1$ flexible isometric embeddings, into the realm of fluid dynamics. These techniques, which go under the umbrella name convex integration, have fundamental analogies the phenomenological theories of hydrodynamic turbulence. Mathematical problems arising in turbulence (such as the Onsager conjecture) have not only sparked "},"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":"1901.09023","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-25T18:47:30Z","cross_cats_sorted":[],"title_canon_sha256":"73923018fd8d730d2ade4b2bce3c63f313c8bb2573d4400f908e989b4b7a4008","abstract_canon_sha256":"02d4af843ca0e97c5e6358cd7ceae2690e3818f944ee6f728e6d29e53d26a1cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:21.926188Z","signature_b64":"+wlvyhTm7bvxCXWWDVsr6bISzI8Iz/7QVwH0ax3ck0tglJ5A6oEEvvt9OxJIpEx/RSAM01WhoczxOD38UuBoDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20872242228fcbdfc4d9c2411b522513abedd7256c19d3c97f67e1cf5fa25911","last_reissued_at":"2026-05-17T23:49:21.925586Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:21.925586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convex integration and phenomenologies in turbulence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tristan Buckmaster, Vlad Vicol","submitted_at":"2019-01-25T18:47:30Z","abstract_excerpt":"In this review article we discuss a number of recent results concerning wild weak solutions of the incompressible Euler and Navier-Stokes equations. These results build on the groundbreaking works of De Lellis and Sz\\'ekelyhidi Jr., who extended Nash's fundamental ideas on $C^1$ flexible isometric embeddings, into the realm of fluid dynamics. These techniques, which go under the umbrella name convex integration, have fundamental analogies the phenomenological theories of hydrodynamic turbulence. Mathematical problems arising in turbulence (such as the Onsager conjecture) have not only sparked "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.09023","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":""},"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":"1901.09023","created_at":"2026-05-17T23:49:21.925696+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.09023v2","created_at":"2026-05-17T23:49:21.925696+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.09023","created_at":"2026-05-17T23:49:21.925696+00:00"},{"alias_kind":"pith_short_12","alias_value":"ECDSEQRCR7F5","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"ECDSEQRCR7F57RGZ","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"ECDSEQRC","created_at":"2026-05-18T12:33:15.570797+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1907.10436","citing_title":"Weak solutions of ideal MHD which do not conserve magnetic helicity","ref_index":12,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ECDSEQRCR7F57RGZYJARWURFCO","json":"https://pith.science/pith/ECDSEQRCR7F57RGZYJARWURFCO.json","graph_json":"https://pith.science/api/pith-number/ECDSEQRCR7F57RGZYJARWURFCO/graph.json","events_json":"https://pith.science/api/pith-number/ECDSEQRCR7F57RGZYJARWURFCO/events.json","paper":"https://pith.science/paper/ECDSEQRC"},"agent_actions":{"view_html":"https://pith.science/pith/ECDSEQRCR7F57RGZYJARWURFCO","download_json":"https://pith.science/pith/ECDSEQRCR7F57RGZYJARWURFCO.json","view_paper":"https://pith.science/paper/ECDSEQRC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.09023&json=true","fetch_graph":"https://pith.science/api/pith-number/ECDSEQRCR7F57RGZYJARWURFCO/graph.json","fetch_events":"https://pith.science/api/pith-number/ECDSEQRCR7F57RGZYJARWURFCO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ECDSEQRCR7F57RGZYJARWURFCO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ECDSEQRCR7F57RGZYJARWURFCO/action/storage_attestation","attest_author":"https://pith.science/pith/ECDSEQRCR7F57RGZYJARWURFCO/action/author_attestation","sign_citation":"https://pith.science/pith/ECDSEQRCR7F57RGZYJARWURFCO/action/citation_signature","submit_replication":"https://pith.science/pith/ECDSEQRCR7F57RGZYJARWURFCO/action/replication_record"}},"created_at":"2026-05-17T23:49:21.925696+00:00","updated_at":"2026-05-17T23:49:21.925696+00:00"}