{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:TKPE3L3DYB33JH6G2FBGK5RNWD","short_pith_number":"pith:TKPE3L3D","schema_version":"1.0","canonical_sha256":"9a9e4daf63c077b49fc6d14265762db0c30afda696a7fd837d47570386053b78","source":{"kind":"arxiv","id":"1405.6838","version":1},"attestation_state":"computed","paper":{"title":"Regularity Conditions of 3D Navier-Stokes flow in terms of large spectral components","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Minha Yoo, Minkyu Kwak, Namkwon Kim","submitted_at":"2014-05-27T09:00:20Z","abstract_excerpt":"We develop Ladyzhenskaya-Prodi-Serrin type spectral regularity criteria for 3D incompressible Navier-Stokes equations in a torus. Concretely, for any $N>0$, let $w_N$ be the sum of all spectral components of the velocity fields whose all three wave numbers are greater than $N$ absolutely. Then, we show that for any $N>0$, the finiteness of the Serrin type norm of $w_N$ implies the regularity of the flow. It implies that if the flow breaks down in a finite time, the energy of the velocity fields cascades down to the arbitrarily large spectral components of $w_N$ and corresponding energy spectru"},"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":"1405.6838","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-27T09:00:20Z","cross_cats_sorted":[],"title_canon_sha256":"7df7681df1b9e5f4f87d6345a0f8c608175e9eaaeeeefab47233b6f3c6d42080","abstract_canon_sha256":"408864e0ec545349df7d45ae5b45c7a809d702bddd65646c5280af16e9b56193"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:00.228094Z","signature_b64":"n9oV+89da+GbSbEPEHwZSaPy2asVQQfQ025dLCAxNCb75uIH2jcaNxa4Hpw0Qv09BHhYQLsLeiSo/qeQb1uTDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a9e4daf63c077b49fc6d14265762db0c30afda696a7fd837d47570386053b78","last_reissued_at":"2026-05-18T02:51:00.227682Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:00.227682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regularity Conditions of 3D Navier-Stokes flow in terms of large spectral components","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Minha Yoo, Minkyu Kwak, Namkwon Kim","submitted_at":"2014-05-27T09:00:20Z","abstract_excerpt":"We develop Ladyzhenskaya-Prodi-Serrin type spectral regularity criteria for 3D incompressible Navier-Stokes equations in a torus. Concretely, for any $N>0$, let $w_N$ be the sum of all spectral components of the velocity fields whose all three wave numbers are greater than $N$ absolutely. Then, we show that for any $N>0$, the finiteness of the Serrin type norm of $w_N$ implies the regularity of the flow. It implies that if the flow breaks down in a finite time, the energy of the velocity fields cascades down to the arbitrarily large spectral components of $w_N$ and corresponding energy spectru"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6838","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":"1405.6838","created_at":"2026-05-18T02:51:00.227745+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.6838v1","created_at":"2026-05-18T02:51:00.227745+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6838","created_at":"2026-05-18T02:51:00.227745+00:00"},{"alias_kind":"pith_short_12","alias_value":"TKPE3L3DYB33","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"TKPE3L3DYB33JH6G","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"TKPE3L3D","created_at":"2026-05-18T12:28:49.207871+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/TKPE3L3DYB33JH6G2FBGK5RNWD","json":"https://pith.science/pith/TKPE3L3DYB33JH6G2FBGK5RNWD.json","graph_json":"https://pith.science/api/pith-number/TKPE3L3DYB33JH6G2FBGK5RNWD/graph.json","events_json":"https://pith.science/api/pith-number/TKPE3L3DYB33JH6G2FBGK5RNWD/events.json","paper":"https://pith.science/paper/TKPE3L3D"},"agent_actions":{"view_html":"https://pith.science/pith/TKPE3L3DYB33JH6G2FBGK5RNWD","download_json":"https://pith.science/pith/TKPE3L3DYB33JH6G2FBGK5RNWD.json","view_paper":"https://pith.science/paper/TKPE3L3D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.6838&json=true","fetch_graph":"https://pith.science/api/pith-number/TKPE3L3DYB33JH6G2FBGK5RNWD/graph.json","fetch_events":"https://pith.science/api/pith-number/TKPE3L3DYB33JH6G2FBGK5RNWD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TKPE3L3DYB33JH6G2FBGK5RNWD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TKPE3L3DYB33JH6G2FBGK5RNWD/action/storage_attestation","attest_author":"https://pith.science/pith/TKPE3L3DYB33JH6G2FBGK5RNWD/action/author_attestation","sign_citation":"https://pith.science/pith/TKPE3L3DYB33JH6G2FBGK5RNWD/action/citation_signature","submit_replication":"https://pith.science/pith/TKPE3L3DYB33JH6G2FBGK5RNWD/action/replication_record"}},"created_at":"2026-05-18T02:51:00.227745+00:00","updated_at":"2026-05-18T02:51:00.227745+00:00"}