{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:IN2F7PNVBAQ7NEY7B4SQH24ZLA","short_pith_number":"pith:IN2F7PNV","schema_version":"1.0","canonical_sha256":"43745fbdb50821f6931f0f2503eb99582f1e1510b509d3644ac66e34a9fcda51","source":{"kind":"arxiv","id":"2204.07479","version":1},"attestation_state":"computed","paper":{"title":"Gagliardo-Nirenberg inequality in anisotropic Lebesgue spaces and energy equality in the Navier-Stokes equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.AP","authors_text":"Wei Wei, Xue Mei, Yanqing Wang","submitted_at":"2022-04-15T14:28:56Z","abstract_excerpt":"In this paper, it is shown that an analogue in mixed norm spaces of Gagliardo-Nirenberg inequality is valid. As an application, some new criteria for energy conservation of Leray-Hopf weak solutions to the 3D Navier-Stokes equations are established in these spaces, which extend the corresponding known results."},"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":"2204.07479","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-04-15T14:28:56Z","cross_cats_sorted":["math.CA","math.FA"],"title_canon_sha256":"cd22109245d2b504c34e472339d4dcf58a581050622bd7b234dd71a39af9d70b","abstract_canon_sha256":"541fab58866002196144876aba259e0d21795a61d8586cf59333c7dbe6cf8e61"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:15:04.560965Z","signature_b64":"1pz8wqPrZj+nqswPhtqE/Zh2v0SlH5tn5mRWEbzKt8dh6QiDevWyymi1C3NWli1Y5VEa1OSlOQBhrjHO4gcsDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43745fbdb50821f6931f0f2503eb99582f1e1510b509d3644ac66e34a9fcda51","last_reissued_at":"2026-07-05T04:15:04.560573Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:15:04.560573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gagliardo-Nirenberg inequality in anisotropic Lebesgue spaces and energy equality in the Navier-Stokes equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.AP","authors_text":"Wei Wei, Xue Mei, Yanqing Wang","submitted_at":"2022-04-15T14:28:56Z","abstract_excerpt":"In this paper, it is shown that an analogue in mixed norm spaces of Gagliardo-Nirenberg inequality is valid. As an application, some new criteria for energy conservation of Leray-Hopf weak solutions to the 3D Navier-Stokes equations are established in these spaces, which extend the corresponding known results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.07479","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/2204.07479/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":"2204.07479","created_at":"2026-07-05T04:15:04.560632+00:00"},{"alias_kind":"arxiv_version","alias_value":"2204.07479v1","created_at":"2026-07-05T04:15:04.560632+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.07479","created_at":"2026-07-05T04:15:04.560632+00:00"},{"alias_kind":"pith_short_12","alias_value":"IN2F7PNVBAQ7","created_at":"2026-07-05T04:15:04.560632+00:00"},{"alias_kind":"pith_short_16","alias_value":"IN2F7PNVBAQ7NEY7","created_at":"2026-07-05T04:15:04.560632+00:00"},{"alias_kind":"pith_short_8","alias_value":"IN2F7PNV","created_at":"2026-07-05T04:15:04.560632+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/IN2F7PNVBAQ7NEY7B4SQH24ZLA","json":"https://pith.science/pith/IN2F7PNVBAQ7NEY7B4SQH24ZLA.json","graph_json":"https://pith.science/api/pith-number/IN2F7PNVBAQ7NEY7B4SQH24ZLA/graph.json","events_json":"https://pith.science/api/pith-number/IN2F7PNVBAQ7NEY7B4SQH24ZLA/events.json","paper":"https://pith.science/paper/IN2F7PNV"},"agent_actions":{"view_html":"https://pith.science/pith/IN2F7PNVBAQ7NEY7B4SQH24ZLA","download_json":"https://pith.science/pith/IN2F7PNVBAQ7NEY7B4SQH24ZLA.json","view_paper":"https://pith.science/paper/IN2F7PNV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2204.07479&json=true","fetch_graph":"https://pith.science/api/pith-number/IN2F7PNVBAQ7NEY7B4SQH24ZLA/graph.json","fetch_events":"https://pith.science/api/pith-number/IN2F7PNVBAQ7NEY7B4SQH24ZLA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IN2F7PNVBAQ7NEY7B4SQH24ZLA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IN2F7PNVBAQ7NEY7B4SQH24ZLA/action/storage_attestation","attest_author":"https://pith.science/pith/IN2F7PNVBAQ7NEY7B4SQH24ZLA/action/author_attestation","sign_citation":"https://pith.science/pith/IN2F7PNVBAQ7NEY7B4SQH24ZLA/action/citation_signature","submit_replication":"https://pith.science/pith/IN2F7PNVBAQ7NEY7B4SQH24ZLA/action/replication_record"}},"created_at":"2026-07-05T04:15:04.560632+00:00","updated_at":"2026-07-05T04:15:04.560632+00:00"}