{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:IN2F7PNVBAQ7NEY7B4SQH24ZLA","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"541fab58866002196144876aba259e0d21795a61d8586cf59333c7dbe6cf8e61","cross_cats_sorted":["math.CA","math.FA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-04-15T14:28:56Z","title_canon_sha256":"cd22109245d2b504c34e472339d4dcf58a581050622bd7b234dd71a39af9d70b"},"schema_version":"1.0","source":{"id":"2204.07479","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.07479","created_at":"2026-07-05T04:15:04Z"},{"alias_kind":"arxiv_version","alias_value":"2204.07479v1","created_at":"2026-07-05T04:15:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.07479","created_at":"2026-07-05T04:15:04Z"},{"alias_kind":"pith_short_12","alias_value":"IN2F7PNVBAQ7","created_at":"2026-07-05T04:15:04Z"},{"alias_kind":"pith_short_16","alias_value":"IN2F7PNVBAQ7NEY7","created_at":"2026-07-05T04:15:04Z"},{"alias_kind":"pith_short_8","alias_value":"IN2F7PNV","created_at":"2026-07-05T04:15:04Z"}],"graph_snapshots":[{"event_id":"sha256:7c7838f058c80867abde8f3c6c59ed968592a52e5734de9aa6c8c82dc9bfab76","target":"graph","created_at":"2026-07-05T04:15:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2204.07479/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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.","authors_text":"Wei Wei, Xue Mei, Yanqing Wang","cross_cats":["math.CA","math.FA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-04-15T14:28:56Z","title":"Gagliardo-Nirenberg inequality in anisotropic Lebesgue spaces and energy equality in the Navier-Stokes equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.07479","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:918573d0821bb0156273ea75b8ca2015d20dc115a829115cd62210172a840ad6","target":"record","created_at":"2026-07-05T04:15:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"541fab58866002196144876aba259e0d21795a61d8586cf59333c7dbe6cf8e61","cross_cats_sorted":["math.CA","math.FA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-04-15T14:28:56Z","title_canon_sha256":"cd22109245d2b504c34e472339d4dcf58a581050622bd7b234dd71a39af9d70b"},"schema_version":"1.0","source":{"id":"2204.07479","kind":"arxiv","version":1}},"canonical_sha256":"43745fbdb50821f6931f0f2503eb99582f1e1510b509d3644ac66e34a9fcda51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43745fbdb50821f6931f0f2503eb99582f1e1510b509d3644ac66e34a9fcda51","first_computed_at":"2026-07-05T04:15:04.560573Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:15:04.560573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1pz8wqPrZj+nqswPhtqE/Zh2v0SlH5tn5mRWEbzKt8dh6QiDevWyymi1C3NWli1Y5VEa1OSlOQBhrjHO4gcsDw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:15:04.560965Z","signed_message":"canonical_sha256_bytes"},"source_id":"2204.07479","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:918573d0821bb0156273ea75b8ca2015d20dc115a829115cd62210172a840ad6","sha256:7c7838f058c80867abde8f3c6c59ed968592a52e5734de9aa6c8c82dc9bfab76"],"state_sha256":"699101d6eeb24c99509dcff4c4ec591f7adb597721b834fddac81b9e9fb46a2b"}