{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CRSH2Y73KCKOFXNHRRESXWAAQV","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":"7901c9a2c22bf1b74c1b110c03fec1f97e15b1d94a7ac76061bae053bdc7c355","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-04T03:22:50Z","title_canon_sha256":"6d11e24d1f626299367c2440fbf824b3b88267bb204a5276c626bd69e66c30eb"},"schema_version":"1.0","source":{"id":"1312.1012","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1012","created_at":"2026-05-18T03:05:35Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1012v1","created_at":"2026-05-18T03:05:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1012","created_at":"2026-05-18T03:05:35Z"},{"alias_kind":"pith_short_12","alias_value":"CRSH2Y73KCKO","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CRSH2Y73KCKOFXNH","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CRSH2Y73","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:c8144d540b62a81717428ced17301b9a81b9737f17f8029bb62b0c3c5745245c","target":"graph","created_at":"2026-05-18T03:05:35Z","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"},"paper":{"abstract_excerpt":"In this paper we consider three-dimensional incompressible magnetohydrodynamics equations. By using interpolation inequalities in anisotropic Lebesgue space, we provide regularity criteria involving the velocity or alternatively involving the fractional derivative of velocity in one direction, which generalize some known results.","authors_text":"Qiru Wang, Qunyi Bie, Zhengan Yao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-04T03:22:50Z","title":"Regularity criteria for the 3D MHD equations in term of velocity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1012","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":"sha256:204921778d06e9d75731a64dcb9802b1bafbd87ce2e523b090d65a93bd9dbe66","target":"record","created_at":"2026-05-18T03:05:35Z","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":"7901c9a2c22bf1b74c1b110c03fec1f97e15b1d94a7ac76061bae053bdc7c355","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-04T03:22:50Z","title_canon_sha256":"6d11e24d1f626299367c2440fbf824b3b88267bb204a5276c626bd69e66c30eb"},"schema_version":"1.0","source":{"id":"1312.1012","kind":"arxiv","version":1}},"canonical_sha256":"14647d63fb5094e2dda78c492bd800854dd5d0039355ddd44f6a0117b9394280","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14647d63fb5094e2dda78c492bd800854dd5d0039355ddd44f6a0117b9394280","first_computed_at":"2026-05-18T03:05:35.164849Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:35.164849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"baGJXZcDW47X/NsQYKKs93JfX8ribbQ8rMYe0CKVNimVRIGTU3ba9ErwbWOM+fzjrgtOb1OSR/UunIfJD0H5CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:35.165485Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1012","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:204921778d06e9d75731a64dcb9802b1bafbd87ce2e523b090d65a93bd9dbe66","sha256:c8144d540b62a81717428ced17301b9a81b9737f17f8029bb62b0c3c5745245c"],"state_sha256":"cc626bd8c426c7d7f9f806fe8c01d6a64c61621874ada7dcdb2c278dec948add"}