{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:AH3HNC26PXP6YQOO22ZA4SSKV3","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":"355b490fff1000f1d0496caaf404e94b427334b73f79b497eaf5493d3b58f781","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-07T13:55:25Z","title_canon_sha256":"4cd4c08196e99049be4ab14695d380734170cd9c7badd7b995cf6bb5987cb694"},"schema_version":"1.0","source":{"id":"1908.02636","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.02636","created_at":"2026-07-04T23:52:22Z"},{"alias_kind":"arxiv_version","alias_value":"1908.02636v2","created_at":"2026-07-04T23:52:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.02636","created_at":"2026-07-04T23:52:22Z"},{"alias_kind":"pith_short_12","alias_value":"AH3HNC26PXP6","created_at":"2026-07-04T23:52:22Z"},{"alias_kind":"pith_short_16","alias_value":"AH3HNC26PXP6YQOO","created_at":"2026-07-04T23:52:22Z"},{"alias_kind":"pith_short_8","alias_value":"AH3HNC26","created_at":"2026-07-04T23:52:22Z"}],"graph_snapshots":[{"event_id":"sha256:f0e8be4273f3e242f928de867ead558b03a23446cd2ac87e1eb4b99ec939a5a2","target":"graph","created_at":"2026-07-04T23:52:22Z","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/1908.02636/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the global well-posedness of magnetohydrodynamic (MHD) equations. The hydrodynamic system consists of the Navier-Stokes equations for the fluid velocity coupled with a reduced from of the Maxwell equations for the magnetic field. The fluid velocity is assumed to satisfy a no-slip boundary condition, while the magnetic field is subject to a time-dependent Dirichlet boundary condition. We first establish the global existence of weak and strong solutions to (1.1)-(1.4). Then we derive the existence of a uniform attractor for (1.1)-(1.4).","authors_text":"Chengfei Ai, Jianfeng Zhou, Zhong Tan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-07T13:55:25Z","title":"Global well-posedness of magnetohydrodynamic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02636","kind":"arxiv","version":2},"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:c42f64509179ddcfe9c42c3862a3e79068a8086356f23103d1a28a9ca897e334","target":"record","created_at":"2026-07-04T23:52:22Z","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":"355b490fff1000f1d0496caaf404e94b427334b73f79b497eaf5493d3b58f781","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-07T13:55:25Z","title_canon_sha256":"4cd4c08196e99049be4ab14695d380734170cd9c7badd7b995cf6bb5987cb694"},"schema_version":"1.0","source":{"id":"1908.02636","kind":"arxiv","version":2}},"canonical_sha256":"01f6768b5e7ddfec41ced6b20e4a4aaee50975690266af25708615330a6d64a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01f6768b5e7ddfec41ced6b20e4a4aaee50975690266af25708615330a6d64a7","first_computed_at":"2026-07-04T23:52:22.850043Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:52:22.850043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+VhbQxjN2rQXO1j8muTzmEYRIV5Uj+UORQRVWnYqLNooDV8N+qvB94LRtpmykxvAVYRqZdua8SC/vtROW8kdDg==","signature_status":"signed_v1","signed_at":"2026-07-04T23:52:22.850408Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.02636","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c42f64509179ddcfe9c42c3862a3e79068a8086356f23103d1a28a9ca897e334","sha256:f0e8be4273f3e242f928de867ead558b03a23446cd2ac87e1eb4b99ec939a5a2"],"state_sha256":"146e584c2a5b3e6910bc749e4bb126c707fd0ec2b7c20e5d5f7e4ee10b5572d0"}