{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:B2Q46JRJAFPJIWPBJKE2PBRGRF","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":"595b09dfe52da1c6077220ad0d60c655e60547b5433bf0aaa0cba8e37fbadcf8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-07T03:40:05Z","title_canon_sha256":"91512cc6ff400adcf068a59c454247d55fddedc20958b31047c3e05e1dc8e4d6"},"schema_version":"1.0","source":{"id":"1906.02887","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.02887","created_at":"2026-05-17T23:43:55Z"},{"alias_kind":"arxiv_version","alias_value":"1906.02887v1","created_at":"2026-05-17T23:43:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.02887","created_at":"2026-05-17T23:43:55Z"},{"alias_kind":"pith_short_12","alias_value":"B2Q46JRJAFPJ","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"B2Q46JRJAFPJIWPB","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"B2Q46JRJ","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:e66e20dabf992aec7352d5bbe2b7d3d5a49556b2b96b288e62fb1b1ee38a45b3","target":"graph","created_at":"2026-05-17T23:43:55Z","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":"We establish the existence and uniqueness of local strong solutions to the Navier-Stokes equations with arbitrary initial data and external forces in the homogeneous Besov-Morrey space. The local solutions can be extended globally in time provided the initial data and external forces are small. We adapt the method introduced in \\cite{ks6}, where the Besov space is considered, to the setting of the homogeneous Besov-Morrey space.","authors_text":"Boling Guo, Guoquan Qin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-07T03:40:05Z","title":"Navier-Stokes equations with external forces in Besov-Morrey spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.02887","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":"sha256:7fccf8e56ac7f645415c525ca84ef18288eee00da839941639d5186bd9431561","target":"record","created_at":"2026-05-17T23:43:55Z","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":"595b09dfe52da1c6077220ad0d60c655e60547b5433bf0aaa0cba8e37fbadcf8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-07T03:40:05Z","title_canon_sha256":"91512cc6ff400adcf068a59c454247d55fddedc20958b31047c3e05e1dc8e4d6"},"schema_version":"1.0","source":{"id":"1906.02887","kind":"arxiv","version":1}},"canonical_sha256":"0ea1cf2629015e9459e14a89a786268971e15094bee0d9147110d19ad94ec968","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ea1cf2629015e9459e14a89a786268971e15094bee0d9147110d19ad94ec968","first_computed_at":"2026-05-17T23:43:55.813744Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:55.813744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zXnN36KsVs24rBwQeV0MHgPzOwwnhnqFXjFcHdb85m72zIZnyo3kezaJVlXuXB+3UJyj3ebXBZ5GS1dhmIaxCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:55.814441Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.02887","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7fccf8e56ac7f645415c525ca84ef18288eee00da839941639d5186bd9431561","sha256:e66e20dabf992aec7352d5bbe2b7d3d5a49556b2b96b288e62fb1b1ee38a45b3"],"state_sha256":"f8394521544666e0e760d8800478356e8710baac0ae0329dc69d8f6851a697f0"}