{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WC2AUG3XHFUCTOA7EJOSOTVHN3","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":"628e85e22155b75ed59dc0a55b95c245df86d633b1843ac628bc7940771a8861","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-20T16:13:23Z","title_canon_sha256":"5aa96db8897ffcc069cfb715a411218974699391eddda2853a01afb00ec34df3"},"schema_version":"1.0","source":{"id":"1801.06696","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.06696","created_at":"2026-05-18T00:25:28Z"},{"alias_kind":"arxiv_version","alias_value":"1801.06696v1","created_at":"2026-05-18T00:25:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.06696","created_at":"2026-05-18T00:25:28Z"},{"alias_kind":"pith_short_12","alias_value":"WC2AUG3XHFUC","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WC2AUG3XHFUCTOA7","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WC2AUG3X","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:c950bee1c9adab600a87fd95adc8c6d0499f2969419affbf73412108347b1e01","target":"graph","created_at":"2026-05-18T00:25:28Z","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, the three-dimensional stochastic nonhomogeneous incompressible Navier-Stokes equations driven by L\\'evy process consisting of the Brownian motion, the compensated Poisson random measure and the Poisson random measure are considered in a bounded domain. We obtain the existence of martingale solutions. The construction of the solution is based on the classical Galerkin approximation method, stopping time, the compactness method and the Jakubowski-Skorokhod theorem.","authors_text":"Dehua Wang, Huaqiao Wang, Robin Ming Chen","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-20T16:13:23Z","title":"Martingale solutions for the three-dimensional stochastic nonhomogeneous incompressible Navier-Stokes equations driven by Levy processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06696","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":"sha256:8d71ebea613b0fd3a960db2e1d7397452db8998b703cf131db91753c779357f3","target":"record","created_at":"2026-05-18T00:25:28Z","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":"628e85e22155b75ed59dc0a55b95c245df86d633b1843ac628bc7940771a8861","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-20T16:13:23Z","title_canon_sha256":"5aa96db8897ffcc069cfb715a411218974699391eddda2853a01afb00ec34df3"},"schema_version":"1.0","source":{"id":"1801.06696","kind":"arxiv","version":1}},"canonical_sha256":"b0b40a1b77396829b81f225d274ea76ede51884cbbc6111d456d68608bd2222b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0b40a1b77396829b81f225d274ea76ede51884cbbc6111d456d68608bd2222b","first_computed_at":"2026-05-18T00:25:28.005282Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:28.005282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"poEAjJyphooanVkdNFWwiPFAcFn4uS41AlixQp6ThvOKJEBRtuoRGKn7aqiHmmcdWLDvDaVEFbdSMqvTOGQcBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:28.006082Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.06696","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d71ebea613b0fd3a960db2e1d7397452db8998b703cf131db91753c779357f3","sha256:c950bee1c9adab600a87fd95adc8c6d0499f2969419affbf73412108347b1e01"],"state_sha256":"e73fd358804018126624faf8753347b8573d4421d6e42a64015167f1b32856ef"}