{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:5ARZJWWHN35LTUA2US3OBUXVYT","short_pith_number":"pith:5ARZJWWH","canonical_record":{"source":{"id":"1702.04619","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-15T14:17:18Z","cross_cats_sorted":[],"title_canon_sha256":"e6d4e38a5c9419e9d3633b66da3e0f13e7fd4d75dd765f9b0b969c49e6bb0eb0","abstract_canon_sha256":"2d755a28ee99b7ac5bb6d5256dc47b9e1f5d502593314a7d3f340c8f44fae05c"},"schema_version":"1.0"},"canonical_sha256":"e82394dac76efab9d01aa4b6e0d2f5c4f6192ad56da6a6faf102176f42837768","source":{"kind":"arxiv","id":"1702.04619","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.04619","created_at":"2026-05-18T00:50:41Z"},{"alias_kind":"arxiv_version","alias_value":"1702.04619v1","created_at":"2026-05-18T00:50:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04619","created_at":"2026-05-18T00:50:41Z"},{"alias_kind":"pith_short_12","alias_value":"5ARZJWWHN35L","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5ARZJWWHN35LTUA2","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5ARZJWWH","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:5ARZJWWHN35LTUA2US3OBUXVYT","target":"record","payload":{"canonical_record":{"source":{"id":"1702.04619","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-15T14:17:18Z","cross_cats_sorted":[],"title_canon_sha256":"e6d4e38a5c9419e9d3633b66da3e0f13e7fd4d75dd765f9b0b969c49e6bb0eb0","abstract_canon_sha256":"2d755a28ee99b7ac5bb6d5256dc47b9e1f5d502593314a7d3f340c8f44fae05c"},"schema_version":"1.0"},"canonical_sha256":"e82394dac76efab9d01aa4b6e0d2f5c4f6192ad56da6a6faf102176f42837768","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:41.127113Z","signature_b64":"a+1rLSF2x19fiulHv++n929tTdLbh/UKjsYbdUa3rhe+QSEqMidmEoOGMNrVMTvL1QBpGrG+Sscd6e7lD25rDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e82394dac76efab9d01aa4b6e0d2f5c4f6192ad56da6a6faf102176f42837768","last_reissued_at":"2026-05-18T00:50:41.126573Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:41.126573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.04619","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:50:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bl6riI+f0+a9zEZM2N7YyZXwHR/Ln98/JuAETodiLJmqC1ymPxV4LuyrOmRaMjj8AnYwJN+PeSAPVrSqOSbvDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:38:36.407215Z"},"content_sha256":"b97822f02361182173b4d2c54d0bd58e9991992708717da6e3b787b06bdc5108","schema_version":"1.0","event_id":"sha256:b97822f02361182173b4d2c54d0bd58e9991992708717da6e3b787b06bdc5108"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:5ARZJWWHN35LTUA2US3OBUXVYT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"2D Stochastic Chemotaxis-Navier-Stokes System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jianliang Zhai, Tusheng Zhang","submitted_at":"2017-02-15T14:17:18Z","abstract_excerpt":"In this paper, we establish the existence and uniqueness of both mild(/variational) solutions and weak (in the sense of PDE) solutions of coupled system of 2D stochastic Chemotaxis-Navier-Stokes equations. The mild/variational solution is obtained through a fixed point argument in a purposely constructed Banach space. To get the weak solution we first prove the existence of a martingale weak solution and then we show that the pathwise uniqueness holds for the martingale solution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04619","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:50:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8IkdyWpZT8mFGg7TS+8Eve228D7esa/IE7DUhxDgAeGZxR5jZ/6ABkOXAnGpuX/PPJ4cYGOi/xlD4HPLv0QNDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:38:36.407570Z"},"content_sha256":"84c2b327a33ed0bf96638fabdec215e18215abc6f31dd045697ca17cb90b99f8","schema_version":"1.0","event_id":"sha256:84c2b327a33ed0bf96638fabdec215e18215abc6f31dd045697ca17cb90b99f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5ARZJWWHN35LTUA2US3OBUXVYT/bundle.json","state_url":"https://pith.science/pith/5ARZJWWHN35LTUA2US3OBUXVYT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5ARZJWWHN35LTUA2US3OBUXVYT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-26T11:38:36Z","links":{"resolver":"https://pith.science/pith/5ARZJWWHN35LTUA2US3OBUXVYT","bundle":"https://pith.science/pith/5ARZJWWHN35LTUA2US3OBUXVYT/bundle.json","state":"https://pith.science/pith/5ARZJWWHN35LTUA2US3OBUXVYT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5ARZJWWHN35LTUA2US3OBUXVYT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5ARZJWWHN35LTUA2US3OBUXVYT","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":"2d755a28ee99b7ac5bb6d5256dc47b9e1f5d502593314a7d3f340c8f44fae05c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-15T14:17:18Z","title_canon_sha256":"e6d4e38a5c9419e9d3633b66da3e0f13e7fd4d75dd765f9b0b969c49e6bb0eb0"},"schema_version":"1.0","source":{"id":"1702.04619","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.04619","created_at":"2026-05-18T00:50:41Z"},{"alias_kind":"arxiv_version","alias_value":"1702.04619v1","created_at":"2026-05-18T00:50:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04619","created_at":"2026-05-18T00:50:41Z"},{"alias_kind":"pith_short_12","alias_value":"5ARZJWWHN35L","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5ARZJWWHN35LTUA2","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5ARZJWWH","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:84c2b327a33ed0bf96638fabdec215e18215abc6f31dd045697ca17cb90b99f8","target":"graph","created_at":"2026-05-18T00:50:41Z","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 establish the existence and uniqueness of both mild(/variational) solutions and weak (in the sense of PDE) solutions of coupled system of 2D stochastic Chemotaxis-Navier-Stokes equations. The mild/variational solution is obtained through a fixed point argument in a purposely constructed Banach space. To get the weak solution we first prove the existence of a martingale weak solution and then we show that the pathwise uniqueness holds for the martingale solution.","authors_text":"Jianliang Zhai, Tusheng Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-15T14:17:18Z","title":"2D Stochastic Chemotaxis-Navier-Stokes System"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04619","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:b97822f02361182173b4d2c54d0bd58e9991992708717da6e3b787b06bdc5108","target":"record","created_at":"2026-05-18T00:50:41Z","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":"2d755a28ee99b7ac5bb6d5256dc47b9e1f5d502593314a7d3f340c8f44fae05c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-15T14:17:18Z","title_canon_sha256":"e6d4e38a5c9419e9d3633b66da3e0f13e7fd4d75dd765f9b0b969c49e6bb0eb0"},"schema_version":"1.0","source":{"id":"1702.04619","kind":"arxiv","version":1}},"canonical_sha256":"e82394dac76efab9d01aa4b6e0d2f5c4f6192ad56da6a6faf102176f42837768","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e82394dac76efab9d01aa4b6e0d2f5c4f6192ad56da6a6faf102176f42837768","first_computed_at":"2026-05-18T00:50:41.126573Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:41.126573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a+1rLSF2x19fiulHv++n929tTdLbh/UKjsYbdUa3rhe+QSEqMidmEoOGMNrVMTvL1QBpGrG+Sscd6e7lD25rDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:41.127113Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.04619","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b97822f02361182173b4d2c54d0bd58e9991992708717da6e3b787b06bdc5108","sha256:84c2b327a33ed0bf96638fabdec215e18215abc6f31dd045697ca17cb90b99f8"],"state_sha256":"413410a0165e0dc4df76d6579917ecd5b775fabc41e9ac62656c723ac697863d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ULH55Diu/EwdroKjnC3sizuGMwY6/NM78sWBqf0qEe/obw171WSQj0mO8flh/syU+PohgazJRXMVLz5zZWkLCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T11:38:36.409497Z","bundle_sha256":"0b542fc0aa3c4688ec14fe1a12c3c15f806e6cbb513b53caf78e934f507ce7e4"}}