{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:RXHCO7JEUCT2RXIJU2VXOIMYTR","short_pith_number":"pith:RXHCO7JE","canonical_record":{"source":{"id":"1706.02022","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-07T01:58:31Z","cross_cats_sorted":[],"title_canon_sha256":"17f63e5ee17ed94880018c97fb37b26829e0d5a012d566354bcaf65718c08eb5","abstract_canon_sha256":"9111199fe0dd4ec2907d8d97afb8cfe13ec6d0f076b0dcafd23c6f896f10b8e5"},"schema_version":"1.0"},"canonical_sha256":"8dce277d24a0a7a8dd09a6ab7721989c76bb306e2c91f3182bcccb6041698bf2","source":{"kind":"arxiv","id":"1706.02022","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02022","created_at":"2026-05-18T00:42:50Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02022v1","created_at":"2026-05-18T00:42:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02022","created_at":"2026-05-18T00:42:50Z"},{"alias_kind":"pith_short_12","alias_value":"RXHCO7JEUCT2","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"RXHCO7JEUCT2RXIJ","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"RXHCO7JE","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:RXHCO7JEUCT2RXIJU2VXOIMYTR","target":"record","payload":{"canonical_record":{"source":{"id":"1706.02022","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-07T01:58:31Z","cross_cats_sorted":[],"title_canon_sha256":"17f63e5ee17ed94880018c97fb37b26829e0d5a012d566354bcaf65718c08eb5","abstract_canon_sha256":"9111199fe0dd4ec2907d8d97afb8cfe13ec6d0f076b0dcafd23c6f896f10b8e5"},"schema_version":"1.0"},"canonical_sha256":"8dce277d24a0a7a8dd09a6ab7721989c76bb306e2c91f3182bcccb6041698bf2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:50.471170Z","signature_b64":"iXMZN5cobdENFX9s6nOpm8fRIXNPH5dLTouKSWcDiNx6cwkhB7k98/2QGiG4XQOiZCw1XIvNh/vr7f6dnqcQAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8dce277d24a0a7a8dd09a6ab7721989c76bb306e2c91f3182bcccb6041698bf2","last_reissued_at":"2026-05-18T00:42:50.470469Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:50.470469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.02022","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":"2026-05-18T00:42:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZXVNrZEbwttkgf5+KrdGDjQ1SJPfJjlyJdqRdaVm1CxCKAYlxXeSjQPbGoNAn1A/SWjbLF/on5es/Nw8ywKQBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:00:06.615388Z"},"content_sha256":"fa8346ca339459ea403b45e300741cfc605258db8a29b8f4565c3b11624a2be9","schema_version":"1.0","event_id":"sha256:fa8346ca339459ea403b45e300741cfc605258db8a29b8f4565c3b11624a2be9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:RXHCO7JEUCT2RXIJU2VXOIMYTR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global existence to a $3D$ chemotaxis-Navier-stokes system with nonlinear diffusion and rotation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dongfang Zhang, Jiashan Zheng, Weifang Yan, Xinhua Zou, Yanyan Li","submitted_at":"2017-06-07T01:58:31Z","abstract_excerpt":"This paper is concerned with the following quasilinear chemotaxis--Navier--Stokes system with nonlinear diffusion and rotation $$ \\left\\{ \\begin{array}{l} n_t+u\\cdot\\nabla n=\\Delta n^m-\\nabla\\cdot(nS(x,n,c)\\cdot\\nabla c),\\quad x\\in \\Omega, t>0, c_t+u\\cdot\\nabla c=\\Delta c-nc,\\quad x\\in \\Omega, t>0,\\\\ u_t+\\kappa(u \\cdot \\nabla)u+\\nabla P=\\Delta u+n\\nabla \\phi ,\\quad x\\in \\Omega, t>0,\\\\ \\nabla\\cdot u=0,\\quad x\\in \\Omega, t>0 \\end{array}\\right.\\eqno(CNF) $$ is considered under the no-flux boundary conditions for $n, c$ and the Dirichlet boundary condition for $u$ in a three-dimensional convex dom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02022","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":"2026-05-18T00:42:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YwZINCy0lM9d5YQe3lg2YXVXfj5vVrc2XhudWhSdBW3KC8XQsjbzABsK2a3uwcFRVEhFzyB/yzzSpcmQmjFzAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:00:06.615744Z"},"content_sha256":"df5c8cd2ac56b45cad7ec6c2bf0cb05453fe13f6909c11d8bf53ed2cf12e886b","schema_version":"1.0","event_id":"sha256:df5c8cd2ac56b45cad7ec6c2bf0cb05453fe13f6909c11d8bf53ed2cf12e886b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RXHCO7JEUCT2RXIJU2VXOIMYTR/bundle.json","state_url":"https://pith.science/pith/RXHCO7JEUCT2RXIJU2VXOIMYTR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RXHCO7JEUCT2RXIJU2VXOIMYTR/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":"2026-06-26T14:00:06Z","links":{"resolver":"https://pith.science/pith/RXHCO7JEUCT2RXIJU2VXOIMYTR","bundle":"https://pith.science/pith/RXHCO7JEUCT2RXIJU2VXOIMYTR/bundle.json","state":"https://pith.science/pith/RXHCO7JEUCT2RXIJU2VXOIMYTR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RXHCO7JEUCT2RXIJU2VXOIMYTR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RXHCO7JEUCT2RXIJU2VXOIMYTR","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":"9111199fe0dd4ec2907d8d97afb8cfe13ec6d0f076b0dcafd23c6f896f10b8e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-07T01:58:31Z","title_canon_sha256":"17f63e5ee17ed94880018c97fb37b26829e0d5a012d566354bcaf65718c08eb5"},"schema_version":"1.0","source":{"id":"1706.02022","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02022","created_at":"2026-05-18T00:42:50Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02022v1","created_at":"2026-05-18T00:42:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02022","created_at":"2026-05-18T00:42:50Z"},{"alias_kind":"pith_short_12","alias_value":"RXHCO7JEUCT2","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"RXHCO7JEUCT2RXIJ","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"RXHCO7JE","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:df5c8cd2ac56b45cad7ec6c2bf0cb05453fe13f6909c11d8bf53ed2cf12e886b","target":"graph","created_at":"2026-05-18T00:42:50Z","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":"This paper is concerned with the following quasilinear chemotaxis--Navier--Stokes system with nonlinear diffusion and rotation $$ \\left\\{ \\begin{array}{l} n_t+u\\cdot\\nabla n=\\Delta n^m-\\nabla\\cdot(nS(x,n,c)\\cdot\\nabla c),\\quad x\\in \\Omega, t>0, c_t+u\\cdot\\nabla c=\\Delta c-nc,\\quad x\\in \\Omega, t>0,\\\\ u_t+\\kappa(u \\cdot \\nabla)u+\\nabla P=\\Delta u+n\\nabla \\phi ,\\quad x\\in \\Omega, t>0,\\\\ \\nabla\\cdot u=0,\\quad x\\in \\Omega, t>0 \\end{array}\\right.\\eqno(CNF) $$ is considered under the no-flux boundary conditions for $n, c$ and the Dirichlet boundary condition for $u$ in a three-dimensional convex dom","authors_text":"Dongfang Zhang, Jiashan Zheng, Weifang Yan, Xinhua Zou, Yanyan Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-07T01:58:31Z","title":"Global existence to a $3D$ chemotaxis-Navier-stokes system with nonlinear diffusion and rotation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02022","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:fa8346ca339459ea403b45e300741cfc605258db8a29b8f4565c3b11624a2be9","target":"record","created_at":"2026-05-18T00:42:50Z","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":"9111199fe0dd4ec2907d8d97afb8cfe13ec6d0f076b0dcafd23c6f896f10b8e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-07T01:58:31Z","title_canon_sha256":"17f63e5ee17ed94880018c97fb37b26829e0d5a012d566354bcaf65718c08eb5"},"schema_version":"1.0","source":{"id":"1706.02022","kind":"arxiv","version":1}},"canonical_sha256":"8dce277d24a0a7a8dd09a6ab7721989c76bb306e2c91f3182bcccb6041698bf2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8dce277d24a0a7a8dd09a6ab7721989c76bb306e2c91f3182bcccb6041698bf2","first_computed_at":"2026-05-18T00:42:50.470469Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:50.470469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iXMZN5cobdENFX9s6nOpm8fRIXNPH5dLTouKSWcDiNx6cwkhB7k98/2QGiG4XQOiZCw1XIvNh/vr7f6dnqcQAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:50.471170Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.02022","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa8346ca339459ea403b45e300741cfc605258db8a29b8f4565c3b11624a2be9","sha256:df5c8cd2ac56b45cad7ec6c2bf0cb05453fe13f6909c11d8bf53ed2cf12e886b"],"state_sha256":"c156fefc1e10f5ac14548425bd3bccfcdc670441f062d29824cea0973f087fee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RCI8pbEL7FgwUJAKzqvSb5VNStH/Ogj7aQXXG/DB2hPEknjV0T6zEwdjbMQ4GG2J/ObZ0pPUXaZh7CYtN2bBCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T14:00:06.617700Z","bundle_sha256":"7c6a1473492b6b03937098d391e5bac179c2aad481c0efe7580dbbc3548855a2"}}