{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:3OQILUFYTHY6ONROIVMKFT5SRK","short_pith_number":"pith:3OQILUFY","schema_version":"1.0","canonical_sha256":"dba085d0b899f1e7362e4558a2cfb28aa70bf580ca1f72db7a0b182ca1a3b63f","source":{"kind":"arxiv","id":"1806.07067","version":2},"attestation_state":"computed","paper":{"title":"An optimal result for global existence and boundedness in a three-dimensional Keller-Segel(-Navier)-Stokes system (involving a tensor-valued sensitivity with saturation)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiashan Zheng","submitted_at":"2018-06-19T07:07:04Z","abstract_excerpt":"The coupled quasilinear Keller-Segel-Navier-Stokes system $$\n  \\left\\{\n  \\begin{array}{l} n_t+u\\cdot\\nabla n=\\Delta n-\\nabla\\cdot(nS(x,n,c)\\nabla c),\\quad x\\in \\Omega, t>0, c_t+u\\cdot\\nabla c=\\Delta c-c+n,\\quad x\\in \\Omega, t>0, u_t+\\kappa(u \\cdot \\nabla)u+\\nabla P=\\Delta u+n\\nabla \\phi,\\quad x\\in \\Omega, t>0, \\nabla\\cdot u=0,\\quad x\\in \\Omega, t>0 \\end{array}\\right.\\eqno(KSNF)\n  $$ is considered under Neumann boundary conditions for $n$ and $c$ and no-slip boundary conditions for $u$ in three-dimensional bounded domains $\\Omega\\subseteq \\mathbb{R}^3$ with smooth boundary, where $\\kappa\\in \\ma"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1806.07067","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-19T07:07:04Z","cross_cats_sorted":[],"title_canon_sha256":"5282b350736032de8f9f5f470715a8bd08967454169e9f26a5002b1815552156","abstract_canon_sha256":"04c074d74d8af9f340a91f89b7841e8d05dcb6065485b4e009ba310bc5ba8fab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:56.600809Z","signature_b64":"OkfC4bU9kz43I36g2LqTds1o10XT9ZFixBvkU//Kpx/SrKwseisFcKPRNZ45id8JiCKqqG2P6XrMRI9FGVcbCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dba085d0b899f1e7362e4558a2cfb28aa70bf580ca1f72db7a0b182ca1a3b63f","last_reissued_at":"2026-05-18T00:11:56.600165Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:56.600165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An optimal result for global existence and boundedness in a three-dimensional Keller-Segel(-Navier)-Stokes system (involving a tensor-valued sensitivity with saturation)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiashan Zheng","submitted_at":"2018-06-19T07:07:04Z","abstract_excerpt":"The coupled quasilinear Keller-Segel-Navier-Stokes system $$\n  \\left\\{\n  \\begin{array}{l} n_t+u\\cdot\\nabla n=\\Delta n-\\nabla\\cdot(nS(x,n,c)\\nabla c),\\quad x\\in \\Omega, t>0, c_t+u\\cdot\\nabla c=\\Delta c-c+n,\\quad x\\in \\Omega, t>0, u_t+\\kappa(u \\cdot \\nabla)u+\\nabla P=\\Delta u+n\\nabla \\phi,\\quad x\\in \\Omega, t>0, \\nabla\\cdot u=0,\\quad x\\in \\Omega, t>0 \\end{array}\\right.\\eqno(KSNF)\n  $$ is considered under Neumann boundary conditions for $n$ and $c$ and no-slip boundary conditions for $u$ in three-dimensional bounded domains $\\Omega\\subseteq \\mathbb{R}^3$ with smooth boundary, where $\\kappa\\in \\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07067","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1806.07067","created_at":"2026-05-18T00:11:56.600250+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.07067v2","created_at":"2026-05-18T00:11:56.600250+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07067","created_at":"2026-05-18T00:11:56.600250+00:00"},{"alias_kind":"pith_short_12","alias_value":"3OQILUFYTHY6","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"3OQILUFYTHY6ONRO","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"3OQILUFY","created_at":"2026-05-18T12:32:02.567920+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3OQILUFYTHY6ONROIVMKFT5SRK","json":"https://pith.science/pith/3OQILUFYTHY6ONROIVMKFT5SRK.json","graph_json":"https://pith.science/api/pith-number/3OQILUFYTHY6ONROIVMKFT5SRK/graph.json","events_json":"https://pith.science/api/pith-number/3OQILUFYTHY6ONROIVMKFT5SRK/events.json","paper":"https://pith.science/paper/3OQILUFY"},"agent_actions":{"view_html":"https://pith.science/pith/3OQILUFYTHY6ONROIVMKFT5SRK","download_json":"https://pith.science/pith/3OQILUFYTHY6ONROIVMKFT5SRK.json","view_paper":"https://pith.science/paper/3OQILUFY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.07067&json=true","fetch_graph":"https://pith.science/api/pith-number/3OQILUFYTHY6ONROIVMKFT5SRK/graph.json","fetch_events":"https://pith.science/api/pith-number/3OQILUFYTHY6ONROIVMKFT5SRK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3OQILUFYTHY6ONROIVMKFT5SRK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3OQILUFYTHY6ONROIVMKFT5SRK/action/storage_attestation","attest_author":"https://pith.science/pith/3OQILUFYTHY6ONROIVMKFT5SRK/action/author_attestation","sign_citation":"https://pith.science/pith/3OQILUFYTHY6ONROIVMKFT5SRK/action/citation_signature","submit_replication":"https://pith.science/pith/3OQILUFYTHY6ONROIVMKFT5SRK/action/replication_record"}},"created_at":"2026-05-18T00:11:56.600250+00:00","updated_at":"2026-05-18T00:11:56.600250+00:00"}