{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:XOXBHZBF5NSIAT4Q5PBXAOBHPS","short_pith_number":"pith:XOXBHZBF","schema_version":"1.0","canonical_sha256":"bbae13e425eb64804f90ebc37038277cb8b5436e976d764be01a56b076695220","source":{"kind":"arxiv","id":"1805.05263","version":1},"attestation_state":"computed","paper":{"title":"The fast signal diffusion limit in Keller-Segel(-fluid) systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Michael Winkler, Yulan Wang, Zhaoyin Xiang","submitted_at":"2018-05-14T16:21:40Z","abstract_excerpt":"This paper deals with convergence of solutions to a class of parabolic Keller-Segel systems, possibly coupled to the (Navier-)Stokes equations in the framework of the full model \\begin{eqnarray*}\n  \\left\\{ \\begin{array}{lcl}\n  \\, \\, \\partial_t n_{\\epsilon} + u_{\\epsilon} \\cdot \\nabla n_{\\epsilon}\n  &=& \\Delta n_{\\epsilon} - \\nabla \\cdot \\Big( n_{\\epsilon} S(x, n_{\\epsilon}, c_{\\epsilon})\\cdot\\nabla c_{\\epsilon}\\Big) + f(x, n_{\\epsilon}, c_{\\epsilon}), \\\\[1mm]\n  \\epsilon \\partial_t c_{\\epsilon} + u_{\\epsilon}\\cdot\\nabla c_{\\epsilon}\n  &=& \\Delta c_{\\epsilon} - c_{\\epsilon} + n_{\\epsilon} , \\\\[1"},"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":"1805.05263","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-14T16:21:40Z","cross_cats_sorted":[],"title_canon_sha256":"943b056f22ea338be4500721e567fad64a0560132b9b73aaa5809ec66d237dc5","abstract_canon_sha256":"c6de408b0f6a5a4ac5114ad3e3fddf22ad0b273ed302e9aed9987f67cf5d7ff0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:03.583154Z","signature_b64":"9IXzTT15F3kwfwhpYnk3vS4H5b1HrxnN8J9sxiukg868PQKaAPZWac5K9kA0jElfLsQHDkon0Tu+NushEhXUAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bbae13e425eb64804f90ebc37038277cb8b5436e976d764be01a56b076695220","last_reissued_at":"2026-05-18T00:16:03.582789Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:03.582789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The fast signal diffusion limit in Keller-Segel(-fluid) systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Michael Winkler, Yulan Wang, Zhaoyin Xiang","submitted_at":"2018-05-14T16:21:40Z","abstract_excerpt":"This paper deals with convergence of solutions to a class of parabolic Keller-Segel systems, possibly coupled to the (Navier-)Stokes equations in the framework of the full model \\begin{eqnarray*}\n  \\left\\{ \\begin{array}{lcl}\n  \\, \\, \\partial_t n_{\\epsilon} + u_{\\epsilon} \\cdot \\nabla n_{\\epsilon}\n  &=& \\Delta n_{\\epsilon} - \\nabla \\cdot \\Big( n_{\\epsilon} S(x, n_{\\epsilon}, c_{\\epsilon})\\cdot\\nabla c_{\\epsilon}\\Big) + f(x, n_{\\epsilon}, c_{\\epsilon}), \\\\[1mm]\n  \\epsilon \\partial_t c_{\\epsilon} + u_{\\epsilon}\\cdot\\nabla c_{\\epsilon}\n  &=& \\Delta c_{\\epsilon} - c_{\\epsilon} + n_{\\epsilon} , \\\\[1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05263","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1805.05263","created_at":"2026-05-18T00:16:03.582849+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.05263v1","created_at":"2026-05-18T00:16:03.582849+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.05263","created_at":"2026-05-18T00:16:03.582849+00:00"},{"alias_kind":"pith_short_12","alias_value":"XOXBHZBF5NSI","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_16","alias_value":"XOXBHZBF5NSIAT4Q","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_8","alias_value":"XOXBHZBF","created_at":"2026-05-18T12:33:01.666342+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/XOXBHZBF5NSIAT4Q5PBXAOBHPS","json":"https://pith.science/pith/XOXBHZBF5NSIAT4Q5PBXAOBHPS.json","graph_json":"https://pith.science/api/pith-number/XOXBHZBF5NSIAT4Q5PBXAOBHPS/graph.json","events_json":"https://pith.science/api/pith-number/XOXBHZBF5NSIAT4Q5PBXAOBHPS/events.json","paper":"https://pith.science/paper/XOXBHZBF"},"agent_actions":{"view_html":"https://pith.science/pith/XOXBHZBF5NSIAT4Q5PBXAOBHPS","download_json":"https://pith.science/pith/XOXBHZBF5NSIAT4Q5PBXAOBHPS.json","view_paper":"https://pith.science/paper/XOXBHZBF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.05263&json=true","fetch_graph":"https://pith.science/api/pith-number/XOXBHZBF5NSIAT4Q5PBXAOBHPS/graph.json","fetch_events":"https://pith.science/api/pith-number/XOXBHZBF5NSIAT4Q5PBXAOBHPS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XOXBHZBF5NSIAT4Q5PBXAOBHPS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XOXBHZBF5NSIAT4Q5PBXAOBHPS/action/storage_attestation","attest_author":"https://pith.science/pith/XOXBHZBF5NSIAT4Q5PBXAOBHPS/action/author_attestation","sign_citation":"https://pith.science/pith/XOXBHZBF5NSIAT4Q5PBXAOBHPS/action/citation_signature","submit_replication":"https://pith.science/pith/XOXBHZBF5NSIAT4Q5PBXAOBHPS/action/replication_record"}},"created_at":"2026-05-18T00:16:03.582849+00:00","updated_at":"2026-05-18T00:16:03.582849+00:00"}