{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3ZNDM7NFB4TAIFQ3J65P5RPRBR","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":"89b58406fb52658b2cfd64f14387f830e7a705935e10c55cb595b8ef1bf783e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-17T12:49:57Z","title_canon_sha256":"e4dc4942ebecc64f1d31dd197cfbb40cb42e4440a30a29d59284a33a755e2f23"},"schema_version":"1.0","source":{"id":"1705.06131","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.06131","created_at":"2026-05-18T00:15:05Z"},{"alias_kind":"arxiv_version","alias_value":"1705.06131v1","created_at":"2026-05-18T00:15:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.06131","created_at":"2026-05-18T00:15:05Z"},{"alias_kind":"pith_short_12","alias_value":"3ZNDM7NFB4TA","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3ZNDM7NFB4TAIFQ3","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3ZNDM7NF","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:b4604a79bd3962ddcc6e23baeb57091c9b4c87ea9a6026cbf890017c5115df11","target":"graph","created_at":"2026-05-18T00:15:05Z","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":"We study the chemotaxis-fluid system \\begin{align*} \\left\\{ \\begin{array}{r@{\\,}c@{\\,}c@{\\ }l@{\\quad}l@{\\quad}l@{\\,}c} n_{t}&+&u\\cdot\\!\\nabla n&=\\Delta n-\\nabla\\!\\cdot(\\frac{n}{c}\\nabla c),\\ &x\\in\\Omega,& t>0, c_{t}&+&u\\cdot\\!\\nabla c&=\\Delta c-nc,\\ &x\\in\\Omega,& t>0, u_{t}&+&\\nabla P&=\\Delta u+n\\nabla\\phi,\\ &x\\in\\Omega,& t>0, &&\\nabla\\cdot u&=0,\\ &x\\in\\Omega,& t>0, \\end{array}\\right. \\end{align*} under homogeneous Neumann boundary conditions for $n$ and $c$ and homogeneous Dirichlet boundary conditions for $u$, where $\\Omega\\subset\\mathbb{R}^2$ is a bounded domain with smooth boundary and $\\p","authors_text":"Tobias Black","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-17T12:49:57Z","title":"Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06131","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":"sha256:452af7e52deced92a87edb5bc08d7b1ba3de27411d754f28ace3b1849dc06c34","target":"record","created_at":"2026-05-18T00:15:05Z","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":"89b58406fb52658b2cfd64f14387f830e7a705935e10c55cb595b8ef1bf783e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-17T12:49:57Z","title_canon_sha256":"e4dc4942ebecc64f1d31dd197cfbb40cb42e4440a30a29d59284a33a755e2f23"},"schema_version":"1.0","source":{"id":"1705.06131","kind":"arxiv","version":1}},"canonical_sha256":"de5a367da50f2604161b4fbafec5f10c460ece2315cbb447eeeb80a1e02f81c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de5a367da50f2604161b4fbafec5f10c460ece2315cbb447eeeb80a1e02f81c5","first_computed_at":"2026-05-18T00:15:05.557113Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:05.557113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sC7wVYWtBBp8Wex1htGnTF1liHQTqzunDdoW/ky9odJP2GAvHh2wiVArGo4ipAT4ajdwI9JrnVyKYvOnjX0YDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:05.557702Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.06131","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:452af7e52deced92a87edb5bc08d7b1ba3de27411d754f28ace3b1849dc06c34","sha256:b4604a79bd3962ddcc6e23baeb57091c9b4c87ea9a6026cbf890017c5115df11"],"state_sha256":"a83421a14808fb4410622a67d4f6916590f734b115aae538345a2161cb58c677"}