{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XTS2ILCVT2NAI4K4JZEIBOFZJU","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":"259103095c2ceeae12755d8a9dced0538cbc38bcd2b22a1f8dd3df78da857591","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-24T16:44:54Z","title_canon_sha256":"55e3e3c284430eb158e9f2e633c73a7829e6186289e338764edb8a3be746270f"},"schema_version":"1.0","source":{"id":"1806.09177","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.09177","created_at":"2026-05-18T00:04:55Z"},{"alias_kind":"arxiv_version","alias_value":"1806.09177v1","created_at":"2026-05-18T00:04:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.09177","created_at":"2026-05-18T00:04:55Z"},{"alias_kind":"pith_short_12","alias_value":"XTS2ILCVT2NA","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XTS2ILCVT2NAI4K4","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XTS2ILCV","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:3ababf884fabccd8fe4959968330300118e07a6b6c09ac787d5c353860ceff40","target":"graph","created_at":"2026-05-18T00:04:55Z","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":"A class of Keller-Segel-Stokes systems generalizing the prototype \\[\n  \\left\\{ \\begin{array}{rcl}\n  n_t + u\\cdot\\nabla n &=& \\Delta n - \\nabla \\cdot \\Big(n(n+1)^{-\\alpha}\\nabla c\\Big),\n  c_t + u\\cdot\\nabla c &=& \\Delta c-c+n,\n  u_t +\\nabla P &=& \\Delta u + n \\nabla \\phi + f(x,t), \\qquad \\nabla\\cdot u =0,\n  \\end{array} \\right.\n  \\qquad \\qquad (\\star) \\] is considered in a bounded domain $\\Omega\\subset R^3$, where $\\phi$ and $f$ are given sufficiently smooth functions such that $f$ is bounded in $\\Omega\\times (0,\\infty)$.\n  It is shown that under the condition that \n\\[\n  \\alpha>\\frac{1}{3}, \\] f","authors_text":"Michael Winkler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-24T16:44:54Z","title":"Does fluid interaction affect regularity in the three-dimensional Keller-Segel system with saturated sensitivity?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09177","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:f81cff15f6906459163daf289ab94c6c663df83526561d9809863ff72ec7a8c5","target":"record","created_at":"2026-05-18T00:04:55Z","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":"259103095c2ceeae12755d8a9dced0538cbc38bcd2b22a1f8dd3df78da857591","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-24T16:44:54Z","title_canon_sha256":"55e3e3c284430eb158e9f2e633c73a7829e6186289e338764edb8a3be746270f"},"schema_version":"1.0","source":{"id":"1806.09177","kind":"arxiv","version":1}},"canonical_sha256":"bce5a42c559e9a04715c4e4880b8b94d045c239a36dbab0a9bf9c75c47f3eac9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bce5a42c559e9a04715c4e4880b8b94d045c239a36dbab0a9bf9c75c47f3eac9","first_computed_at":"2026-05-18T00:04:55.828059Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:55.828059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kgF9016/XLashA7+k/TYUuG6YcjZ3dxf43iaT6OOhlnecAAlOhzNUPhRmBh60WrQkshmiuvKObZwXgUJrCHxAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:55.828514Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.09177","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f81cff15f6906459163daf289ab94c6c663df83526561d9809863ff72ec7a8c5","sha256:3ababf884fabccd8fe4959968330300118e07a6b6c09ac787d5c353860ceff40"],"state_sha256":"a79a325ab6e66656ec759574b6bdb6c22c496c00c95410606cc9395bdbd983f2"}