{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4YWSWHJFD6ILFKB6I4CJRRXHGK","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":"61b724d2cd13ed8fc407259de5ee42e4cf808623540569656f417df8f82b8239","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-28T06:07:15Z","title_canon_sha256":"ed5cb3c66485d4647befdb29bd07bbc81cc2a73fa78de7e77edd01b1656f2c9e"},"schema_version":"1.0","source":{"id":"1901.00045","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.00045","created_at":"2026-05-17T23:47:15Z"},{"alias_kind":"arxiv_version","alias_value":"1901.00045v2","created_at":"2026-05-17T23:47:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.00045","created_at":"2026-05-17T23:47:15Z"},{"alias_kind":"pith_short_12","alias_value":"4YWSWHJFD6IL","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4YWSWHJFD6ILFKB6","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4YWSWHJF","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:5908ec926716b2903eaa9d8c44ad28931e460e2b6d73a43219eab7eb7b622e18","target":"graph","created_at":"2026-05-17T23:47:15Z","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":"The current paper is concerned with the spatial spreading speed and minimal wave speed of the following Keller-Segel chemoattraction system, \\begin{equation}\\label{abstract-eq1} \\begin{cases} u_t=u_{xx}-\\chi(uv_x)_x +u(a-bu),\\quad x\\in\\R\\cr 0=v_{xx}- \\lambda v+\\mu u,\\quad x\\in\\R, \\end{cases} \\end{equation} where $\\chi$, $a$, $b$, $\\lambda$, and $\\mu$ are positive constants.\n  Assume $b>\\chi\\mu$. Then if in addition, $\\big(1+\\frac{1}{2}\\frac{(\\sqrt{a}-\\sqrt{\\lambda})_+}{(\\sqrt{a}+\\sqrt{\\la})}\\big)\\chi\\mu { \\leq} b$ holds, it is proved that $c_0^*=2\\sqrt a$ is the spreading speed of the solution","authors_text":"Rachidi B. Salako, Shuwen Xue, Wenxian Shen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-28T06:07:15Z","title":"Can chemotaxis speed up or slow down the spatial spreading in parabolic-elliptic Keller-Segel systems with logistic source?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.00045","kind":"arxiv","version":2},"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":"sha256:4d1066412093576174887e7e8aaa3a06b1bf733a6506775112981e89f4807ff9","target":"record","created_at":"2026-05-17T23:47:15Z","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":"61b724d2cd13ed8fc407259de5ee42e4cf808623540569656f417df8f82b8239","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-28T06:07:15Z","title_canon_sha256":"ed5cb3c66485d4647befdb29bd07bbc81cc2a73fa78de7e77edd01b1656f2c9e"},"schema_version":"1.0","source":{"id":"1901.00045","kind":"arxiv","version":2}},"canonical_sha256":"e62d2b1d251f90b2a83e470498c6e732bf744ed9622ed05c0d2d67bdb141130c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e62d2b1d251f90b2a83e470498c6e732bf744ed9622ed05c0d2d67bdb141130c","first_computed_at":"2026-05-17T23:47:15.724480Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:15.724480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hmfpFwRFcZft1uZAp7/E19Sf1hRWYkQBzqw0aYR9UQev6s+CtZX+s3ilKsrcBDc7KoVzj0FEQ8u5hG4241OBAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:15.724877Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.00045","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d1066412093576174887e7e8aaa3a06b1bf733a6506775112981e89f4807ff9","sha256:5908ec926716b2903eaa9d8c44ad28931e460e2b6d73a43219eab7eb7b622e18"],"state_sha256":"9fb54987b8fd2e04608ffd0bbec9bfffa5b6ef9115c446947070e40c70592375"}