{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:3RR6TFQRTLWZPGKOJSB3YVQKIH","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":"c4b4f350324d7d645f527969a67ff7a7a75ab79932c58736f2b441d50dcf3a6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-26T08:12:49Z","title_canon_sha256":"27b7940ee30d4db9bf2da11104428b7b7690a3224358d09d69435bdd04331709"},"schema_version":"1.0","source":{"id":"1902.09787","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.09787","created_at":"2026-05-17T23:52:35Z"},{"alias_kind":"arxiv_version","alias_value":"1902.09787v1","created_at":"2026-05-17T23:52:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.09787","created_at":"2026-05-17T23:52:35Z"},{"alias_kind":"pith_short_12","alias_value":"3RR6TFQRTLWZ","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"3RR6TFQRTLWZPGKO","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"3RR6TFQR","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:4b3a846c8c2809625a2ad80323100c9f7e7790a88bb5b86e0cba1abb7801cfa0","target":"graph","created_at":"2026-05-17T23:52:35Z","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":"This paper deals with a lower bound for the blow-up time for solutions of the fully parabolic chemotaxis system \\begin{equation*}\n  \\begin{cases}\n  u_t=\\nabla \\cdot [(u+\\alpha)^{m_1-1}\n  \\nabla u-\\chi u(u+\\alpha)^{m_2-2}\n  \\nabla v]\n  & {\\rm in} \\; \\Omega \\times (0,T), \\\\[1mm]\n  v_t=\\Delta v-v+u\n  & {\\rm in} \\; \\Omega \\times (0,T)\n  \\end{cases} \\end{equation*} under Neumann boundary conditions and initial conditions, where $\\Omega$ is a general bounded domain in $\\mathbb{R}^n$ with smooth boundary, $\\alpha>0$, $\\chi>0$, $m_1, m_2 \\in \\mathbb{R}$ and $T>0$. Recently, Anderson-Deng (2017) gave a","authors_text":"Teruto Nishino, Tomomi Yokota","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-26T08:12:49Z","title":"Effect of nonlinear diffusion on a lower bound for the blow-up time in a fully parabolic chemotaxis system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09787","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":"sha256:4e516c6b7da358541277e62a69d56d89b4187e8bec1edcf8920f7e95c8c27bbb","target":"record","created_at":"2026-05-17T23:52:35Z","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":"c4b4f350324d7d645f527969a67ff7a7a75ab79932c58736f2b441d50dcf3a6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-26T08:12:49Z","title_canon_sha256":"27b7940ee30d4db9bf2da11104428b7b7690a3224358d09d69435bdd04331709"},"schema_version":"1.0","source":{"id":"1902.09787","kind":"arxiv","version":1}},"canonical_sha256":"dc63e996119aed97994e4c83bc560a41cadec8413d94bad0936ea6c0e4022c44","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc63e996119aed97994e4c83bc560a41cadec8413d94bad0936ea6c0e4022c44","first_computed_at":"2026-05-17T23:52:35.372423Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:35.372423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PrRCTA/hwsjbZOMVn4EwzXg9j2KJXj5DAICLbo4sPv+g6aIIyAdSn3xoJsSdgqjFhH+8nsC50V7S3S8tAWOeAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:35.372996Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.09787","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e516c6b7da358541277e62a69d56d89b4187e8bec1edcf8920f7e95c8c27bbb","sha256:4b3a846c8c2809625a2ad80323100c9f7e7790a88bb5b86e0cba1abb7801cfa0"],"state_sha256":"e3cfdb30a8f0188822909cae5a165970a975eaf990c0eac7667e775de9c22d66"}