{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:TC2AK3EUU77WYX6JOS2U6YSAYJ","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":"6702f23d3b7f00b2c4d250bca09f40bf6ab9fd9a50ffe15e33bc98dc0be0e7c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-19T18:15:50Z","title_canon_sha256":"80ff62564f56b4b168eae6d24a5fdf656ba3b5c8c4457ef3c84c7612adfc5d7d"},"schema_version":"1.0","source":{"id":"1903.08196","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.08196","created_at":"2026-05-17T23:50:50Z"},{"alias_kind":"arxiv_version","alias_value":"1903.08196v1","created_at":"2026-05-17T23:50:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.08196","created_at":"2026-05-17T23:50:50Z"},{"alias_kind":"pith_short_12","alias_value":"TC2AK3EUU77W","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"TC2AK3EUU77WYX6J","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"TC2AK3EU","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:151c7528e137d08b8595dda7e5426dcc2967a626aaa448a3375d94d2cbaddcc7","target":"graph","created_at":"2026-05-17T23:50:50Z","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":"In this paper we study classical solutions to the zero--flux attraction--repulsion chemotaxis--system \\begin{equation}\\label{ProblemAbstract} \\tag{$\\Diamond$} \\begin{cases} u_{ t}=\\Delta u -\\chi \\nabla \\cdot (u\\nabla v)+\\xi \\nabla \\cdot (u\\nabla w) & \\textrm{in }\\Omega\\times (0,t^*), \\\\ 0=\\Delta v+\\alpha u-\\beta v & \\textrm{in } \\Omega\\times (0,t^*),\\\\ 0=\\Delta w+\\gamma u-\\delta w & \\textrm{in } \\Omega\\times (0,t^*),\\\\ \\end{cases} \\end{equation} where $\\Omega$ is a smooth and bounded domain of $\\mathbb{R}^2$, $t^*$ is the blow--up time and $\\alpha,\\beta,\\gamma,\\delta,\\chi,\\xi$ are positive rea","authors_text":"Giuseppe Viglialoro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-19T18:15:50Z","title":"Explicit lower bound of blow--up time for an attraction--repulsion chemotaxis system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.08196","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:e48ebe3b73774f9dc1816a451cd606197bb53fe2c6610a01a0b79e95d293f2e2","target":"record","created_at":"2026-05-17T23:50:50Z","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":"6702f23d3b7f00b2c4d250bca09f40bf6ab9fd9a50ffe15e33bc98dc0be0e7c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-19T18:15:50Z","title_canon_sha256":"80ff62564f56b4b168eae6d24a5fdf656ba3b5c8c4457ef3c84c7612adfc5d7d"},"schema_version":"1.0","source":{"id":"1903.08196","kind":"arxiv","version":1}},"canonical_sha256":"98b4056c94a7ff6c5fc974b54f6240c2589a42dc449cfba82c72b8e45787ae09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98b4056c94a7ff6c5fc974b54f6240c2589a42dc449cfba82c72b8e45787ae09","first_computed_at":"2026-05-17T23:50:50.089726Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:50.089726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q0ktEhK2CXc7HMwYT8cPo7lBx9DhdXY3obl1Qa/m+/f0iOuvSXOpNrqiobqugMqYZfrosTAmkFWraEiRWRe7BQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:50.090461Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.08196","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e48ebe3b73774f9dc1816a451cd606197bb53fe2c6610a01a0b79e95d293f2e2","sha256:151c7528e137d08b8595dda7e5426dcc2967a626aaa448a3375d94d2cbaddcc7"],"state_sha256":"7f88f4f8da9e55807e60ba3039e42f4e3136cc53c86398f0d503d67f8ba1d289"}