{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZHB7PXHGLJUU2ULLGA5EDNT7AE","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":"f8509313901a76e17ae84bedd02394b2c93883c808bf853d0cb8705bbd645961","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-19T10:25:58Z","title_canon_sha256":"e305984509b1c73baa21ba4f15cfc6b8a74eae55612000b7ef35deefd3cf04e8"},"schema_version":"1.0","source":{"id":"1712.06853","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.06853","created_at":"2026-05-18T00:13:04Z"},{"alias_kind":"arxiv_version","alias_value":"1712.06853v2","created_at":"2026-05-18T00:13:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.06853","created_at":"2026-05-18T00:13:04Z"},{"alias_kind":"pith_short_12","alias_value":"ZHB7PXHGLJUU","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZHB7PXHGLJUU2ULL","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZHB7PXHG","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:621c4997637c89d0f2057b495bb7c6d323ffff926299cb6b9af3ef13348c778e","target":"graph","created_at":"2026-05-18T00:13:04Z","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 introduce a straightforward method to analyze the blow-up of systems of ordinary differential inequalities, and apply it to study the blow- up of solutions to a weakly coupled system of semilinear heat equations. We prove that the solution blows up in a finite time under the subcritical condition. Moreover, we give estimates of lifespan of the solution and lower estimates of the blow-up rate for a localized average of each component.","authors_text":"Kazumasa Fujiwara, Masahiro Ikeda, Yuta Wakasugi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-19T10:25:58Z","title":"Revisit on the blow-up rate of solutions for a weakly coupled system of semilinear heat equations in the subcritical case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06853","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":"sha256:0a7fbe79b81e6e83adc14eeaf7c22d68010a62bfa085c597f5057fb72d75e7a6","target":"record","created_at":"2026-05-18T00:13:04Z","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":"f8509313901a76e17ae84bedd02394b2c93883c808bf853d0cb8705bbd645961","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-19T10:25:58Z","title_canon_sha256":"e305984509b1c73baa21ba4f15cfc6b8a74eae55612000b7ef35deefd3cf04e8"},"schema_version":"1.0","source":{"id":"1712.06853","kind":"arxiv","version":2}},"canonical_sha256":"c9c3f7dce65a694d516b303a41b67f01205083f262173fbf48b96c18c8090c8e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9c3f7dce65a694d516b303a41b67f01205083f262173fbf48b96c18c8090c8e","first_computed_at":"2026-05-18T00:13:04.928624Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:04.928624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZdnVC/L4zu+J9hnVknkLqS06m/8GSjrLRRfA3U2LlRtZPKLJIOF5X0LZio+mmmC7Y22yf5VpRYy+hY5Nb7JEDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:04.929257Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.06853","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a7fbe79b81e6e83adc14eeaf7c22d68010a62bfa085c597f5057fb72d75e7a6","sha256:621c4997637c89d0f2057b495bb7c6d323ffff926299cb6b9af3ef13348c778e"],"state_sha256":"46d72d6ec39274c33d6355168051a6f3317e2263c68c15d9d3d403dd5155e62e"}