{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DLFK3W7G7YOFHL7WV5IFUQWIJJ","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":"ec536dea990dac657178d1a71ded2d720aa7941c92afa8a69ad7738e09032b57","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-19T11:46:52Z","title_canon_sha256":"f422c75d768601c6c92ce85742439f21ff4c885bd3759b22b55748e1baf6be31"},"schema_version":"1.0","source":{"id":"1704.05702","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05702","created_at":"2026-05-18T00:46:06Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05702v1","created_at":"2026-05-18T00:46:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05702","created_at":"2026-05-18T00:46:06Z"},{"alias_kind":"pith_short_12","alias_value":"DLFK3W7G7YOF","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"DLFK3W7G7YOFHL7W","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"DLFK3W7G","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:e75e1d79b1e907072eb9203c1805ca9fdaf1015eea8e3793fdea649178c4caab","target":"graph","created_at":"2026-05-18T00:46:06Z","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":"Let $G=(V,E)$ be a locally finite connected weighted graph, $\\Delta$ be the usual graph Laplacian. In this paper, we study the blow-up problems for the nonlinear parabolic equation $u_t=\\Delta u + f(u)$ on $G$. The blow-up phenomenons of the equation are discussed in terms of two cases: (i) an initial condition is given; (ii) a Dirichlet boundary condition is given. We prove that if $f$ satisfies appropriate conditions, then the solution of the equation blows up in a finite time.","authors_text":"Yiting Wu, Yong Lin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-19T11:46:52Z","title":"Blow-up problems for nonlinear parabolic equations on locally finite graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05702","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":"sha256:99343366ce308ee6cdaca9fb79b4f0b2ccbc2c0e61ac75251882c1e4c3d9de4a","target":"record","created_at":"2026-05-18T00:46:06Z","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":"ec536dea990dac657178d1a71ded2d720aa7941c92afa8a69ad7738e09032b57","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-19T11:46:52Z","title_canon_sha256":"f422c75d768601c6c92ce85742439f21ff4c885bd3759b22b55748e1baf6be31"},"schema_version":"1.0","source":{"id":"1704.05702","kind":"arxiv","version":1}},"canonical_sha256":"1acaaddbe6fe1c53aff6af505a42c84a43c001658ab64c51210606fdde3a1954","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1acaaddbe6fe1c53aff6af505a42c84a43c001658ab64c51210606fdde3a1954","first_computed_at":"2026-05-18T00:46:06.743261Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:06.743261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tVvYXPDYI5BVwUYK62QGwIuH8OvmSzgtTqmvdQCgpO/txcvFyO0Oal93GC9pQu5Shvj36oiFoNOHZxk1JAJeCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:06.743825Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.05702","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99343366ce308ee6cdaca9fb79b4f0b2ccbc2c0e61ac75251882c1e4c3d9de4a","sha256:e75e1d79b1e907072eb9203c1805ca9fdaf1015eea8e3793fdea649178c4caab"],"state_sha256":"269a1f2ccab8a13a0433707bc270af2566cce94ac46e1273117acc606f6fc66c"}