{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:R55QFNMUUEYGPIRCPXFTJ7X4NN","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":"486440747b9411a3fd3b51456c605515a9ed4904f13e42246ea206d9d9db3f7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-02-25T22:59:26Z","title_canon_sha256":"76ae7690ffaae74a9323f3ca12d33b002f31c4e963bd0f59d83f644041cb87a1"},"schema_version":"1.0","source":{"id":"1402.6365","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.6365","created_at":"2026-05-18T02:40:18Z"},{"alias_kind":"arxiv_version","alias_value":"1402.6365v2","created_at":"2026-05-18T02:40:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.6365","created_at":"2026-05-18T02:40:18Z"},{"alias_kind":"pith_short_12","alias_value":"R55QFNMUUEYG","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"R55QFNMUUEYGPIRC","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"R55QFNMU","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:97c9d45ae05559a3165d962304c678f408b7cb36a19fa80cb6f75bccff11a7e5","target":"graph","created_at":"2026-05-18T02:40:18Z","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 is concerned with effects of noise on the solutions of partial differential equations. We first provide a sufficient condition to ensure the existence of a unique positive solution for a class of stochastic parabolic equations. Then, we prove that noise could induce singularities (finite time blow up of solutions). Finally, we show that a stochastic Allen-Cahn equation does not have finite time singularities and the unique solution exists globally.","authors_text":"Guangying Lv, Jinqiao Duan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-02-25T22:59:26Z","title":"Impacts of Noise on a Class of Partial Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6365","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":"sha256:1876bfa42437c3846070ef664592eb2935a4259e0bbb66855f0714aa10a870ee","target":"record","created_at":"2026-05-18T02:40:18Z","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":"486440747b9411a3fd3b51456c605515a9ed4904f13e42246ea206d9d9db3f7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-02-25T22:59:26Z","title_canon_sha256":"76ae7690ffaae74a9323f3ca12d33b002f31c4e963bd0f59d83f644041cb87a1"},"schema_version":"1.0","source":{"id":"1402.6365","kind":"arxiv","version":2}},"canonical_sha256":"8f7b02b594a13067a2227dcb34fefc6b5e942fd9ff21249a6b3d45c6f92e0388","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f7b02b594a13067a2227dcb34fefc6b5e942fd9ff21249a6b3d45c6f92e0388","first_computed_at":"2026-05-18T02:40:18.428388Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:18.428388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4t924S5/ZLcsC8AC6FyIWCAbGxdROO5mAPdbPVJWjFYwn3s+d8fok5fy2oVAltk+MUIZCpuu7VX+5p+Zjy5zCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:18.429046Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.6365","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1876bfa42437c3846070ef664592eb2935a4259e0bbb66855f0714aa10a870ee","sha256:97c9d45ae05559a3165d962304c678f408b7cb36a19fa80cb6f75bccff11a7e5"],"state_sha256":"cd82a0554c6138c36d43ad290155700658381e473c8c558f74f614d258c36a37"}