{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:WU2NF6F7GDDQKG2UYZ33UVXC2E","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":"8bac97fb9bb99ebf8276039cefcc6636a7557f77da7766a5eb07ef4cf7467810","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-03-03T02:40:39Z","title_canon_sha256":"48825dfb4fc256f15a0096d836c98a7b79d1adca0898c34f17df0fae0485010f"},"schema_version":"1.0","source":{"id":"0903.0428","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.0428","created_at":"2026-05-18T03:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"0903.0428v2","created_at":"2026-05-18T03:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.0428","created_at":"2026-05-18T03:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"WU2NF6F7GDDQ","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"WU2NF6F7GDDQKG2U","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"WU2NF6F7","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:6f57dc6eae9ceb90bcbdd8ac2ee26ecc17d262a0ad24d10a4aaaf3e4489b43c0","target":"graph","created_at":"2026-05-18T03:52:12Z","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 describe the asymptotic behavior, in the exponential time scale, of solutions to quasi-linear parabolic equations with a small parameter at the second order term and the long time behavior of corresponding diffusion processes. In particular, we discuss the exit problem and metastability for the processes corresponding to quasi-linear initial-boundary value problems.","authors_text":"L. Koralov, M. Freidlin","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-03-03T02:40:39Z","title":"Nonlinear Stochastic Perturbations of Dynamical Systems and Quasi-linear Parabolic PDE's with a Small Parameter"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.0428","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:fc61771f31a3852ffad0f7360cd8ee47ae40b6b713be613fb6367cae835e3e7f","target":"record","created_at":"2026-05-18T03:52:12Z","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":"8bac97fb9bb99ebf8276039cefcc6636a7557f77da7766a5eb07ef4cf7467810","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-03-03T02:40:39Z","title_canon_sha256":"48825dfb4fc256f15a0096d836c98a7b79d1adca0898c34f17df0fae0485010f"},"schema_version":"1.0","source":{"id":"0903.0428","kind":"arxiv","version":2}},"canonical_sha256":"b534d2f8bf30c7051b54c677ba56e2d1397ab0dfe5ccc8f32536448bf3b1c79b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b534d2f8bf30c7051b54c677ba56e2d1397ab0dfe5ccc8f32536448bf3b1c79b","first_computed_at":"2026-05-18T03:52:12.766291Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:12.766291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cRO9wV2jKnMERQHZzxDuAlmC8VBoc9mFwqKAtEimtAFmEKgySCg5OWLAt396AiGwCba1uwpza33ZHPWo1e5MAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:12.767156Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.0428","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc61771f31a3852ffad0f7360cd8ee47ae40b6b713be613fb6367cae835e3e7f","sha256:6f57dc6eae9ceb90bcbdd8ac2ee26ecc17d262a0ad24d10a4aaaf3e4489b43c0"],"state_sha256":"9655f49263ac7c6a1fd4eb165cf03a65296c7e76c2d62c42fb331fc9d7fb53ef"}