{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:2FDZ4IBI3X7WSUA5CJSEDKY4J5","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":"8fb067997ea88c3ee8c360d6bdef02a2e16ca61e0e582a5943ba5c7a48f791dc","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-05-14T12:20:58Z","title_canon_sha256":"64f7764c724dc06f6aaae20606fa4cecb1a1a97d27c3d932d397def5421d2d56"},"schema_version":"1.0","source":{"id":"1005.2505","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.2505","created_at":"2026-05-18T04:34:37Z"},{"alias_kind":"arxiv_version","alias_value":"1005.2505v1","created_at":"2026-05-18T04:34:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.2505","created_at":"2026-05-18T04:34:37Z"},{"alias_kind":"pith_short_12","alias_value":"2FDZ4IBI3X7W","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2FDZ4IBI3X7WSUA5","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2FDZ4IBI","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:bfea5b62cd1d2c973a61bd29eaf15c92217580e7fee40988a3ac2125be334ca4","target":"graph","created_at":"2026-05-18T04:34:37Z","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":"Second initial boundary problem in narrow domains of width $\\epsilon\\ll 1$ for linear second order differential equations with nonlinear boundary conditions is considered in this paper. Using probabilistic methods we show that the solution of such a problem converges as $\\epsilon \\downarrow 0$ to the solution of a standard reaction-diffusion equation in a domain of reduced dimension. This reduction allows to obtain some results concerning wave front propagation in narrow domains. In particular, we describe conditions leading to jumps of the wave front.","authors_text":"Konstantinos Spiliopoulos, Mark Freidlin","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-05-14T12:20:58Z","title":"Reaction Diffusion Equations with Nonlinear Boundary Conditions in Narrow Domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2505","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:b62d565596e813d0d6f55658ac2d82bd2a2522fc67bed4e67a5d5525db149dba","target":"record","created_at":"2026-05-18T04:34:37Z","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":"8fb067997ea88c3ee8c360d6bdef02a2e16ca61e0e582a5943ba5c7a48f791dc","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-05-14T12:20:58Z","title_canon_sha256":"64f7764c724dc06f6aaae20606fa4cecb1a1a97d27c3d932d397def5421d2d56"},"schema_version":"1.0","source":{"id":"1005.2505","kind":"arxiv","version":1}},"canonical_sha256":"d1479e2028ddff69501d126441ab1c4f6bf34892b551b23dbcd7e5cdd74ff70d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1479e2028ddff69501d126441ab1c4f6bf34892b551b23dbcd7e5cdd74ff70d","first_computed_at":"2026-05-18T04:34:37.120915Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:37.120915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RMpPaesa5ZcJ2ro7G9VWPxiuwwd2zgdzEDLUgQ4nFHXk1tnsSB8MNsQ3KrV13xIklLRekvhwl+N5VCyjZte3CA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:37.121631Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.2505","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b62d565596e813d0d6f55658ac2d82bd2a2522fc67bed4e67a5d5525db149dba","sha256:bfea5b62cd1d2c973a61bd29eaf15c92217580e7fee40988a3ac2125be334ca4"],"state_sha256":"151fff1b944604538c11e3bcc482410faa54036898adc01adc07c808d9b91921"}