{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GTDPB72PQLQPEZO5C5UYONDJK7","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":"987e5a41924d6903014c7213ad46dfb1b7a0e6e2a00d00e9c78f52106adbfcf2","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-05T16:05:46Z","title_canon_sha256":"e088eb310b2ef955de3d71d57dde7d5cacbda1a003dd7bba54f61472fb0ff785"},"schema_version":"1.0","source":{"id":"1812.02069","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.02069","created_at":"2026-07-05T02:18:48Z"},{"alias_kind":"arxiv_version","alias_value":"1812.02069v2","created_at":"2026-07-05T02:18:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.02069","created_at":"2026-07-05T02:18:48Z"},{"alias_kind":"pith_short_12","alias_value":"GTDPB72PQLQP","created_at":"2026-07-05T02:18:48Z"},{"alias_kind":"pith_short_16","alias_value":"GTDPB72PQLQPEZO5","created_at":"2026-07-05T02:18:48Z"},{"alias_kind":"pith_short_8","alias_value":"GTDPB72P","created_at":"2026-07-05T02:18:48Z"}],"graph_snapshots":[{"event_id":"sha256:3dbe724d0c4407f95d0e8712fbcdb12afda78806a36e6d361ffba5dab8614a7d","target":"graph","created_at":"2026-07-05T02:18:48Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1812.02069/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article, we prove that a small random perturbation of dynamical system with multiple stable equilibria converges to a Markov chain whose states are neighborhoods of the deepest stable equilibria, under a suitable time-rescaling, provided that the perturbed dynamics is reversible in time. Such a result has been anticipated from 1970s, when the foundation of mathematical treatment for this problem has been established by Freidlin and Wentzell. We solve this long-standing problem by reducing the entire analysis to an investigation of the solution of an associated Poisson equation, and fur","authors_text":"Fraydoun Rezakhanlou, Insuk Seo","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-05T16:05:46Z","title":"Scaling Limit of Small Random Perturbation of Dynamical Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02069","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":"sha256:8f481d87437f7cd6d33bfe49fc245711af0902be8e9cc6d01a1e0b8e7df89424","target":"record","created_at":"2026-07-05T02:18:48Z","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":"987e5a41924d6903014c7213ad46dfb1b7a0e6e2a00d00e9c78f52106adbfcf2","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-05T16:05:46Z","title_canon_sha256":"e088eb310b2ef955de3d71d57dde7d5cacbda1a003dd7bba54f61472fb0ff785"},"schema_version":"1.0","source":{"id":"1812.02069","kind":"arxiv","version":2}},"canonical_sha256":"34c6f0ff4f82e0f265dd176987346957e5640e0c3669ccf3e50418cf9389b69c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34c6f0ff4f82e0f265dd176987346957e5640e0c3669ccf3e50418cf9389b69c","first_computed_at":"2026-07-05T02:18:48.147696Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:18:48.147696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oQrr7wIwEJB1BiUkmTZHJYKc5tIN7Fr0HEJcYb3tx+pK4zCo8jRg6P+lylwuhpmF6GiMLK2VLuZpZlC/FohLDA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:18:48.148130Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.02069","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f481d87437f7cd6d33bfe49fc245711af0902be8e9cc6d01a1e0b8e7df89424","sha256:3dbe724d0c4407f95d0e8712fbcdb12afda78806a36e6d361ffba5dab8614a7d"],"state_sha256":"6fd4a4721b6d4f36476e4045924fcb7ace0a6c0ec715be6c48329df341f24233"}