{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:U3P2VT5KDDXCBH6DDR23KE7MQ3","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":"8afb6b91f577c61005dbd101c9794b22722d7cc9ecc161814cb86c4f612c7f61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2008-09-08T14:26:25Z","title_canon_sha256":"3301b4c3d4d221a63aef6a93343958bc5d65a0eb4ab56a1b5c27dfb5d5072358"},"schema_version":"1.0","source":{"id":"0809.1345","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.1345","created_at":"2026-05-18T02:15:35Z"},{"alias_kind":"arxiv_version","alias_value":"0809.1345v2","created_at":"2026-05-18T02:15:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.1345","created_at":"2026-05-18T02:15:35Z"},{"alias_kind":"pith_short_12","alias_value":"U3P2VT5KDDXC","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"U3P2VT5KDDXCBH6D","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"U3P2VT5K","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:9b85d76f2a881e50d38c98f0992b908de589a7e74b5d2835e592c6473114c45b","target":"graph","created_at":"2026-05-18T02:15:35Z","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":"We consider a stochastic environment with two time scales and outline a general theory that compares two methods to reduce the dimension of the original system. The first method involves the computation of the underlying deterministic center manifold followed by a naive replacement of the stochastic term. The second method allows one to more accurately describe the stochastic effects and involves the derivation of a normal form coordinate transform that is used to find the stochastic center manifold. The results of both methods are used along with the path integral formalism of large fluctuati","authors_text":"Eric Forgoston, Ira B. Schwartz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2008-09-08T14:26:25Z","title":"Escape Rates in a Stochastic Environment with Multiple Scales"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.1345","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:ee7e4b9fb6024e98abdfe81519378ca1e0bbe93c0642aa8568676a1ceedef33a","target":"record","created_at":"2026-05-18T02:15:35Z","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":"8afb6b91f577c61005dbd101c9794b22722d7cc9ecc161814cb86c4f612c7f61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2008-09-08T14:26:25Z","title_canon_sha256":"3301b4c3d4d221a63aef6a93343958bc5d65a0eb4ab56a1b5c27dfb5d5072358"},"schema_version":"1.0","source":{"id":"0809.1345","kind":"arxiv","version":2}},"canonical_sha256":"a6dfaacfaa18ee209fc31c75b513ec86cca6ae6cb8842ef01dd076e06d74e354","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6dfaacfaa18ee209fc31c75b513ec86cca6ae6cb8842ef01dd076e06d74e354","first_computed_at":"2026-05-18T02:15:35.214404Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:35.214404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f+oCHjyOCRTka///FzKV+fCH/hrLDIEO7fx7RdB0QkFnMwuB7QlJ3HK0KEVA6ADUE38MYnqrMDeHafk89+4XDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:35.215078Z","signed_message":"canonical_sha256_bytes"},"source_id":"0809.1345","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee7e4b9fb6024e98abdfe81519378ca1e0bbe93c0642aa8568676a1ceedef33a","sha256:9b85d76f2a881e50d38c98f0992b908de589a7e74b5d2835e592c6473114c45b"],"state_sha256":"0fe7bc4e69b6875baa2642fadeec917a15b9357e4cb40a5526a621f63e5e3b3c"}