{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:YIPUKVUBNP3KKFM4IQJQWVZDVE","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":"ebc6cb4b0d1f25a650053a46c129352b2b082c0d3dbc42fa3422eaae3f5fd3fc","cross_cats_sorted":[],"license":"","primary_cat":"nlin.CD","submitted_at":"2002-04-29T15:04:44Z","title_canon_sha256":"e05e55fc6731fe67fdd9bdb412a48dbe6a821905d5cb555f176c5e10611008b0"},"schema_version":"1.0","source":{"id":"nlin/0204068","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0204068","created_at":"2026-07-04T14:41:42Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0204068v1","created_at":"2026-07-04T14:41:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0204068","created_at":"2026-07-04T14:41:42Z"},{"alias_kind":"pith_short_12","alias_value":"YIPUKVUBNP3K","created_at":"2026-07-04T14:41:42Z"},{"alias_kind":"pith_short_16","alias_value":"YIPUKVUBNP3KKFM4","created_at":"2026-07-04T14:41:42Z"},{"alias_kind":"pith_short_8","alias_value":"YIPUKVUB","created_at":"2026-07-04T14:41:42Z"}],"graph_snapshots":[{"event_id":"sha256:1dba081550ed40e8868d4022ae13a48d37ab8398f6f46045a5f85b0bda6de4f0","target":"graph","created_at":"2026-07-04T14:41:42Z","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/nlin/0204068/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For a class of idealized chaotic systems (hyperbolic systems) correlations decay exponentially in time. This result is asymptotic and rigorous. The decay rate is related to the Ruelle-Pollicott resonances. Nearly all chaotic model systems, that are studied by physicists, are not hyperbolic. For many such systems it is known that exponential decay takes place for a long time. It may not be asymptotic, but it may persist for a very long time, longer than any time of experimental relevance. In this review a heuristic method for calculation of this exponential decay of correlations in time is pres","authors_text":"Saar Rahav, Shmuel Fishman","cross_cats":[],"headline":"","license":"","primary_cat":"nlin.CD","submitted_at":"2002-04-29T15:04:44Z","title":"Relaxation and Noise in Chaotic Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0204068","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":"sha256:5234bf702c794fd7835be0bb1cc4bfa83ffe8d64faa31a7d42f5d659d2e7c19e","target":"record","created_at":"2026-07-04T14:41:42Z","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":"ebc6cb4b0d1f25a650053a46c129352b2b082c0d3dbc42fa3422eaae3f5fd3fc","cross_cats_sorted":[],"license":"","primary_cat":"nlin.CD","submitted_at":"2002-04-29T15:04:44Z","title_canon_sha256":"e05e55fc6731fe67fdd9bdb412a48dbe6a821905d5cb555f176c5e10611008b0"},"schema_version":"1.0","source":{"id":"nlin/0204068","kind":"arxiv","version":1}},"canonical_sha256":"c21f4556816bf6a5159c44130b5723a939cd8f36d60f6d797543e4cdf0db9e81","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c21f4556816bf6a5159c44130b5723a939cd8f36d60f6d797543e4cdf0db9e81","first_computed_at":"2026-07-04T14:41:42.639361Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:41:42.639361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gDy9SbtQMLtUZt/N2YNBigLdyoN33oCl4PzJPbBW3oJGGzAsxKG6+++Qxl1ZoXGh/4wcO1sXNpIpYMqRbZVTCw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:41:42.639707Z","signed_message":"canonical_sha256_bytes"},"source_id":"nlin/0204068","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5234bf702c794fd7835be0bb1cc4bfa83ffe8d64faa31a7d42f5d659d2e7c19e","sha256:1dba081550ed40e8868d4022ae13a48d37ab8398f6f46045a5f85b0bda6de4f0"],"state_sha256":"6b11d7c0a889704a96c1794b70815dfb77e83559f080e9db4d952944c0fff56f"}