{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:EISJ7JYS2WTUNFD6ZCTZUNAQSD","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":"b73b4fa6056c27bdc4f2f1069e1c2a31c66058c6c57d32698772293ee9b51e2f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-11-04T01:51:19Z","title_canon_sha256":"eb0fa8bab8c1d9e9a27f7159f41fa9497cd4aeb962d0dacf9eab77b31b6129fa"},"schema_version":"1.0","source":{"id":"0911.0717","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.0717","created_at":"2026-05-18T04:28:45Z"},{"alias_kind":"arxiv_version","alias_value":"0911.0717v2","created_at":"2026-05-18T04:28:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.0717","created_at":"2026-05-18T04:28:45Z"},{"alias_kind":"pith_short_12","alias_value":"EISJ7JYS2WTU","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"EISJ7JYS2WTUNFD6","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"EISJ7JYS","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:9154a36a54ef8e1b7d24809dd20c367f1900a1e4ade57aa0943da45bac3bf97e","target":"graph","created_at":"2026-05-18T04:28:45Z","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 describe a mathematical formalism and numerical algorithms for identifying and tracking slowly mixing objects in nonautonomous dynamical systems. In the autonomous setting, such objects are variously known as almost-invariant sets, metastable sets, persistent patterns, or strange eigenmodes, and have proved to be important in a variety of applications. In this current work, we explain how to extend existing autonomous approaches to the nonautonomous setting. We call the new time-dependent slowly mixing objects coherent sets as they represent regions of phase space that disperse very slowly ","authors_text":"Gary Froyland, Naratip Santitissadeekorn, Simon Lloyd","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-11-04T01:51:19Z","title":"Coherent sets for nonautonomous dynamical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.0717","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:d564707dc9067614ab81d44210a7523bf0f780028234907d53ed28da73ddb06a","target":"record","created_at":"2026-05-18T04:28:45Z","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":"b73b4fa6056c27bdc4f2f1069e1c2a31c66058c6c57d32698772293ee9b51e2f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-11-04T01:51:19Z","title_canon_sha256":"eb0fa8bab8c1d9e9a27f7159f41fa9497cd4aeb962d0dacf9eab77b31b6129fa"},"schema_version":"1.0","source":{"id":"0911.0717","kind":"arxiv","version":2}},"canonical_sha256":"22249fa712d5a746947ec8a79a341090e23e59f4e99c687fb9a189ae2191fbf9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22249fa712d5a746947ec8a79a341090e23e59f4e99c687fb9a189ae2191fbf9","first_computed_at":"2026-05-18T04:28:45.798667Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:45.798667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Do4vdhiklVyQuN2hjp4MAj5HcrSJ8zs7yKWvjMNX/x66HyX2mEYdWLo674GiAZemiOcOrcH9UMHooHYauqUvBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:45.799157Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.0717","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d564707dc9067614ab81d44210a7523bf0f780028234907d53ed28da73ddb06a","sha256:9154a36a54ef8e1b7d24809dd20c367f1900a1e4ade57aa0943da45bac3bf97e"],"state_sha256":"dd7840365605b65e8f28de6ed8420c5ba7c77f64eb147591d2b14798ed147e24"}