{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LTSVVI2J6V3BC7YDSGD5JE5MO4","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":"ed837bbe556480fb4ae571d1339c518f1b83f758127cb61e31e8e23f4b4239b3","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-18T15:43:07Z","title_canon_sha256":"110edcfd12545b58d644ab8547c17ca5c5317c3ebbebce401257dba75c62ee55"},"schema_version":"1.0","source":{"id":"1512.05997","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.05997","created_at":"2026-05-18T01:01:44Z"},{"alias_kind":"arxiv_version","alias_value":"1512.05997v3","created_at":"2026-05-18T01:01:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.05997","created_at":"2026-05-18T01:01:44Z"},{"alias_kind":"pith_short_12","alias_value":"LTSVVI2J6V3B","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LTSVVI2J6V3BC7YD","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LTSVVI2J","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:8d093c32c40b20d422a42199a287a15ef8d743a830458638a5a0c217e1c04ab1","target":"graph","created_at":"2026-05-18T01:01:44Z","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":"Information about the behavior of dynamical systems can often be obtained by analyzing the eigenvalues and corresponding eigenfunctions of linear operators associated with a dynamical system. Examples of such operators are the Perron-Frobenius and the Koopman operator. In this paper, we will review different methods that have been developed over the last decades to compute finite-dimensional approximations of these infinite-dimensional operators - e.g. Ulam's method and Extended Dynamic Mode Decomposition (EDMD) - and highlight the similarities and differences between these approaches. The res","authors_text":"Christof Sch\\\"utte, P\\'eter Koltai, Stefan Klus","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-18T15:43:07Z","title":"On the numerical approximation of the Perron-Frobenius and Koopman operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05997","kind":"arxiv","version":3},"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":"sha256:2d805ea2da6e59f8ab7140e2c305b68b9535df9472f00f53a0b071d62d04bce2","target":"record","created_at":"2026-05-18T01:01:44Z","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":"ed837bbe556480fb4ae571d1339c518f1b83f758127cb61e31e8e23f4b4239b3","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-18T15:43:07Z","title_canon_sha256":"110edcfd12545b58d644ab8547c17ca5c5317c3ebbebce401257dba75c62ee55"},"schema_version":"1.0","source":{"id":"1512.05997","kind":"arxiv","version":3}},"canonical_sha256":"5ce55aa349f576117f039187d493ac772999f30ec3d3f939d0c70b79ab764937","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ce55aa349f576117f039187d493ac772999f30ec3d3f939d0c70b79ab764937","first_computed_at":"2026-05-18T01:01:44.735846Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:44.735846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YwC98GVwwtd3c3RwLb72QUh5KcFyNhJtOZOqLHw8FlHeCmPkMZ/fduVGc4ZcIB4I+VwWl1xlRt9JOhhLTkCfAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:44.736620Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.05997","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d805ea2da6e59f8ab7140e2c305b68b9535df9472f00f53a0b071d62d04bce2","sha256:8d093c32c40b20d422a42199a287a15ef8d743a830458638a5a0c217e1c04ab1"],"state_sha256":"03551d65501fd7497968ff65e9522cdeb6e882ba9e6a9fb4f0e4fad77f3cf68c"}