{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:GZUB65EJPZ4VGA6UGT3FMAVMPY","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":"ecfb70dcd53a87c04e0b49b20102698b19c5f4870e113bd474e11c38d0ec657d","cross_cats_sorted":["math.OC","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-02-26T21:43:57Z","title_canon_sha256":"feae302052ec74e02bc7e0ff0e851c79e9f48d141b283d5c1c9b558b28ede9c4"},"schema_version":"1.0","source":{"id":"1902.10239","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.10239","created_at":"2026-05-17T23:52:31Z"},{"alias_kind":"arxiv_version","alias_value":"1902.10239v1","created_at":"2026-05-17T23:52:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.10239","created_at":"2026-05-17T23:52:31Z"},{"alias_kind":"pith_short_12","alias_value":"GZUB65EJPZ4V","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"GZUB65EJPZ4VGA6U","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"GZUB65EJ","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:13f5c581c9fd84f6c0c2646fef4af451370ba52dbe1aaa0fc4e8ec51dc0fa572","target":"graph","created_at":"2026-05-17T23:52:31Z","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":"The Koopman and Perron Frobenius transport operators are fundamentally changing how we approach dynamical systems, providing linear representations for even strongly nonlinear dynamics. Although there is tremendous potential benefit of such a linear representation for estimation and control, transport operators are infinite-dimensional, making them difficult to work with numerically. Obtaining low-dimensional matrix approximations of these operators is paramount for applications, and the dynamic mode decomposition has quickly become a standard numerical algorithm to approximate the Koopman ope","authors_text":"Eurika Kaiser, J. Nathan Kutz, Steven L. Brunton","cross_cats":["math.OC","physics.data-an"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-02-26T21:43:57Z","title":"Data-driven approximations of dynamical systems operators for control"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10239","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:ec648fbdf33f0c7485adc82facf0a1154b11f39f4462338e11bae5e1c47c316a","target":"record","created_at":"2026-05-17T23:52:31Z","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":"ecfb70dcd53a87c04e0b49b20102698b19c5f4870e113bd474e11c38d0ec657d","cross_cats_sorted":["math.OC","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-02-26T21:43:57Z","title_canon_sha256":"feae302052ec74e02bc7e0ff0e851c79e9f48d141b283d5c1c9b558b28ede9c4"},"schema_version":"1.0","source":{"id":"1902.10239","kind":"arxiv","version":1}},"canonical_sha256":"36681f74897e795303d434f65602ac7e179c62df8e1fdd0760c887894d37c0c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36681f74897e795303d434f65602ac7e179c62df8e1fdd0760c887894d37c0c5","first_computed_at":"2026-05-17T23:52:31.403032Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:31.403032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jtBvYOeK5InDWWFhZz6e8VphxYc6YtqvvgrjEg/oODYM5Fe+8A5uj4dxz7U5tHJsG7AJvbSiM7rl+sx6qoYnBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:31.403838Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.10239","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec648fbdf33f0c7485adc82facf0a1154b11f39f4462338e11bae5e1c47c316a","sha256:13f5c581c9fd84f6c0c2646fef4af451370ba52dbe1aaa0fc4e8ec51dc0fa572"],"state_sha256":"9775ac46e85ae6ca68edd81d3a8464c1a39cd70009ca50fee43808ff4e6f3e8a"}