{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:4JCWX32EQAE7WXYS27LBOWJNCK","short_pith_number":"pith:4JCWX32E","canonical_record":{"source":{"id":"2408.12277","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"eess.SY","submitted_at":"2024-08-22T10:22:07Z","cross_cats_sorted":["cs.SY","math.DS"],"title_canon_sha256":"58a80d64bad11c247924cae06043371d93103d152b13f30cc86fac2bcd9c1d2a","abstract_canon_sha256":"50c8b68942c89d3034b4296d64925cedd9e3fdc35795658f652f8f2eed83c481"},"schema_version":"1.0"},"canonical_sha256":"e2456bef448009fb5f12d7d617592d12b270167707c6077535a9d89a90be98b7","source":{"kind":"arxiv","id":"2408.12277","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.12277","created_at":"2026-07-05T08:58:06Z"},{"alias_kind":"arxiv_version","alias_value":"2408.12277v1","created_at":"2026-07-05T08:58:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.12277","created_at":"2026-07-05T08:58:06Z"},{"alias_kind":"pith_short_12","alias_value":"4JCWX32EQAE7","created_at":"2026-07-05T08:58:06Z"},{"alias_kind":"pith_short_16","alias_value":"4JCWX32EQAE7WXYS","created_at":"2026-07-05T08:58:06Z"},{"alias_kind":"pith_short_8","alias_value":"4JCWX32E","created_at":"2026-07-05T08:58:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:4JCWX32EQAE7WXYS27LBOWJNCK","target":"record","payload":{"canonical_record":{"source":{"id":"2408.12277","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"eess.SY","submitted_at":"2024-08-22T10:22:07Z","cross_cats_sorted":["cs.SY","math.DS"],"title_canon_sha256":"58a80d64bad11c247924cae06043371d93103d152b13f30cc86fac2bcd9c1d2a","abstract_canon_sha256":"50c8b68942c89d3034b4296d64925cedd9e3fdc35795658f652f8f2eed83c481"},"schema_version":"1.0"},"canonical_sha256":"e2456bef448009fb5f12d7d617592d12b270167707c6077535a9d89a90be98b7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:58:06.849510Z","signature_b64":"xc2VnH2KLyyLOMHIn10iXl4/r9rmHkBgXi6bJIjBY9EcL6alrtUyVziurQJpSG/UQtrB9W9agW4qd2B4L0tQAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2456bef448009fb5f12d7d617592d12b270167707c6077535a9d89a90be98b7","last_reissued_at":"2026-07-05T08:58:06.849091Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:58:06.849091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2408.12277","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:58:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t79g6fTwSe1Sw/370DEeoDpqrldeK9dF/72IJUcdacXc6YT7rRu/Nw/yvgHvc43rtOOz75qzVHcKJ17Z0qk+Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T19:14:09.218414Z"},"content_sha256":"87f24857d12ee3800f137034f94b669f94be05c8e47f39e7384e64cd7d9c5a05","schema_version":"1.0","event_id":"sha256:87f24857d12ee3800f137034f94b669f94be05c8e47f39e7384e64cd7d9c5a05"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:4JCWX32EQAE7WXYS27LBOWJNCK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modularized data-driven approximation of the Koopman operator and generator","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.SY","math.DS"],"primary_cat":"eess.SY","authors_text":"Karl Worthmann, Manuel Schaller, Stefan Streif, Yang Guo","submitted_at":"2024-08-22T10:22:07Z","abstract_excerpt":"Extended Dynamic Mode Decomposition (EDMD) is a widely-used data-driven approach to learn an approximation of the Koopman operator. Consequently, it provides a powerful tool for data-driven analysis, prediction, and control of nonlinear dynamical (control) systems. In this work, we propose a novel modularized EDMD scheme tailored to interconnected systems. To this end, we utilize the structure of the Koopman generator that allows to learn the dynamics of subsystems individually and thus alleviates the curse of dimensionality by considering observable functions on smaller state spaces. Moreover"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.12277","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2408.12277/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:58:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PM/gau8RVKIdta93wdOydvYI6jXCYQCKIkRhzgwkqMuzzOw1hCyYHZZrk+HO5RpCc+k8enrYA1VBk1MOtGUWCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T19:14:09.218794Z"},"content_sha256":"fd90a850055a956d15aa2f16231b83ac0ee0fc253903facae48b1b46889d8b0b","schema_version":"1.0","event_id":"sha256:fd90a850055a956d15aa2f16231b83ac0ee0fc253903facae48b1b46889d8b0b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4JCWX32EQAE7WXYS27LBOWJNCK/bundle.json","state_url":"https://pith.science/pith/4JCWX32EQAE7WXYS27LBOWJNCK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4JCWX32EQAE7WXYS27LBOWJNCK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-14T19:14:09Z","links":{"resolver":"https://pith.science/pith/4JCWX32EQAE7WXYS27LBOWJNCK","bundle":"https://pith.science/pith/4JCWX32EQAE7WXYS27LBOWJNCK/bundle.json","state":"https://pith.science/pith/4JCWX32EQAE7WXYS27LBOWJNCK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4JCWX32EQAE7WXYS27LBOWJNCK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:4JCWX32EQAE7WXYS27LBOWJNCK","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":"50c8b68942c89d3034b4296d64925cedd9e3fdc35795658f652f8f2eed83c481","cross_cats_sorted":["cs.SY","math.DS"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"eess.SY","submitted_at":"2024-08-22T10:22:07Z","title_canon_sha256":"58a80d64bad11c247924cae06043371d93103d152b13f30cc86fac2bcd9c1d2a"},"schema_version":"1.0","source":{"id":"2408.12277","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.12277","created_at":"2026-07-05T08:58:06Z"},{"alias_kind":"arxiv_version","alias_value":"2408.12277v1","created_at":"2026-07-05T08:58:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.12277","created_at":"2026-07-05T08:58:06Z"},{"alias_kind":"pith_short_12","alias_value":"4JCWX32EQAE7","created_at":"2026-07-05T08:58:06Z"},{"alias_kind":"pith_short_16","alias_value":"4JCWX32EQAE7WXYS","created_at":"2026-07-05T08:58:06Z"},{"alias_kind":"pith_short_8","alias_value":"4JCWX32E","created_at":"2026-07-05T08:58:06Z"}],"graph_snapshots":[{"event_id":"sha256:fd90a850055a956d15aa2f16231b83ac0ee0fc253903facae48b1b46889d8b0b","target":"graph","created_at":"2026-07-05T08:58:06Z","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/2408.12277/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Extended Dynamic Mode Decomposition (EDMD) is a widely-used data-driven approach to learn an approximation of the Koopman operator. Consequently, it provides a powerful tool for data-driven analysis, prediction, and control of nonlinear dynamical (control) systems. In this work, we propose a novel modularized EDMD scheme tailored to interconnected systems. To this end, we utilize the structure of the Koopman generator that allows to learn the dynamics of subsystems individually and thus alleviates the curse of dimensionality by considering observable functions on smaller state spaces. Moreover","authors_text":"Karl Worthmann, Manuel Schaller, Stefan Streif, Yang Guo","cross_cats":["cs.SY","math.DS"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"eess.SY","submitted_at":"2024-08-22T10:22:07Z","title":"Modularized data-driven approximation of the Koopman operator and generator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.12277","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":"sha256:87f24857d12ee3800f137034f94b669f94be05c8e47f39e7384e64cd7d9c5a05","target":"record","created_at":"2026-07-05T08:58:06Z","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":"50c8b68942c89d3034b4296d64925cedd9e3fdc35795658f652f8f2eed83c481","cross_cats_sorted":["cs.SY","math.DS"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"eess.SY","submitted_at":"2024-08-22T10:22:07Z","title_canon_sha256":"58a80d64bad11c247924cae06043371d93103d152b13f30cc86fac2bcd9c1d2a"},"schema_version":"1.0","source":{"id":"2408.12277","kind":"arxiv","version":1}},"canonical_sha256":"e2456bef448009fb5f12d7d617592d12b270167707c6077535a9d89a90be98b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2456bef448009fb5f12d7d617592d12b270167707c6077535a9d89a90be98b7","first_computed_at":"2026-07-05T08:58:06.849091Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:58:06.849091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xc2VnH2KLyyLOMHIn10iXl4/r9rmHkBgXi6bJIjBY9EcL6alrtUyVziurQJpSG/UQtrB9W9agW4qd2B4L0tQAg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:58:06.849510Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.12277","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87f24857d12ee3800f137034f94b669f94be05c8e47f39e7384e64cd7d9c5a05","sha256:fd90a850055a956d15aa2f16231b83ac0ee0fc253903facae48b1b46889d8b0b"],"state_sha256":"a206471977f9bacfb2e2c4788262a6d0957a32be9fce217d7d919ec13a959b38"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U8xvsP0z9maNnzOy9kGRBsRMBzxqmWCnqNJyPwaPhDQixX7jW6Yi3WBaKL7J78nToRiLDjYvPNt5ZnC9cvx6AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T19:14:09.222278Z","bundle_sha256":"2661bf743a67c20cfa1cca188f5bfff3478a108816b6a7113be0a31fb2e6a83d"}}