{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:XAQ2NCNB3E25RM3WDUOXUARXKG","short_pith_number":"pith:XAQ2NCNB","canonical_record":{"source":{"id":"2204.14021","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2022-04-29T11:37:16Z","cross_cats_sorted":["cs.SY","math.DS","math.OC"],"title_canon_sha256":"a0a08612241be3c2c8a143334416ca3bca22bd8e46035e1730f4b3a584c4ff2f","abstract_canon_sha256":"f24a069c5612ae1b6194b57a183fdd89fa418e719a9d38113cb3507356b847c5"},"schema_version":"1.0"},"canonical_sha256":"b821a689a1d935d8b3761d1d7a023751bd169b97adbd397a7c1e12d663dccb92","source":{"kind":"arxiv","id":"2204.14021","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.14021","created_at":"2026-07-05T04:18:56Z"},{"alias_kind":"arxiv_version","alias_value":"2204.14021v1","created_at":"2026-07-05T04:18:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.14021","created_at":"2026-07-05T04:18:56Z"},{"alias_kind":"pith_short_12","alias_value":"XAQ2NCNB3E25","created_at":"2026-07-05T04:18:56Z"},{"alias_kind":"pith_short_16","alias_value":"XAQ2NCNB3E25RM3W","created_at":"2026-07-05T04:18:56Z"},{"alias_kind":"pith_short_8","alias_value":"XAQ2NCNB","created_at":"2026-07-05T04:18:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:XAQ2NCNB3E25RM3WDUOXUARXKG","target":"record","payload":{"canonical_record":{"source":{"id":"2204.14021","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2022-04-29T11:37:16Z","cross_cats_sorted":["cs.SY","math.DS","math.OC"],"title_canon_sha256":"a0a08612241be3c2c8a143334416ca3bca22bd8e46035e1730f4b3a584c4ff2f","abstract_canon_sha256":"f24a069c5612ae1b6194b57a183fdd89fa418e719a9d38113cb3507356b847c5"},"schema_version":"1.0"},"canonical_sha256":"b821a689a1d935d8b3761d1d7a023751bd169b97adbd397a7c1e12d663dccb92","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:18:56.363105Z","signature_b64":"EDIUBRdtbBV84w2+dxJXZ/mJpwU8i9ckWNAoo0pwL6IfT0pTV+bP5U+02p8lJli52cJiPfrlhO/OWy5lCA8YCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b821a689a1d935d8b3761d1d7a023751bd169b97adbd397a7c1e12d663dccb92","last_reissued_at":"2026-07-05T04:18:56.362642Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:18:56.362642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2204.14021","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":"2026-07-05T04:18:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UCfigPDXH1gEmPvPE2ZHfZjJCitHZwkzxgA9MiOM4b6bjPlHMutwJ6Jv1bo27itR3r10CYkCJUTumoYgo7lDDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T11:19:30.385348Z"},"content_sha256":"8d691f5a5d19c2d6a4116453f04379b1c3334e655bb6e3f7b848a38bce822c30","schema_version":"1.0","event_id":"sha256:8d691f5a5d19c2d6a4116453f04379b1c3334e655bb6e3f7b848a38bce822c30"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:XAQ2NCNB3E25RM3WDUOXUARXKG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Sampling Theorem for Exact Identification of Continuous-time Nonlinear Dynamical Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math.DS","math.OC"],"primary_cat":"eess.SY","authors_text":"Alexandre Mauroy, Jorge Goncalves, Ye Yuan, Zhexuan Zeng, Zuogong Yue","submitted_at":"2022-04-29T11:37:16Z","abstract_excerpt":"Low sampling frequency challenges the exact identification of the continuous-time (CT) dynamical system from sampled data, even when its model is identifiable. The necessary and sufficient condition is proposed -- which is built from Koopman operator -- to the exact identification of the CT system from sampled data. The condition gives a Nyquist-Shannon-like critical frequency for exact identification of CT nonlinear dynamical systems with Koopman invariant subspaces: 1) it establishes a sufficient condition for a sampling frequency that permits a discretized sequence of samples to discover th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.14021","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/2204.14021/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":"2026-07-05T04:18:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5x961y71eIdIJEYrVEwpSYV4M6nKA46N0y/rVwFyLqsG2KnBYEkacfCHqXdvjWe6IQ4xrxEKqr2QY7WIfFtZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T11:19:30.385835Z"},"content_sha256":"7cdd84ac48a5db8ae49feab5ee5317325cfb0b9bc653084a14a1feea2ac56135","schema_version":"1.0","event_id":"sha256:7cdd84ac48a5db8ae49feab5ee5317325cfb0b9bc653084a14a1feea2ac56135"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XAQ2NCNB3E25RM3WDUOXUARXKG/bundle.json","state_url":"https://pith.science/pith/XAQ2NCNB3E25RM3WDUOXUARXKG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XAQ2NCNB3E25RM3WDUOXUARXKG/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":"2026-08-04T11:19:30Z","links":{"resolver":"https://pith.science/pith/XAQ2NCNB3E25RM3WDUOXUARXKG","bundle":"https://pith.science/pith/XAQ2NCNB3E25RM3WDUOXUARXKG/bundle.json","state":"https://pith.science/pith/XAQ2NCNB3E25RM3WDUOXUARXKG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XAQ2NCNB3E25RM3WDUOXUARXKG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:XAQ2NCNB3E25RM3WDUOXUARXKG","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":"f24a069c5612ae1b6194b57a183fdd89fa418e719a9d38113cb3507356b847c5","cross_cats_sorted":["cs.SY","math.DS","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2022-04-29T11:37:16Z","title_canon_sha256":"a0a08612241be3c2c8a143334416ca3bca22bd8e46035e1730f4b3a584c4ff2f"},"schema_version":"1.0","source":{"id":"2204.14021","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.14021","created_at":"2026-07-05T04:18:56Z"},{"alias_kind":"arxiv_version","alias_value":"2204.14021v1","created_at":"2026-07-05T04:18:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.14021","created_at":"2026-07-05T04:18:56Z"},{"alias_kind":"pith_short_12","alias_value":"XAQ2NCNB3E25","created_at":"2026-07-05T04:18:56Z"},{"alias_kind":"pith_short_16","alias_value":"XAQ2NCNB3E25RM3W","created_at":"2026-07-05T04:18:56Z"},{"alias_kind":"pith_short_8","alias_value":"XAQ2NCNB","created_at":"2026-07-05T04:18:56Z"}],"graph_snapshots":[{"event_id":"sha256:7cdd84ac48a5db8ae49feab5ee5317325cfb0b9bc653084a14a1feea2ac56135","target":"graph","created_at":"2026-07-05T04:18:56Z","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/2204.14021/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Low sampling frequency challenges the exact identification of the continuous-time (CT) dynamical system from sampled data, even when its model is identifiable. The necessary and sufficient condition is proposed -- which is built from Koopman operator -- to the exact identification of the CT system from sampled data. The condition gives a Nyquist-Shannon-like critical frequency for exact identification of CT nonlinear dynamical systems with Koopman invariant subspaces: 1) it establishes a sufficient condition for a sampling frequency that permits a discretized sequence of samples to discover th","authors_text":"Alexandre Mauroy, Jorge Goncalves, Ye Yuan, Zhexuan Zeng, Zuogong Yue","cross_cats":["cs.SY","math.DS","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2022-04-29T11:37:16Z","title":"A Sampling Theorem for Exact Identification of Continuous-time Nonlinear Dynamical Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.14021","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":"sha256:8d691f5a5d19c2d6a4116453f04379b1c3334e655bb6e3f7b848a38bce822c30","target":"record","created_at":"2026-07-05T04:18:56Z","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":"f24a069c5612ae1b6194b57a183fdd89fa418e719a9d38113cb3507356b847c5","cross_cats_sorted":["cs.SY","math.DS","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2022-04-29T11:37:16Z","title_canon_sha256":"a0a08612241be3c2c8a143334416ca3bca22bd8e46035e1730f4b3a584c4ff2f"},"schema_version":"1.0","source":{"id":"2204.14021","kind":"arxiv","version":1}},"canonical_sha256":"b821a689a1d935d8b3761d1d7a023751bd169b97adbd397a7c1e12d663dccb92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b821a689a1d935d8b3761d1d7a023751bd169b97adbd397a7c1e12d663dccb92","first_computed_at":"2026-07-05T04:18:56.362642Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:18:56.362642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EDIUBRdtbBV84w2+dxJXZ/mJpwU8i9ckWNAoo0pwL6IfT0pTV+bP5U+02p8lJli52cJiPfrlhO/OWy5lCA8YCw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:18:56.363105Z","signed_message":"canonical_sha256_bytes"},"source_id":"2204.14021","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d691f5a5d19c2d6a4116453f04379b1c3334e655bb6e3f7b848a38bce822c30","sha256:7cdd84ac48a5db8ae49feab5ee5317325cfb0b9bc653084a14a1feea2ac56135"],"state_sha256":"bc639a56e0d4c99ae510af5b025870d41a4f34b91f3a4de0ca8e43dbd24f9e05"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"95D/jC2dC4hdUj0XRihBWEdvyxWWJjY9T08i1enbp24BArzRkF9EkewX3tO6ksNyk9kagZscdWFO/yerjiXhBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T11:19:30.390502Z","bundle_sha256":"809a610015189216008161ef9f698fa1a08cd54bb414dbfe62dff3c4ab33e5f0"}}