{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:ITNKX2XM3OJ26MLQMO2WGCQSDT","short_pith_number":"pith:ITNKX2XM","canonical_record":{"source":{"id":"2010.09961","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2020-10-20T02:10:23Z","cross_cats_sorted":[],"title_canon_sha256":"dcfc9f2476d6835eb296ad5abe4903ba1290dd0c4f6e5735449f20a87f5c2e20","abstract_canon_sha256":"8928df31845169556be585ae775509b36e933803521f9ac6e3745a2e30fb8fc2"},"schema_version":"1.0"},"canonical_sha256":"44daabeaecdb93af317063b5630a121cc4c7edf7a25441c27ef7a47ccb8b6e84","source":{"kind":"arxiv","id":"2010.09961","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.09961","created_at":"2026-07-05T01:51:22Z"},{"alias_kind":"arxiv_version","alias_value":"2010.09961v3","created_at":"2026-07-05T01:51:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.09961","created_at":"2026-07-05T01:51:22Z"},{"alias_kind":"pith_short_12","alias_value":"ITNKX2XM3OJ2","created_at":"2026-07-05T01:51:22Z"},{"alias_kind":"pith_short_16","alias_value":"ITNKX2XM3OJ26MLQ","created_at":"2026-07-05T01:51:22Z"},{"alias_kind":"pith_short_8","alias_value":"ITNKX2XM","created_at":"2026-07-05T01:51:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:ITNKX2XM3OJ26MLQMO2WGCQSDT","target":"record","payload":{"canonical_record":{"source":{"id":"2010.09961","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2020-10-20T02:10:23Z","cross_cats_sorted":[],"title_canon_sha256":"dcfc9f2476d6835eb296ad5abe4903ba1290dd0c4f6e5735449f20a87f5c2e20","abstract_canon_sha256":"8928df31845169556be585ae775509b36e933803521f9ac6e3745a2e30fb8fc2"},"schema_version":"1.0"},"canonical_sha256":"44daabeaecdb93af317063b5630a121cc4c7edf7a25441c27ef7a47ccb8b6e84","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:51:22.310736Z","signature_b64":"o2PgQ1CLRqMX9YprV7BG2HQ9kwJeYWaV+ENfWssLdr3fGHHlISNqoTcmFxXGxAZQ2vC912GTCGMcfzoCb5o+Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44daabeaecdb93af317063b5630a121cc4c7edf7a25441c27ef7a47ccb8b6e84","last_reissued_at":"2026-07-05T01:51:22.310392Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:51:22.310392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2010.09961","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:51:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2tKT4vlgPr3oxtJXSd+U5lhiU6T9DlxdbZJwzbO4nNKD04+dzV4BqrjSE9+S7rR6orBRBTNVPFsURltFx03TAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T12:34:15.730333Z"},"content_sha256":"2be091229e152550fb70044d7315d440ac846fa9886519622e5b9b90c1a2124a","schema_version":"1.0","event_id":"sha256:2be091229e152550fb70044d7315d440ac846fa9886519622e5b9b90c1a2124a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:ITNKX2XM3OJ26MLQMO2WGCQSDT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Advantages of Bilinear Koopman Realizations for the Modeling and Control of Systems with Unknown Dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.RO","authors_text":"Daniel Bruder, Ram Vasudevan, Xun Fu","submitted_at":"2020-10-20T02:10:23Z","abstract_excerpt":"Nonlinear dynamical systems can be made easier to control by lifting them into the space of observable functions, where their evolution is described by the linear Koopman operator. This paper describes how the Koopman operator can be used to generate approximate linear, bilinear, and nonlinear model realizations from data, and argues in favor of bilinear realizations for characterizing systems with unknown dynamics. Necessary and sufficient conditions for a dynamical system to have a valid linear or bilinear realization over a given set of observable functions are presented and used to show th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.09961","kind":"arxiv","version":3},"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/2010.09961/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":"2026-07-05T01:51:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vrkr2c9YlBLLkOZFeU+s2ZRw6Wje72DFcF4BnK8ftgcCcS1XpD7ZfAwHAU5Am9IrpnNUbfgc1Vynv1rWH8ddCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T12:34:15.730724Z"},"content_sha256":"a7d80d482997ea3988ae7db891055ff802e413772541c9c327d6f3dfaeff5a84","schema_version":"1.0","event_id":"sha256:a7d80d482997ea3988ae7db891055ff802e413772541c9c327d6f3dfaeff5a84"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ITNKX2XM3OJ26MLQMO2WGCQSDT/bundle.json","state_url":"https://pith.science/pith/ITNKX2XM3OJ26MLQMO2WGCQSDT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ITNKX2XM3OJ26MLQMO2WGCQSDT/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":"2026-07-05T12:34:15Z","links":{"resolver":"https://pith.science/pith/ITNKX2XM3OJ26MLQMO2WGCQSDT","bundle":"https://pith.science/pith/ITNKX2XM3OJ26MLQMO2WGCQSDT/bundle.json","state":"https://pith.science/pith/ITNKX2XM3OJ26MLQMO2WGCQSDT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ITNKX2XM3OJ26MLQMO2WGCQSDT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:ITNKX2XM3OJ26MLQMO2WGCQSDT","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":"8928df31845169556be585ae775509b36e933803521f9ac6e3745a2e30fb8fc2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2020-10-20T02:10:23Z","title_canon_sha256":"dcfc9f2476d6835eb296ad5abe4903ba1290dd0c4f6e5735449f20a87f5c2e20"},"schema_version":"1.0","source":{"id":"2010.09961","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.09961","created_at":"2026-07-05T01:51:22Z"},{"alias_kind":"arxiv_version","alias_value":"2010.09961v3","created_at":"2026-07-05T01:51:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.09961","created_at":"2026-07-05T01:51:22Z"},{"alias_kind":"pith_short_12","alias_value":"ITNKX2XM3OJ2","created_at":"2026-07-05T01:51:22Z"},{"alias_kind":"pith_short_16","alias_value":"ITNKX2XM3OJ26MLQ","created_at":"2026-07-05T01:51:22Z"},{"alias_kind":"pith_short_8","alias_value":"ITNKX2XM","created_at":"2026-07-05T01:51:22Z"}],"graph_snapshots":[{"event_id":"sha256:a7d80d482997ea3988ae7db891055ff802e413772541c9c327d6f3dfaeff5a84","target":"graph","created_at":"2026-07-05T01:51:22Z","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/2010.09961/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Nonlinear dynamical systems can be made easier to control by lifting them into the space of observable functions, where their evolution is described by the linear Koopman operator. This paper describes how the Koopman operator can be used to generate approximate linear, bilinear, and nonlinear model realizations from data, and argues in favor of bilinear realizations for characterizing systems with unknown dynamics. Necessary and sufficient conditions for a dynamical system to have a valid linear or bilinear realization over a given set of observable functions are presented and used to show th","authors_text":"Daniel Bruder, Ram Vasudevan, Xun Fu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2020-10-20T02:10:23Z","title":"Advantages of Bilinear Koopman Realizations for the Modeling and Control of Systems with Unknown Dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.09961","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":"sha256:2be091229e152550fb70044d7315d440ac846fa9886519622e5b9b90c1a2124a","target":"record","created_at":"2026-07-05T01:51:22Z","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":"8928df31845169556be585ae775509b36e933803521f9ac6e3745a2e30fb8fc2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2020-10-20T02:10:23Z","title_canon_sha256":"dcfc9f2476d6835eb296ad5abe4903ba1290dd0c4f6e5735449f20a87f5c2e20"},"schema_version":"1.0","source":{"id":"2010.09961","kind":"arxiv","version":3}},"canonical_sha256":"44daabeaecdb93af317063b5630a121cc4c7edf7a25441c27ef7a47ccb8b6e84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44daabeaecdb93af317063b5630a121cc4c7edf7a25441c27ef7a47ccb8b6e84","first_computed_at":"2026-07-05T01:51:22.310392Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:51:22.310392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o2PgQ1CLRqMX9YprV7BG2HQ9kwJeYWaV+ENfWssLdr3fGHHlISNqoTcmFxXGxAZQ2vC912GTCGMcfzoCb5o+Dg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:51:22.310736Z","signed_message":"canonical_sha256_bytes"},"source_id":"2010.09961","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2be091229e152550fb70044d7315d440ac846fa9886519622e5b9b90c1a2124a","sha256:a7d80d482997ea3988ae7db891055ff802e413772541c9c327d6f3dfaeff5a84"],"state_sha256":"4589b66066aec5b5b8d7caf49f8e750b149a3ef59a31caa25497f3c1b136ada3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3IFNc6ItvPRxuQOkPCEKf48Z7vBbiVNJsLFL6dug5jhM11266hJ6cVktHFZZnkTjbqJS9NLTgeqjq0+tnhY5Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T12:34:15.732745Z","bundle_sha256":"d2439fda8ce1c57a5ebebbd56190666ea63c351a48c9fc973339c8e8584bbea1"}}