{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:YUTZME2OJMIMLH3CDVMIJZLXIU","short_pith_number":"pith:YUTZME2O","canonical_record":{"source":{"id":"1709.02883","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-09T00:18:36Z","cross_cats_sorted":[],"title_canon_sha256":"104945b69dcc2a2aa3bda776e820767bada7b3a441cf79f7a8b3de82ac15cdd3","abstract_canon_sha256":"e60660f429a9d9c6c2d83d4bfe83ec1f3bc7fb8f84263c200cc43e4cbb22f78a"},"schema_version":"1.0"},"canonical_sha256":"c52796134e4b10c59f621d5884e577450cceb2385d687c6e1552cbd6a0a67d88","source":{"kind":"arxiv","id":"1709.02883","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.02883","created_at":"2026-05-18T00:35:40Z"},{"alias_kind":"arxiv_version","alias_value":"1709.02883v1","created_at":"2026-05-18T00:35:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.02883","created_at":"2026-05-18T00:35:40Z"},{"alias_kind":"pith_short_12","alias_value":"YUTZME2OJMIM","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YUTZME2OJMIMLH3C","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YUTZME2O","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:YUTZME2OJMIMLH3CDVMIJZLXIU","target":"record","payload":{"canonical_record":{"source":{"id":"1709.02883","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-09T00:18:36Z","cross_cats_sorted":[],"title_canon_sha256":"104945b69dcc2a2aa3bda776e820767bada7b3a441cf79f7a8b3de82ac15cdd3","abstract_canon_sha256":"e60660f429a9d9c6c2d83d4bfe83ec1f3bc7fb8f84263c200cc43e4cbb22f78a"},"schema_version":"1.0"},"canonical_sha256":"c52796134e4b10c59f621d5884e577450cceb2385d687c6e1552cbd6a0a67d88","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:40.249965Z","signature_b64":"Bp31RJ7MhTes1rZ9P7LDlgjLfRmRsvOS0FnafbdsGSnjw6sAG2jtD9oaSyU+AVbW4SpTamuuA8m+i+JzC2mDBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c52796134e4b10c59f621d5884e577450cceb2385d687c6e1552cbd6a0a67d88","last_reissued_at":"2026-05-18T00:35:40.249241Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:40.249241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.02883","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":"2026-05-18T00:35:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"crKj5rgWIMxXhPY/mM+ntFSCOUgciDwBxt/AQqvpjc2V9H2DSukR65iRtE0y656ynpmUQarasmhmbFSt/fnpAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:53:14.341898Z"},"content_sha256":"4dbcd84fdbf7827878fd06b44e6cc0de0abf4f2cfccce06ac786bc7b471a958f","schema_version":"1.0","event_id":"sha256:4dbcd84fdbf7827878fd06b44e6cc0de0abf4f2cfccce06ac786bc7b471a958f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:YUTZME2OJMIMLH3CDVMIJZLXIU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamic mode decomposition for interconnected control systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Byron Heersink, Heiko Hoffmann, Michael A. Warren","submitted_at":"2017-09-09T00:18:36Z","abstract_excerpt":"Dynamic mode decomposition (DMD) is a data-driven technique used for capturing the dynamics of complex systems. DMD has been connected to spectral analysis of the Koopman operator, and essentially extracts spatial-temporal modes of the dynamics from an estimate of the Koopman operator obtained from data. Recent work of Proctor, Brunton, and Kutz has extended DMD and Koopman theory to accommodate systems with control inputs: dynamic mode decomposition with control (DMDc) and Koopman with inputs and control (KIC). In this paper, we introduce a technique, called Network dynamic mode decomposition"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.02883","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":""},"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":"2026-05-18T00:35:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gSJdz01M3SSDsDbWmmiywNR4RJoxCQVtAq/SSHkpD5agZxbPYU9ywtndRrwmUdxsitQL9QrK3CADYrEJ5qC0AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:53:14.342245Z"},"content_sha256":"a0f96b141318112c9b5862fa0356f7eac3bdd114d8913a068fe5e627bb2ed834","schema_version":"1.0","event_id":"sha256:a0f96b141318112c9b5862fa0356f7eac3bdd114d8913a068fe5e627bb2ed834"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YUTZME2OJMIMLH3CDVMIJZLXIU/bundle.json","state_url":"https://pith.science/pith/YUTZME2OJMIMLH3CDVMIJZLXIU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YUTZME2OJMIMLH3CDVMIJZLXIU/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":"2026-06-02T07:53:14Z","links":{"resolver":"https://pith.science/pith/YUTZME2OJMIMLH3CDVMIJZLXIU","bundle":"https://pith.science/pith/YUTZME2OJMIMLH3CDVMIJZLXIU/bundle.json","state":"https://pith.science/pith/YUTZME2OJMIMLH3CDVMIJZLXIU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YUTZME2OJMIMLH3CDVMIJZLXIU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YUTZME2OJMIMLH3CDVMIJZLXIU","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":"e60660f429a9d9c6c2d83d4bfe83ec1f3bc7fb8f84263c200cc43e4cbb22f78a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-09T00:18:36Z","title_canon_sha256":"104945b69dcc2a2aa3bda776e820767bada7b3a441cf79f7a8b3de82ac15cdd3"},"schema_version":"1.0","source":{"id":"1709.02883","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.02883","created_at":"2026-05-18T00:35:40Z"},{"alias_kind":"arxiv_version","alias_value":"1709.02883v1","created_at":"2026-05-18T00:35:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.02883","created_at":"2026-05-18T00:35:40Z"},{"alias_kind":"pith_short_12","alias_value":"YUTZME2OJMIM","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YUTZME2OJMIMLH3C","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YUTZME2O","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:a0f96b141318112c9b5862fa0356f7eac3bdd114d8913a068fe5e627bb2ed834","target":"graph","created_at":"2026-05-18T00:35:40Z","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":"Dynamic mode decomposition (DMD) is a data-driven technique used for capturing the dynamics of complex systems. DMD has been connected to spectral analysis of the Koopman operator, and essentially extracts spatial-temporal modes of the dynamics from an estimate of the Koopman operator obtained from data. Recent work of Proctor, Brunton, and Kutz has extended DMD and Koopman theory to accommodate systems with control inputs: dynamic mode decomposition with control (DMDc) and Koopman with inputs and control (KIC). In this paper, we introduce a technique, called Network dynamic mode decomposition","authors_text":"Byron Heersink, Heiko Hoffmann, Michael A. Warren","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-09T00:18:36Z","title":"Dynamic mode decomposition for interconnected control systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.02883","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":"sha256:4dbcd84fdbf7827878fd06b44e6cc0de0abf4f2cfccce06ac786bc7b471a958f","target":"record","created_at":"2026-05-18T00:35:40Z","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":"e60660f429a9d9c6c2d83d4bfe83ec1f3bc7fb8f84263c200cc43e4cbb22f78a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-09T00:18:36Z","title_canon_sha256":"104945b69dcc2a2aa3bda776e820767bada7b3a441cf79f7a8b3de82ac15cdd3"},"schema_version":"1.0","source":{"id":"1709.02883","kind":"arxiv","version":1}},"canonical_sha256":"c52796134e4b10c59f621d5884e577450cceb2385d687c6e1552cbd6a0a67d88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c52796134e4b10c59f621d5884e577450cceb2385d687c6e1552cbd6a0a67d88","first_computed_at":"2026-05-18T00:35:40.249241Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:40.249241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Bp31RJ7MhTes1rZ9P7LDlgjLfRmRsvOS0FnafbdsGSnjw6sAG2jtD9oaSyU+AVbW4SpTamuuA8m+i+JzC2mDBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:40.249965Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.02883","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4dbcd84fdbf7827878fd06b44e6cc0de0abf4f2cfccce06ac786bc7b471a958f","sha256:a0f96b141318112c9b5862fa0356f7eac3bdd114d8913a068fe5e627bb2ed834"],"state_sha256":"281db6eb0da1b4ab55737b5dcd7d9674174e8934ff8a47121b567338ab1692b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7vyCbqsKTTXlYgVi/z57Y0A4gkhruBLWbDbMywklF09G1s8cb39nuvopu/aiX7VCVP1YxtbC4pN+3B6K4L5MAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T07:53:14.344293Z","bundle_sha256":"724ca2297e5d2a2b2dfe6ef9f37e85ff8ff956285f1130fbbbf800acfb1bb7b5"}}