{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ZGBF53LESEI5OG5EG2NJVNWTXR","short_pith_number":"pith:ZGBF53LE","canonical_record":{"source":{"id":"1712.09707","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-12-27T23:10:35Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"205dbe251950012c2e2927211b9a264387f31f73c020da6375bca026f60efbab","abstract_canon_sha256":"e8b91caa4d5836663e9aa63571506f90e2d0c5c90faea7358a3f03f56e1e7822"},"schema_version":"1.0"},"canonical_sha256":"c9825eed649111d71ba4369a9ab6d3bc6cef6ded15c8cef10c0904b5ff9d2ccc","source":{"kind":"arxiv","id":"1712.09707","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.09707","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"arxiv_version","alias_value":"1712.09707v2","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.09707","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"pith_short_12","alias_value":"ZGBF53LESEI5","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZGBF53LESEI5OG5E","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZGBF53LE","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ZGBF53LESEI5OG5EG2NJVNWTXR","target":"record","payload":{"canonical_record":{"source":{"id":"1712.09707","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-12-27T23:10:35Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"205dbe251950012c2e2927211b9a264387f31f73c020da6375bca026f60efbab","abstract_canon_sha256":"e8b91caa4d5836663e9aa63571506f90e2d0c5c90faea7358a3f03f56e1e7822"},"schema_version":"1.0"},"canonical_sha256":"c9825eed649111d71ba4369a9ab6d3bc6cef6ded15c8cef10c0904b5ff9d2ccc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:08.186535Z","signature_b64":"oG1qcLCSKt0VJnyz+SGzWn6ptjdfwPsfGKKE5FHPPJ3Pqz4l6QTcGyRWKYNkN/X0GQbPuShJkh7GCxYMQAtvBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9825eed649111d71ba4369a9ab6d3bc6cef6ded15c8cef10c0904b5ff9d2ccc","last_reissued_at":"2026-05-17T23:52:08.185864Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:08.185864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.09707","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0q5oQlN60YIxMSav2jn/CxQ6t5mAqfcvvhCUUFza/kN9J4kWgSerNofCd+HFQkg6hS7juDEUyijJxUOUPOHODA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T00:42:20.282599Z"},"content_sha256":"f4f6c4df54d19c9ca0a4268bcde24a5d3bdb201d136084b948ec51dbfc2e0a17","schema_version":"1.0","event_id":"sha256:f4f6c4df54d19c9ca0a4268bcde24a5d3bdb201d136084b948ec51dbfc2e0a17"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ZGBF53LESEI5OG5EG2NJVNWTXR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Deep learning for universal linear embeddings of nonlinear dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"math.DS","authors_text":"Bethany Lusch, J. Nathan Kutz, Steven L. Brunton","submitted_at":"2017-12-27T23:10:35Z","abstract_excerpt":"Identifying coordinate transformations that make strongly nonlinear dynamics approximately linear is a central challenge in modern dynamical systems. These transformations have the potential to enable prediction, estimation, and control of nonlinear systems using standard linear theory. The Koopman operator has emerged as a leading data-driven embedding, as eigenfunctions of this operator provide intrinsic coordinates that globally linearize the dynamics. However, identifying and representing these eigenfunctions has proven to be mathematically and computationally challenging. This work levera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09707","kind":"arxiv","version":2},"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":"2026-05-17T23:52:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AqxB9HiZEtV824g0jtztraSAByeH9tSckUL6ql6GxOctkFux5ry+u54Ifp6w/iOBtbHGyP7DYcjQL0BQTFhCCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T00:42:20.282975Z"},"content_sha256":"5cad017d9ad1d70eff7a1195f16366bb68336bbbe2b9c86ecf221cf86bdb396f","schema_version":"1.0","event_id":"sha256:5cad017d9ad1d70eff7a1195f16366bb68336bbbe2b9c86ecf221cf86bdb396f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZGBF53LESEI5OG5EG2NJVNWTXR/bundle.json","state_url":"https://pith.science/pith/ZGBF53LESEI5OG5EG2NJVNWTXR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZGBF53LESEI5OG5EG2NJVNWTXR/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":"2026-06-09T00:42:20Z","links":{"resolver":"https://pith.science/pith/ZGBF53LESEI5OG5EG2NJVNWTXR","bundle":"https://pith.science/pith/ZGBF53LESEI5OG5EG2NJVNWTXR/bundle.json","state":"https://pith.science/pith/ZGBF53LESEI5OG5EG2NJVNWTXR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZGBF53LESEI5OG5EG2NJVNWTXR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZGBF53LESEI5OG5EG2NJVNWTXR","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":"e8b91caa4d5836663e9aa63571506f90e2d0c5c90faea7358a3f03f56e1e7822","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-12-27T23:10:35Z","title_canon_sha256":"205dbe251950012c2e2927211b9a264387f31f73c020da6375bca026f60efbab"},"schema_version":"1.0","source":{"id":"1712.09707","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.09707","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"arxiv_version","alias_value":"1712.09707v2","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.09707","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"pith_short_12","alias_value":"ZGBF53LESEI5","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZGBF53LESEI5OG5E","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZGBF53LE","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:5cad017d9ad1d70eff7a1195f16366bb68336bbbe2b9c86ecf221cf86bdb396f","target":"graph","created_at":"2026-05-17T23:52:08Z","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":"Identifying coordinate transformations that make strongly nonlinear dynamics approximately linear is a central challenge in modern dynamical systems. These transformations have the potential to enable prediction, estimation, and control of nonlinear systems using standard linear theory. The Koopman operator has emerged as a leading data-driven embedding, as eigenfunctions of this operator provide intrinsic coordinates that globally linearize the dynamics. However, identifying and representing these eigenfunctions has proven to be mathematically and computationally challenging. This work levera","authors_text":"Bethany Lusch, J. Nathan Kutz, Steven L. Brunton","cross_cats":["cs.LG","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-12-27T23:10:35Z","title":"Deep learning for universal linear embeddings of nonlinear dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09707","kind":"arxiv","version":2},"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:f4f6c4df54d19c9ca0a4268bcde24a5d3bdb201d136084b948ec51dbfc2e0a17","target":"record","created_at":"2026-05-17T23:52:08Z","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":"e8b91caa4d5836663e9aa63571506f90e2d0c5c90faea7358a3f03f56e1e7822","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-12-27T23:10:35Z","title_canon_sha256":"205dbe251950012c2e2927211b9a264387f31f73c020da6375bca026f60efbab"},"schema_version":"1.0","source":{"id":"1712.09707","kind":"arxiv","version":2}},"canonical_sha256":"c9825eed649111d71ba4369a9ab6d3bc6cef6ded15c8cef10c0904b5ff9d2ccc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9825eed649111d71ba4369a9ab6d3bc6cef6ded15c8cef10c0904b5ff9d2ccc","first_computed_at":"2026-05-17T23:52:08.185864Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:08.185864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oG1qcLCSKt0VJnyz+SGzWn6ptjdfwPsfGKKE5FHPPJ3Pqz4l6QTcGyRWKYNkN/X0GQbPuShJkh7GCxYMQAtvBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:08.186535Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.09707","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4f6c4df54d19c9ca0a4268bcde24a5d3bdb201d136084b948ec51dbfc2e0a17","sha256:5cad017d9ad1d70eff7a1195f16366bb68336bbbe2b9c86ecf221cf86bdb396f"],"state_sha256":"3381e11dbb2c52f0a3cb0624b5b314a9336a2969512821fcfa0f2450ecaa64da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ysuSVzDCEMHNMLq2K300Tw02fpNAtt1YqICl346FUP1wbWBFR2N6sZp7MpAVAVAyq7uF8yKkZVghjmjL0S2kCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T00:42:20.284925Z","bundle_sha256":"2e6e63a9f191a13952548d3b48bf7a15f32dab4124f3aa229a64288ee6696abe"}}