{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:WQXT5PHQ7YSLCVQMKQPCSZL23X","short_pith_number":"pith:WQXT5PHQ","canonical_record":{"source":{"id":"2501.16489","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ML","submitted_at":"2025-01-27T20:48:10Z","cross_cats_sorted":["cs.LG","cs.SY","eess.SY"],"title_canon_sha256":"0959d1ea57e493198d91d15bac47ef39f8efb2dd2c51d76c76f068a684019aed","abstract_canon_sha256":"cf4ca20c319bd3fac453721cfc96d419c1e4c773f250fd84092dec96aa355cc5"},"schema_version":"1.0"},"canonical_sha256":"b42f3ebcf0fe24b1560c541e29657addc5da2001116cf503938283c4e80cfef0","source":{"kind":"arxiv","id":"2501.16489","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.16489","created_at":"2026-07-05T10:09:52Z"},{"alias_kind":"arxiv_version","alias_value":"2501.16489v2","created_at":"2026-07-05T10:09:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.16489","created_at":"2026-07-05T10:09:52Z"},{"alias_kind":"pith_short_12","alias_value":"WQXT5PHQ7YSL","created_at":"2026-07-05T10:09:52Z"},{"alias_kind":"pith_short_16","alias_value":"WQXT5PHQ7YSLCVQM","created_at":"2026-07-05T10:09:52Z"},{"alias_kind":"pith_short_8","alias_value":"WQXT5PHQ","created_at":"2026-07-05T10:09:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:WQXT5PHQ7YSLCVQMKQPCSZL23X","target":"record","payload":{"canonical_record":{"source":{"id":"2501.16489","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ML","submitted_at":"2025-01-27T20:48:10Z","cross_cats_sorted":["cs.LG","cs.SY","eess.SY"],"title_canon_sha256":"0959d1ea57e493198d91d15bac47ef39f8efb2dd2c51d76c76f068a684019aed","abstract_canon_sha256":"cf4ca20c319bd3fac453721cfc96d419c1e4c773f250fd84092dec96aa355cc5"},"schema_version":"1.0"},"canonical_sha256":"b42f3ebcf0fe24b1560c541e29657addc5da2001116cf503938283c4e80cfef0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:09:52.288791Z","signature_b64":"6jQVsSLjTm+GA+df8pGrDtU1VQK0+3RfI35HkdelRUxlSz6BOfiD/Oue6r1MMqufrMnJ5lSflnOQ11l3PayqAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b42f3ebcf0fe24b1560c541e29657addc5da2001116cf503938283c4e80cfef0","last_reissued_at":"2026-07-05T10:09:52.288391Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:09:52.288391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.16489","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":"2026-07-05T10:09:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JXNRbAjzub82+PAstmCgaf8Q9dE8qmNRszSm3LCwTEbnv/bnVjJzcfHy/QBJXKNEkbvdf42z6GvKu//77sP8Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T07:48:06.242844Z"},"content_sha256":"69fdd508324d59d580179a499c949a7e0a0c08399bda88323e945ac70dd3ded0","schema_version":"1.0","event_id":"sha256:69fdd508324d59d580179a499c949a7e0a0c08399bda88323e945ac70dd3ded0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:WQXT5PHQ7YSLCVQMKQPCSZL23X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonparametric Sparse Online Learning of the Koopman Operator","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.LG","cs.SY","eess.SY"],"primary_cat":"stat.ML","authors_text":"Alec Koppel, Boya Hou, Nathan Dahlin, Sina Sanjari, Subhonmesh Bose","submitted_at":"2025-01-27T20:48:10Z","abstract_excerpt":"The Koopman operator provides a powerful framework for representing the dynamics of general nonlinear dynamical systems. Data-driven techniques to learn the Koopman operator typically assume that the chosen function space is closed under system dynamics. In this paper, we study the Koopman operator via its action on the reproducing kernel Hilbert space (RKHS), and explore the mis-specified scenario where the dynamics may escape the chosen function space. We relate the Koopman operator to the conditional mean embeddings (CME) operator and then present an operator stochastic approximation algori"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.16489","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.16489/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":"2026-07-05T10:09:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VtoIxmHG4P4o3+e9YrjwphydiDo9xxt7QuJVAxoCXinxK7/VtOfmHCfgzwW7Q11WL4K3BKXL7wHu0UnpFOT5Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T07:48:06.243469Z"},"content_sha256":"c9cc79ab9bed3fbe2ed79e4826f312b5dba9281bf09ea3149b9e49483b9dcfa0","schema_version":"1.0","event_id":"sha256:c9cc79ab9bed3fbe2ed79e4826f312b5dba9281bf09ea3149b9e49483b9dcfa0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WQXT5PHQ7YSLCVQMKQPCSZL23X/bundle.json","state_url":"https://pith.science/pith/WQXT5PHQ7YSLCVQMKQPCSZL23X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WQXT5PHQ7YSLCVQMKQPCSZL23X/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":"2026-08-04T07:48:06Z","links":{"resolver":"https://pith.science/pith/WQXT5PHQ7YSLCVQMKQPCSZL23X","bundle":"https://pith.science/pith/WQXT5PHQ7YSLCVQMKQPCSZL23X/bundle.json","state":"https://pith.science/pith/WQXT5PHQ7YSLCVQMKQPCSZL23X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WQXT5PHQ7YSLCVQMKQPCSZL23X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:WQXT5PHQ7YSLCVQMKQPCSZL23X","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":"cf4ca20c319bd3fac453721cfc96d419c1e4c773f250fd84092dec96aa355cc5","cross_cats_sorted":["cs.LG","cs.SY","eess.SY"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ML","submitted_at":"2025-01-27T20:48:10Z","title_canon_sha256":"0959d1ea57e493198d91d15bac47ef39f8efb2dd2c51d76c76f068a684019aed"},"schema_version":"1.0","source":{"id":"2501.16489","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.16489","created_at":"2026-07-05T10:09:52Z"},{"alias_kind":"arxiv_version","alias_value":"2501.16489v2","created_at":"2026-07-05T10:09:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.16489","created_at":"2026-07-05T10:09:52Z"},{"alias_kind":"pith_short_12","alias_value":"WQXT5PHQ7YSL","created_at":"2026-07-05T10:09:52Z"},{"alias_kind":"pith_short_16","alias_value":"WQXT5PHQ7YSLCVQM","created_at":"2026-07-05T10:09:52Z"},{"alias_kind":"pith_short_8","alias_value":"WQXT5PHQ","created_at":"2026-07-05T10:09:52Z"}],"graph_snapshots":[{"event_id":"sha256:c9cc79ab9bed3fbe2ed79e4826f312b5dba9281bf09ea3149b9e49483b9dcfa0","target":"graph","created_at":"2026-07-05T10:09:52Z","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/2501.16489/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Koopman operator provides a powerful framework for representing the dynamics of general nonlinear dynamical systems. Data-driven techniques to learn the Koopman operator typically assume that the chosen function space is closed under system dynamics. In this paper, we study the Koopman operator via its action on the reproducing kernel Hilbert space (RKHS), and explore the mis-specified scenario where the dynamics may escape the chosen function space. We relate the Koopman operator to the conditional mean embeddings (CME) operator and then present an operator stochastic approximation algori","authors_text":"Alec Koppel, Boya Hou, Nathan Dahlin, Sina Sanjari, Subhonmesh Bose","cross_cats":["cs.LG","cs.SY","eess.SY"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ML","submitted_at":"2025-01-27T20:48:10Z","title":"Nonparametric Sparse Online Learning of the Koopman Operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.16489","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":"sha256:69fdd508324d59d580179a499c949a7e0a0c08399bda88323e945ac70dd3ded0","target":"record","created_at":"2026-07-05T10:09:52Z","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":"cf4ca20c319bd3fac453721cfc96d419c1e4c773f250fd84092dec96aa355cc5","cross_cats_sorted":["cs.LG","cs.SY","eess.SY"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ML","submitted_at":"2025-01-27T20:48:10Z","title_canon_sha256":"0959d1ea57e493198d91d15bac47ef39f8efb2dd2c51d76c76f068a684019aed"},"schema_version":"1.0","source":{"id":"2501.16489","kind":"arxiv","version":2}},"canonical_sha256":"b42f3ebcf0fe24b1560c541e29657addc5da2001116cf503938283c4e80cfef0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b42f3ebcf0fe24b1560c541e29657addc5da2001116cf503938283c4e80cfef0","first_computed_at":"2026-07-05T10:09:52.288391Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:09:52.288391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6jQVsSLjTm+GA+df8pGrDtU1VQK0+3RfI35HkdelRUxlSz6BOfiD/Oue6r1MMqufrMnJ5lSflnOQ11l3PayqAw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:09:52.288791Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.16489","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69fdd508324d59d580179a499c949a7e0a0c08399bda88323e945ac70dd3ded0","sha256:c9cc79ab9bed3fbe2ed79e4826f312b5dba9281bf09ea3149b9e49483b9dcfa0"],"state_sha256":"fdc45e7bbfc5474457709510e192dce93449f8419942d062149e9d9229317e46"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sc7LBDnC4MjvPijglqwk+cixtOI7F+2X73YbfPcexSRDsRVaW9ye7d/3GP1mBXSGpBSU6WyfRtZRa/P70kC+CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T07:48:06.248055Z","bundle_sha256":"567f9ad2ed7a159ea978d054e6489ebb42e3caf439a20f269319c82262de0a0b"}}