{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:DUZXDF6J4FBVH3HIH5E5AEUAUA","short_pith_number":"pith:DUZXDF6J","schema_version":"1.0","canonical_sha256":"1d337197c9e14353ece83f49d01280a02ddd03b0224cd41c976c497423731056","source":{"kind":"arxiv","id":"2311.13033","version":4},"attestation_state":"computed","paper":{"title":"Invariance Proximity: Closed-Form Error Bounds for Finite-Dimensional Koopman-Based Models","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.SY","eess.SY","math.DS"],"primary_cat":"math.OC","authors_text":"Jorge Cort\\'es, Masih Haseli","submitted_at":"2023-11-21T22:45:07Z","abstract_excerpt":"A popular way to approximate the Koopman operator's action on a finite-dimensional subspace of functions is via orthogonal projections. The quality of the projected model directly depends on the selected subspace, specifically on how close it is to being invariant under the Koopman operator. The notion of invariance proximity provides a tight upper bound on the worst-case relative prediction error of the finite-dimensional model. However, its direct calculation is computationally challenging. This paper leverages the geometric structure behind the definition of invariance proximity to provide "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2311.13033","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.OC","submitted_at":"2023-11-21T22:45:07Z","cross_cats_sorted":["cs.SY","eess.SY","math.DS"],"title_canon_sha256":"ad7b38d370c6b67b45c129055740400e0e14e2cccf8cfde1273e4c0d90cdda9a","abstract_canon_sha256":"5a4988ae8c653c227b6dfc0e86a7da12e22fa9c4117b7faa93604c63097db29e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:00:33.846287Z","signature_b64":"390jCr1X4iQPPgOGaWX0Ah/nqkvd5ahDd+552ko7rve6ChYgaes32cJKRkBep/MEUmsS6aBu8GJjtI5tPf0sCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d337197c9e14353ece83f49d01280a02ddd03b0224cd41c976c497423731056","last_reissued_at":"2026-07-05T10:00:33.845796Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:00:33.845796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invariance Proximity: Closed-Form Error Bounds for Finite-Dimensional Koopman-Based Models","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.SY","eess.SY","math.DS"],"primary_cat":"math.OC","authors_text":"Jorge Cort\\'es, Masih Haseli","submitted_at":"2023-11-21T22:45:07Z","abstract_excerpt":"A popular way to approximate the Koopman operator's action on a finite-dimensional subspace of functions is via orthogonal projections. The quality of the projected model directly depends on the selected subspace, specifically on how close it is to being invariant under the Koopman operator. The notion of invariance proximity provides a tight upper bound on the worst-case relative prediction error of the finite-dimensional model. However, its direct calculation is computationally challenging. This paper leverages the geometric structure behind the definition of invariance proximity to provide "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.13033","kind":"arxiv","version":4},"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/2311.13033/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2311.13033","created_at":"2026-07-05T10:00:33.845862+00:00"},{"alias_kind":"arxiv_version","alias_value":"2311.13033v4","created_at":"2026-07-05T10:00:33.845862+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.13033","created_at":"2026-07-05T10:00:33.845862+00:00"},{"alias_kind":"pith_short_12","alias_value":"DUZXDF6J4FBV","created_at":"2026-07-05T10:00:33.845862+00:00"},{"alias_kind":"pith_short_16","alias_value":"DUZXDF6J4FBVH3HI","created_at":"2026-07-05T10:00:33.845862+00:00"},{"alias_kind":"pith_short_8","alias_value":"DUZXDF6J","created_at":"2026-07-05T10:00:33.845862+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":6,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2607.01819","citing_title":"Koopman operator theory: fundamentals, control, and applications","ref_index":36,"is_internal_anchor":false},{"citing_arxiv_id":"2606.07758","citing_title":"Koopman meets input-output data: Data-driven output-feedback control of nonlinear systems with closed-loop guarantees","ref_index":4,"is_internal_anchor":false},{"citing_arxiv_id":"2605.13135","citing_title":"Subspace Pruning via Principal Vectors for Accurate Koopman-Based Approximations","ref_index":45,"is_internal_anchor":false},{"citing_arxiv_id":"2605.31438","citing_title":"Flow map learning in nonlinear vector autoregressive models: influence of the feature-library structure on the training error","ref_index":94,"is_internal_anchor":false},{"citing_arxiv_id":"2605.16660","citing_title":"Trajectory-based Safety of Monotone Systems: Verification and Control Synthesis","ref_index":26,"is_internal_anchor":false},{"citing_arxiv_id":"2605.13135","citing_title":"Subspace Pruning via Principal Vectors for Accurate Koopman-Based Approximations","ref_index":45,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DUZXDF6J4FBVH3HIH5E5AEUAUA","json":"https://pith.science/pith/DUZXDF6J4FBVH3HIH5E5AEUAUA.json","graph_json":"https://pith.science/api/pith-number/DUZXDF6J4FBVH3HIH5E5AEUAUA/graph.json","events_json":"https://pith.science/api/pith-number/DUZXDF6J4FBVH3HIH5E5AEUAUA/events.json","paper":"https://pith.science/paper/DUZXDF6J"},"agent_actions":{"view_html":"https://pith.science/pith/DUZXDF6J4FBVH3HIH5E5AEUAUA","download_json":"https://pith.science/pith/DUZXDF6J4FBVH3HIH5E5AEUAUA.json","view_paper":"https://pith.science/paper/DUZXDF6J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2311.13033&json=true","fetch_graph":"https://pith.science/api/pith-number/DUZXDF6J4FBVH3HIH5E5AEUAUA/graph.json","fetch_events":"https://pith.science/api/pith-number/DUZXDF6J4FBVH3HIH5E5AEUAUA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DUZXDF6J4FBVH3HIH5E5AEUAUA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DUZXDF6J4FBVH3HIH5E5AEUAUA/action/storage_attestation","attest_author":"https://pith.science/pith/DUZXDF6J4FBVH3HIH5E5AEUAUA/action/author_attestation","sign_citation":"https://pith.science/pith/DUZXDF6J4FBVH3HIH5E5AEUAUA/action/citation_signature","submit_replication":"https://pith.science/pith/DUZXDF6J4FBVH3HIH5E5AEUAUA/action/replication_record"}},"created_at":"2026-07-05T10:00:33.845862+00:00","updated_at":"2026-07-05T10:00:33.845862+00:00"}