{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:77SOKYWE4NE6K6NVBUIXJMTZ4P","short_pith_number":"pith:77SOKYWE","schema_version":"1.0","canonical_sha256":"ffe4e562c4e349e579b50d1174b279e3c1a9b506bfce46eb1ad1bf58e261cf1c","source":{"kind":"arxiv","id":"2310.19078","version":1},"attestation_state":"computed","paper":{"title":"Koopman Spectral Linearization vs. Carleman Linearization: A Computational Comparison Study","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.DS","authors_text":"Dongwei Shi, Xiu Yang","submitted_at":"2023-10-29T17:00:23Z","abstract_excerpt":"Nonlinearity presents a significant challenge in problems involving dynamical systems, prompting the exploration of various linearization techniques, including the well-known Carleman Linearization. In this paper, we introduce the Koopman Spectral Linearization method tailored for nonlinear autonomous dynamical systems. This innovative linearization approach harnesses the Chebyshev differentiation matrix and the Koopman Operator to yield a lifted linear system. It holds the promise of serving as an alternative approach that can be employed in scenarios where Carleman linearization is tradition"},"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":"2310.19078","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-10-29T17:00:23Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"cc9cdb047039fd27a2235ef3ae26dddf20e6ee6608bd9dd2ecc3f1135af6df42","abstract_canon_sha256":"8db0a8753851ee42fb1e10a532438c01188070c9a76c8dbb89279b441907ae66"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:06:45.825005Z","signature_b64":"mcC3BnWqGm5+42HeAvRXWfUvb7Xt25vflOGoutSTNW3pgwffhC7tPXnXbKr98QFQPC2en/YHSLJV1xyRiOatBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ffe4e562c4e349e579b50d1174b279e3c1a9b506bfce46eb1ad1bf58e261cf1c","last_reissued_at":"2026-07-05T07:06:45.824541Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:06:45.824541Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Koopman Spectral Linearization vs. Carleman Linearization: A Computational Comparison Study","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.DS","authors_text":"Dongwei Shi, Xiu Yang","submitted_at":"2023-10-29T17:00:23Z","abstract_excerpt":"Nonlinearity presents a significant challenge in problems involving dynamical systems, prompting the exploration of various linearization techniques, including the well-known Carleman Linearization. In this paper, we introduce the Koopman Spectral Linearization method tailored for nonlinear autonomous dynamical systems. This innovative linearization approach harnesses the Chebyshev differentiation matrix and the Koopman Operator to yield a lifted linear system. It holds the promise of serving as an alternative approach that can be employed in scenarios where Carleman linearization is tradition"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.19078","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2310.19078/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":"2310.19078","created_at":"2026-07-05T07:06:45.824597+00:00"},{"alias_kind":"arxiv_version","alias_value":"2310.19078v1","created_at":"2026-07-05T07:06:45.824597+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.19078","created_at":"2026-07-05T07:06:45.824597+00:00"},{"alias_kind":"pith_short_12","alias_value":"77SOKYWE4NE6","created_at":"2026-07-05T07:06:45.824597+00:00"},{"alias_kind":"pith_short_16","alias_value":"77SOKYWE4NE6K6NV","created_at":"2026-07-05T07:06:45.824597+00:00"},{"alias_kind":"pith_short_8","alias_value":"77SOKYWE","created_at":"2026-07-05T07:06:45.824597+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.08349","citing_title":"Quantum algorithms for stochastic nonlinear differential equations","ref_index":15,"is_internal_anchor":false},{"citing_arxiv_id":"2605.15366","citing_title":"Measurement-Efficient Variational Quantum Linear Solver for Carleman-Linearized Nonlinear Dynamics","ref_index":12,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/77SOKYWE4NE6K6NVBUIXJMTZ4P","json":"https://pith.science/pith/77SOKYWE4NE6K6NVBUIXJMTZ4P.json","graph_json":"https://pith.science/api/pith-number/77SOKYWE4NE6K6NVBUIXJMTZ4P/graph.json","events_json":"https://pith.science/api/pith-number/77SOKYWE4NE6K6NVBUIXJMTZ4P/events.json","paper":"https://pith.science/paper/77SOKYWE"},"agent_actions":{"view_html":"https://pith.science/pith/77SOKYWE4NE6K6NVBUIXJMTZ4P","download_json":"https://pith.science/pith/77SOKYWE4NE6K6NVBUIXJMTZ4P.json","view_paper":"https://pith.science/paper/77SOKYWE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2310.19078&json=true","fetch_graph":"https://pith.science/api/pith-number/77SOKYWE4NE6K6NVBUIXJMTZ4P/graph.json","fetch_events":"https://pith.science/api/pith-number/77SOKYWE4NE6K6NVBUIXJMTZ4P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/77SOKYWE4NE6K6NVBUIXJMTZ4P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/77SOKYWE4NE6K6NVBUIXJMTZ4P/action/storage_attestation","attest_author":"https://pith.science/pith/77SOKYWE4NE6K6NVBUIXJMTZ4P/action/author_attestation","sign_citation":"https://pith.science/pith/77SOKYWE4NE6K6NVBUIXJMTZ4P/action/citation_signature","submit_replication":"https://pith.science/pith/77SOKYWE4NE6K6NVBUIXJMTZ4P/action/replication_record"}},"created_at":"2026-07-05T07:06:45.824597+00:00","updated_at":"2026-07-05T07:06:45.824597+00:00"}