{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:JO7BMM4G2EGMY3M2AO2YQQN5NQ","short_pith_number":"pith:JO7BMM4G","schema_version":"1.0","canonical_sha256":"4bbe163386d10ccc6d9a03b58841bd6c27ae6ac47e4bda86f8c8208e0da09037","source":{"kind":"arxiv","id":"1806.10296","version":1},"attestation_state":"computed","paper":{"title":"On the approximation of Koopman spectra of measure-preserving flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Igor Mezi\\'c, Nithin Govindarajan, Ryan Mohr, Shivkumar Chandrasekaran","submitted_at":"2018-06-27T04:40:24Z","abstract_excerpt":"The method of using periodic approximations to compute the spectral decomposition of the Koop- man operator is generalized to the class of measure-preserving flows on compact metric spaces. It is shown that the spectral decomposition of the continuous one-parameter unitary group can be approximated from an intermediate time discretization of the flow. A sufficient condition is established between the time-discretization of the flow and the spatial discretization of the periodic approximation, so that weak convergence of spectra will occur in the limit. This condition effectively translates to "},"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":"1806.10296","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-06-27T04:40:24Z","cross_cats_sorted":[],"title_canon_sha256":"ddf52697bbd43d6c8c62f185f99510ed9eb396829ed66cb9f2eb5b7aec11d988","abstract_canon_sha256":"b899b491af50225de2c10f62dbad5e2259c5adb035f57aa5f38de5fba8f1a281"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:12.913251Z","signature_b64":"CTqsIW8GlxwKKTTYUocjfywXkFvpCX0tDeIIHjUICc7X1ElPFZvTqDwpm+RFlH6dheWovuNkATsTtvjnMvqNAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4bbe163386d10ccc6d9a03b58841bd6c27ae6ac47e4bda86f8c8208e0da09037","last_reissued_at":"2026-05-18T00:12:12.912675Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:12.912675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the approximation of Koopman spectra of measure-preserving flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Igor Mezi\\'c, Nithin Govindarajan, Ryan Mohr, Shivkumar Chandrasekaran","submitted_at":"2018-06-27T04:40:24Z","abstract_excerpt":"The method of using periodic approximations to compute the spectral decomposition of the Koop- man operator is generalized to the class of measure-preserving flows on compact metric spaces. It is shown that the spectral decomposition of the continuous one-parameter unitary group can be approximated from an intermediate time discretization of the flow. A sufficient condition is established between the time-discretization of the flow and the spatial discretization of the periodic approximation, so that weak convergence of spectra will occur in the limit. This condition effectively translates to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10296","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1806.10296","created_at":"2026-05-18T00:12:12.912761+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.10296v1","created_at":"2026-05-18T00:12:12.912761+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10296","created_at":"2026-05-18T00:12:12.912761+00:00"},{"alias_kind":"pith_short_12","alias_value":"JO7BMM4G2EGM","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_16","alias_value":"JO7BMM4G2EGMY3M2","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_8","alias_value":"JO7BMM4G","created_at":"2026-05-18T12:32:31.084164+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JO7BMM4G2EGMY3M2AO2YQQN5NQ","json":"https://pith.science/pith/JO7BMM4G2EGMY3M2AO2YQQN5NQ.json","graph_json":"https://pith.science/api/pith-number/JO7BMM4G2EGMY3M2AO2YQQN5NQ/graph.json","events_json":"https://pith.science/api/pith-number/JO7BMM4G2EGMY3M2AO2YQQN5NQ/events.json","paper":"https://pith.science/paper/JO7BMM4G"},"agent_actions":{"view_html":"https://pith.science/pith/JO7BMM4G2EGMY3M2AO2YQQN5NQ","download_json":"https://pith.science/pith/JO7BMM4G2EGMY3M2AO2YQQN5NQ.json","view_paper":"https://pith.science/paper/JO7BMM4G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.10296&json=true","fetch_graph":"https://pith.science/api/pith-number/JO7BMM4G2EGMY3M2AO2YQQN5NQ/graph.json","fetch_events":"https://pith.science/api/pith-number/JO7BMM4G2EGMY3M2AO2YQQN5NQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JO7BMM4G2EGMY3M2AO2YQQN5NQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JO7BMM4G2EGMY3M2AO2YQQN5NQ/action/storage_attestation","attest_author":"https://pith.science/pith/JO7BMM4G2EGMY3M2AO2YQQN5NQ/action/author_attestation","sign_citation":"https://pith.science/pith/JO7BMM4G2EGMY3M2AO2YQQN5NQ/action/citation_signature","submit_replication":"https://pith.science/pith/JO7BMM4G2EGMY3M2AO2YQQN5NQ/action/replication_record"}},"created_at":"2026-05-18T00:12:12.912761+00:00","updated_at":"2026-05-18T00:12:12.912761+00:00"}