{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:JO7BMM4G2EGMY3M2AO2YQQN5NQ","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":"b899b491af50225de2c10f62dbad5e2259c5adb035f57aa5f38de5fba8f1a281","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-06-27T04:40:24Z","title_canon_sha256":"ddf52697bbd43d6c8c62f185f99510ed9eb396829ed66cb9f2eb5b7aec11d988"},"schema_version":"1.0","source":{"id":"1806.10296","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10296","created_at":"2026-05-18T00:12:12Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10296v1","created_at":"2026-05-18T00:12:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10296","created_at":"2026-05-18T00:12:12Z"},{"alias_kind":"pith_short_12","alias_value":"JO7BMM4G2EGM","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"JO7BMM4G2EGMY3M2","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"JO7BMM4G","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:379e1c025b4ef40f2d665ed3ffd5eb76f58a75dfe36c353c20ca15fd1277f2b3","target":"graph","created_at":"2026-05-18T00:12:12Z","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":"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 ","authors_text":"Igor Mezi\\'c, Nithin Govindarajan, Ryan Mohr, Shivkumar Chandrasekaran","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-06-27T04:40:24Z","title":"On the approximation of Koopman spectra of measure-preserving flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10296","kind":"arxiv","version":1},"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":"sha256:00bd06288fa56d2f2541bbc157f1cf72395f5622643cb0eddf7daf6708283db5","target":"record","created_at":"2026-05-18T00:12:12Z","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":"b899b491af50225de2c10f62dbad5e2259c5adb035f57aa5f38de5fba8f1a281","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-06-27T04:40:24Z","title_canon_sha256":"ddf52697bbd43d6c8c62f185f99510ed9eb396829ed66cb9f2eb5b7aec11d988"},"schema_version":"1.0","source":{"id":"1806.10296","kind":"arxiv","version":1}},"canonical_sha256":"4bbe163386d10ccc6d9a03b58841bd6c27ae6ac47e4bda86f8c8208e0da09037","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4bbe163386d10ccc6d9a03b58841bd6c27ae6ac47e4bda86f8c8208e0da09037","first_computed_at":"2026-05-18T00:12:12.912675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:12.912675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CTqsIW8GlxwKKTTYUocjfywXkFvpCX0tDeIIHjUICc7X1ElPFZvTqDwpm+RFlH6dheWovuNkATsTtvjnMvqNAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:12.913251Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.10296","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00bd06288fa56d2f2541bbc157f1cf72395f5622643cb0eddf7daf6708283db5","sha256:379e1c025b4ef40f2d665ed3ffd5eb76f58a75dfe36c353c20ca15fd1277f2b3"],"state_sha256":"3dea875d7dfd03dd69eb9e52946ee0583d0bf77f3362e44d7789bad3f55d6a34"}