{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:T2UFVA6KPDSKGDDD55NBG5WAT7","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":"8ef51dcd54fa4102498d1f0c3c742682b7509114b7620b0c76132eeee1d9ada2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-21T03:46:07Z","title_canon_sha256":"f2ff7fc226cfcec5a62bf41039350ba30caf874a81b8ce1c7da90a719f862408"},"schema_version":"1.0","source":{"id":"1701.05978","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.05978","created_at":"2026-05-17T23:59:27Z"},{"alias_kind":"arxiv_version","alias_value":"1701.05978v4","created_at":"2026-05-17T23:59:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05978","created_at":"2026-05-17T23:59:27Z"},{"alias_kind":"pith_short_12","alias_value":"T2UFVA6KPDSK","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"T2UFVA6KPDSKGDDD","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"T2UFVA6K","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:7d83faf6a7cff564abd1d107f8c2f6b3ba7bc806f84246129695d85512f9014c","target":"graph","created_at":"2026-05-17T23:59:27Z","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":"We analyse various perturbations and projections of Kalman-Bucy semigroups and Riccati equations. For example, covariance inflation-type perturbations and localisation methods (projections) are common in the ensemble Kalman filtering literature. In the limit of these ensemble methods, the regularised sample covariance tends toward a solution of a perturbed/projected Riccati equation. With this motivation, results are given characterising the error between the nominal and regularised Riccati flows and Kalman-Bucy filtering distributions. New projection-type models are also discussed; e.g. Bose-","authors_text":"Adrian N. Bishop, Pierre Del Moral, Sahani D. Pathiraja","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-21T03:46:07Z","title":"Perturbations and projections of Kalman-Bucy semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05978","kind":"arxiv","version":4},"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":"sha256:5a889984cf9083393723fd2fc3da4535c9357660b709f84685f0641f7d5b207f","target":"record","created_at":"2026-05-17T23:59:27Z","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":"8ef51dcd54fa4102498d1f0c3c742682b7509114b7620b0c76132eeee1d9ada2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-21T03:46:07Z","title_canon_sha256":"f2ff7fc226cfcec5a62bf41039350ba30caf874a81b8ce1c7da90a719f862408"},"schema_version":"1.0","source":{"id":"1701.05978","kind":"arxiv","version":4}},"canonical_sha256":"9ea85a83ca78e4a30c63ef5a1376c09ff8dfb569d2a40e94a3ff2d43113b52d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ea85a83ca78e4a30c63ef5a1376c09ff8dfb569d2a40e94a3ff2d43113b52d1","first_computed_at":"2026-05-17T23:59:27.993995Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:27.993995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hhlPlCpHy2ojB807FTdpq2HfDTi+t1BwXjNPrzso371Gz9i+0/Hr1j+qEY2B9EmWD8/INqviXuRRJtsFDf7EBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:27.994413Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.05978","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a889984cf9083393723fd2fc3da4535c9357660b709f84685f0641f7d5b207f","sha256:7d83faf6a7cff564abd1d107f8c2f6b3ba7bc806f84246129695d85512f9014c"],"state_sha256":"b278c7278c5c7ba88076b9f47ff4719963a79eb85a82e63aedb0d4f33db3acc5"}