{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:RX6WIAR4MJKDTSIE2M4ZR6OD2A","short_pith_number":"pith:RX6WIAR4","schema_version":"1.0","canonical_sha256":"8dfd64023c625439c904d33998f9c3d02ec1f52f8a58406e871d054825778900","source":{"kind":"arxiv","id":"1311.1831","version":3},"attestation_state":"computed","paper":{"title":"Linear theory for filtering nonlinear multiscale systems with model error","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"John Harlim, Tyrus Berry","submitted_at":"2013-11-07T21:52:28Z","abstract_excerpt":"We study filtering of multiscale dynamical systems with model error arising from unresolved smaller scale processes. The analysis assumes continuous-time noisy observations of all components of the slow variables alone. For a linear model with Gaussian noise, we prove existence of a unique choice of parameters in a linear reduced model for the slow variables. The linear theory extends to to a non-Gaussian, nonlinear test problem, where we assume we know the optimal stochastic parameterization and the correct observation model. We show that when the parameterization is inappropriate, parameters"},"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":"1311.1831","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-07T21:52:28Z","cross_cats_sorted":[],"title_canon_sha256":"9e9abb405fac954fd4515ff614657c2c99a51f2ed4fc729557007a2d0326bcff","abstract_canon_sha256":"888b5189fea80d2082eb6667897bb3058dc2a41d5c1481583c2ae95abcbb808e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:22.516577Z","signature_b64":"nAKk3/VnplKiHA83L6hbHr+s9+nZJeqfO//3KbbBmQ9NrzZevPH8JGEubGj6cVPGj/QYlA0SZC5PX6+lfooSAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8dfd64023c625439c904d33998f9c3d02ec1f52f8a58406e871d054825778900","last_reissued_at":"2026-05-18T02:32:22.516165Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:22.516165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Linear theory for filtering nonlinear multiscale systems with model error","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"John Harlim, Tyrus Berry","submitted_at":"2013-11-07T21:52:28Z","abstract_excerpt":"We study filtering of multiscale dynamical systems with model error arising from unresolved smaller scale processes. The analysis assumes continuous-time noisy observations of all components of the slow variables alone. For a linear model with Gaussian noise, we prove existence of a unique choice of parameters in a linear reduced model for the slow variables. The linear theory extends to to a non-Gaussian, nonlinear test problem, where we assume we know the optimal stochastic parameterization and the correct observation model. We show that when the parameterization is inappropriate, parameters"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1831","kind":"arxiv","version":3},"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":"1311.1831","created_at":"2026-05-18T02:32:22.516237+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.1831v3","created_at":"2026-05-18T02:32:22.516237+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.1831","created_at":"2026-05-18T02:32:22.516237+00:00"},{"alias_kind":"pith_short_12","alias_value":"RX6WIAR4MJKD","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"RX6WIAR4MJKDTSIE","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"RX6WIAR4","created_at":"2026-05-18T12:27:59.945178+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/RX6WIAR4MJKDTSIE2M4ZR6OD2A","json":"https://pith.science/pith/RX6WIAR4MJKDTSIE2M4ZR6OD2A.json","graph_json":"https://pith.science/api/pith-number/RX6WIAR4MJKDTSIE2M4ZR6OD2A/graph.json","events_json":"https://pith.science/api/pith-number/RX6WIAR4MJKDTSIE2M4ZR6OD2A/events.json","paper":"https://pith.science/paper/RX6WIAR4"},"agent_actions":{"view_html":"https://pith.science/pith/RX6WIAR4MJKDTSIE2M4ZR6OD2A","download_json":"https://pith.science/pith/RX6WIAR4MJKDTSIE2M4ZR6OD2A.json","view_paper":"https://pith.science/paper/RX6WIAR4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.1831&json=true","fetch_graph":"https://pith.science/api/pith-number/RX6WIAR4MJKDTSIE2M4ZR6OD2A/graph.json","fetch_events":"https://pith.science/api/pith-number/RX6WIAR4MJKDTSIE2M4ZR6OD2A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RX6WIAR4MJKDTSIE2M4ZR6OD2A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RX6WIAR4MJKDTSIE2M4ZR6OD2A/action/storage_attestation","attest_author":"https://pith.science/pith/RX6WIAR4MJKDTSIE2M4ZR6OD2A/action/author_attestation","sign_citation":"https://pith.science/pith/RX6WIAR4MJKDTSIE2M4ZR6OD2A/action/citation_signature","submit_replication":"https://pith.science/pith/RX6WIAR4MJKDTSIE2M4ZR6OD2A/action/replication_record"}},"created_at":"2026-05-18T02:32:22.516237+00:00","updated_at":"2026-05-18T02:32:22.516237+00:00"}