{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:K4DUGY7HFE42IEFWHRRUSFGXHD","short_pith_number":"pith:K4DUGY7H","canonical_record":{"source":{"id":"1203.6626","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-29T18:52:06Z","cross_cats_sorted":[],"title_canon_sha256":"333afdd0da06d4740d0ee8e369071d7ea3bbf08a4e20fe91023bd2ff2f68cd74","abstract_canon_sha256":"a0b59f5a6b9853f4b0dfc1d2f3e58871ce8be3b1124d194f86c30c15ad5cd4b6"},"schema_version":"1.0"},"canonical_sha256":"57074363e72939a410b63c634914d738e470dbe8a203b95088006ed1f25c75d4","source":{"kind":"arxiv","id":"1203.6626","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.6626","created_at":"2026-05-18T03:43:27Z"},{"alias_kind":"arxiv_version","alias_value":"1203.6626v2","created_at":"2026-05-18T03:43:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6626","created_at":"2026-05-18T03:43:27Z"},{"alias_kind":"pith_short_12","alias_value":"K4DUGY7HFE42","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"K4DUGY7HFE42IEFW","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"K4DUGY7H","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:K4DUGY7HFE42IEFWHRRUSFGXHD","target":"record","payload":{"canonical_record":{"source":{"id":"1203.6626","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-29T18:52:06Z","cross_cats_sorted":[],"title_canon_sha256":"333afdd0da06d4740d0ee8e369071d7ea3bbf08a4e20fe91023bd2ff2f68cd74","abstract_canon_sha256":"a0b59f5a6b9853f4b0dfc1d2f3e58871ce8be3b1124d194f86c30c15ad5cd4b6"},"schema_version":"1.0"},"canonical_sha256":"57074363e72939a410b63c634914d738e470dbe8a203b95088006ed1f25c75d4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:27.181904Z","signature_b64":"wGODbO7eCaL1xNJAgcXOdrRMPPaZJ6hk/ba1ZAFaFbF0ppOg7LMs1WJKy/99/s4h11UpBfTBhuCtzP1HEv9kBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57074363e72939a410b63c634914d738e470dbe8a203b95088006ed1f25c75d4","last_reissued_at":"2026-05-18T03:43:27.181332Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:27.181332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.6626","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:43:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l4dXfQJ/upoJC3podoGdGiXNubYRETCdmIkAYceTQApihsSjjYidGuLTipWgz7n232f/J3JWzd7cDVf+kcuQAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:57:49.445798Z"},"content_sha256":"47f39c57d1ce2355ba771620cc4ea98e92b214390bba89594765f9ea82759030","schema_version":"1.0","event_id":"sha256:47f39c57d1ce2355ba771620cc4ea98e92b214390bba89594765f9ea82759030"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:K4DUGY7HFE42IEFWHRRUSFGXHD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinear Filters for Hidden Markov Models of Regime Change with Fast Mean-Reverting States","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andrew Papanicolaou","submitted_at":"2012-03-29T18:52:06Z","abstract_excerpt":"We consider filtering for a hidden Markov model that evolves with multiple time scales in the hidden states. In particular, we consider the case where one of the states is a scaled Ornstein-Uhlenbeck process with fast reversion to a shifting-mean that is controlled by a continuous time Markov chain modeling regime change. We show that the nonlinear filter for such a process can be approximated by an averaged filter that asymptotically coincides with the true nonlinear filter of the regime-changing Markov chain as the rate of mean reversion approaches infinity. The asymptotics exploit weak conv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6626","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:43:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aPP7Ks2eQC8HnUErD6evPvsqlVRbXIAHZQ2qlujkRTS8tRNq6VrXZe0Aoj0/Lk5U8AAuv2RMRwS2ps33b4CKCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:57:49.446487Z"},"content_sha256":"4c5512974a5d2479cc1bf797cf09ba91bb0efca522fb1211bdcde947e006f759","schema_version":"1.0","event_id":"sha256:4c5512974a5d2479cc1bf797cf09ba91bb0efca522fb1211bdcde947e006f759"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K4DUGY7HFE42IEFWHRRUSFGXHD/bundle.json","state_url":"https://pith.science/pith/K4DUGY7HFE42IEFWHRRUSFGXHD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K4DUGY7HFE42IEFWHRRUSFGXHD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-11T02:57:49Z","links":{"resolver":"https://pith.science/pith/K4DUGY7HFE42IEFWHRRUSFGXHD","bundle":"https://pith.science/pith/K4DUGY7HFE42IEFWHRRUSFGXHD/bundle.json","state":"https://pith.science/pith/K4DUGY7HFE42IEFWHRRUSFGXHD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K4DUGY7HFE42IEFWHRRUSFGXHD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:K4DUGY7HFE42IEFWHRRUSFGXHD","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":"a0b59f5a6b9853f4b0dfc1d2f3e58871ce8be3b1124d194f86c30c15ad5cd4b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-29T18:52:06Z","title_canon_sha256":"333afdd0da06d4740d0ee8e369071d7ea3bbf08a4e20fe91023bd2ff2f68cd74"},"schema_version":"1.0","source":{"id":"1203.6626","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.6626","created_at":"2026-05-18T03:43:27Z"},{"alias_kind":"arxiv_version","alias_value":"1203.6626v2","created_at":"2026-05-18T03:43:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6626","created_at":"2026-05-18T03:43:27Z"},{"alias_kind":"pith_short_12","alias_value":"K4DUGY7HFE42","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"K4DUGY7HFE42IEFW","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"K4DUGY7H","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:4c5512974a5d2479cc1bf797cf09ba91bb0efca522fb1211bdcde947e006f759","target":"graph","created_at":"2026-05-18T03:43:27Z","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 consider filtering for a hidden Markov model that evolves with multiple time scales in the hidden states. In particular, we consider the case where one of the states is a scaled Ornstein-Uhlenbeck process with fast reversion to a shifting-mean that is controlled by a continuous time Markov chain modeling regime change. We show that the nonlinear filter for such a process can be approximated by an averaged filter that asymptotically coincides with the true nonlinear filter of the regime-changing Markov chain as the rate of mean reversion approaches infinity. The asymptotics exploit weak conv","authors_text":"Andrew Papanicolaou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-29T18:52:06Z","title":"Nonlinear Filters for Hidden Markov Models of Regime Change with Fast Mean-Reverting States"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6626","kind":"arxiv","version":2},"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":"sha256:47f39c57d1ce2355ba771620cc4ea98e92b214390bba89594765f9ea82759030","target":"record","created_at":"2026-05-18T03:43:27Z","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":"a0b59f5a6b9853f4b0dfc1d2f3e58871ce8be3b1124d194f86c30c15ad5cd4b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-29T18:52:06Z","title_canon_sha256":"333afdd0da06d4740d0ee8e369071d7ea3bbf08a4e20fe91023bd2ff2f68cd74"},"schema_version":"1.0","source":{"id":"1203.6626","kind":"arxiv","version":2}},"canonical_sha256":"57074363e72939a410b63c634914d738e470dbe8a203b95088006ed1f25c75d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57074363e72939a410b63c634914d738e470dbe8a203b95088006ed1f25c75d4","first_computed_at":"2026-05-18T03:43:27.181332Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:27.181332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wGODbO7eCaL1xNJAgcXOdrRMPPaZJ6hk/ba1ZAFaFbF0ppOg7LMs1WJKy/99/s4h11UpBfTBhuCtzP1HEv9kBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:27.181904Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.6626","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47f39c57d1ce2355ba771620cc4ea98e92b214390bba89594765f9ea82759030","sha256:4c5512974a5d2479cc1bf797cf09ba91bb0efca522fb1211bdcde947e006f759"],"state_sha256":"5f1c365c4a0367e11bb9dca6bce1b6ef62d1ee8beb482109b60a9f48423b3df6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p806V/6wDVqTCzPZfd46Uqg7/3IpsWinH3uDqry1Ak77NAc/5APz8VC/6h8bU/RGwcYUYYKFPCNhbNbXTIHmAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T02:57:49.450348Z","bundle_sha256":"afba25b5ac26e138f6702cfc065c68a573275cb2afd368c996d0c82e61c66064"}}