{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:YVTWMFBE4EKFQNFWICAZ5DTVO4","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":"9b69928774d75614d4cb10e3c3a88c8645bb960d2ed8622af0903d98283a0a62","cross_cats_sorted":["math.PR"],"license":"","primary_cat":"math.OC","submitted_at":"2006-06-23T11:20:43Z","title_canon_sha256":"8dd87b0549ba79490ef38ce9f5b77732493f2aee4c05042517bde5d90a684624"},"schema_version":"1.0","source":{"id":"math/0606591","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0606591","created_at":"2026-05-18T02:48:26Z"},{"alias_kind":"arxiv_version","alias_value":"math/0606591v2","created_at":"2026-05-18T02:48:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0606591","created_at":"2026-05-18T02:48:26Z"},{"alias_kind":"pith_short_12","alias_value":"YVTWMFBE4EKF","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"YVTWMFBE4EKFQNFW","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"YVTWMFBE","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:038dddf4b871e8a5bf91cb9978aea788715261b468b2abaf1776a76938ca66ca","target":"graph","created_at":"2026-05-18T02:48:26Z","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 aim at the construction of a Hidden Markov Model (HMM) of assigned complexity (number of states of the underlying Markov chain) which best approximates, in Kullback-Leibler divergence rate, a given stationary process. We establish, under mild conditions, the existence of the divergence rate between a stationary process and an HMM. Since in general there is no analytic expression available for this divergence rate, we approximate it with a properly defined, and easily computable, divergence between Hankel matrices, which we use as our approximation criterion. We propose a three-step algorith","authors_text":"Angela Grassi, Lorenzo Finesso, Peter Spreij","cross_cats":["math.PR"],"headline":"","license":"","primary_cat":"math.OC","submitted_at":"2006-06-23T11:20:43Z","title":"Approximation of stationary processes by Hidden Markov Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606591","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:a999b8494a4ee4678fdc46540ca66a1928247ce192a502284ae2c465751cdbf9","target":"record","created_at":"2026-05-18T02:48:26Z","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":"9b69928774d75614d4cb10e3c3a88c8645bb960d2ed8622af0903d98283a0a62","cross_cats_sorted":["math.PR"],"license":"","primary_cat":"math.OC","submitted_at":"2006-06-23T11:20:43Z","title_canon_sha256":"8dd87b0549ba79490ef38ce9f5b77732493f2aee4c05042517bde5d90a684624"},"schema_version":"1.0","source":{"id":"math/0606591","kind":"arxiv","version":2}},"canonical_sha256":"c567661424e1145834b640819e8e7577177d79853d19c8c81a3490f7b4ea2aef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c567661424e1145834b640819e8e7577177d79853d19c8c81a3490f7b4ea2aef","first_computed_at":"2026-05-18T02:48:26.324743Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:26.324743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4+/7DJfw7PEeJx5iFsGjVhhwiy6GiRnB4lrKtWEKz33F4V7ncK92mYyIAsYKktCBrXJ7HKNOqdEp8BA+WHbQDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:26.325242Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0606591","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a999b8494a4ee4678fdc46540ca66a1928247ce192a502284ae2c465751cdbf9","sha256:038dddf4b871e8a5bf91cb9978aea788715261b468b2abaf1776a76938ca66ca"],"state_sha256":"299df26fb2eec2e12f0e9fe1148e9254787e05cef2ac86c81f98d53ed2453e14"}