{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:4SUJT3W6JIZG4WUGA7XJHDEPA5","short_pith_number":"pith:4SUJT3W6","canonical_record":{"source":{"id":"math/0107144","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2001-07-20T09:27:44Z","cross_cats_sorted":[],"title_canon_sha256":"7e68d2faf2f312dd2a0701fb9b6f680b504f80ac581719048501d83dd059b802","abstract_canon_sha256":"67ee31635135d1b0da104a09925c174df0b20c089efbd8ea15c9b90ddd871381"},"schema_version":"1.0"},"canonical_sha256":"e4a899eede4a326e5a8607ee938c8f077cc617db522d2285d16c65db4f03074e","source":{"kind":"arxiv","id":"math/0107144","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0107144","created_at":"2026-05-18T02:47:41Z"},{"alias_kind":"arxiv_version","alias_value":"math/0107144v1","created_at":"2026-05-18T02:47:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0107144","created_at":"2026-05-18T02:47:41Z"},{"alias_kind":"pith_short_12","alias_value":"4SUJT3W6JIZG","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"4SUJT3W6JIZG4WUG","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"4SUJT3W6","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:4SUJT3W6JIZG4WUGA7XJHDEPA5","target":"record","payload":{"canonical_record":{"source":{"id":"math/0107144","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2001-07-20T09:27:44Z","cross_cats_sorted":[],"title_canon_sha256":"7e68d2faf2f312dd2a0701fb9b6f680b504f80ac581719048501d83dd059b802","abstract_canon_sha256":"67ee31635135d1b0da104a09925c174df0b20c089efbd8ea15c9b90ddd871381"},"schema_version":"1.0"},"canonical_sha256":"e4a899eede4a326e5a8607ee938c8f077cc617db522d2285d16c65db4f03074e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:41.660755Z","signature_b64":"MIihb83WytkS2h086nONfeEt77w01W/sdveuUfNGgzYHJPBfY+itAVCh+/rjl02LCJii3hCud2ExCdWZa3wZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4a899eede4a326e5a8607ee938c8f077cc617db522d2285d16c65db4f03074e","last_reissued_at":"2026-05-18T02:47:41.660004Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:41.660004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0107144","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:47:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GJGM1PQkB8faIEUage6zTXtstjN6N+/2MOucHG1nGQDPVSQB63IvFtaX2d9L75y9ZC5PSIMF4hT4gTuRNAodBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T15:37:45.115840Z"},"content_sha256":"3c03623c5b67ca21ace456441dd88c0765ca6c8c5ecd8e05fc70bb2d677fbfa1","schema_version":"1.0","event_id":"sha256:3c03623c5b67ca21ace456441dd88c0765ca6c8c5ecd8e05fc70bb2d677fbfa1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:4SUJT3W6JIZG4WUGA7XJHDEPA5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On hidden Markov chains and finite stochastic systems","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Peter Spreij","submitted_at":"2001-07-20T09:27:44Z","abstract_excerpt":"In this paper we study various properties of finite stochastic systems or hidden Markov chains as they are alternatively called. We discuss their construction following different approaches and we also derive recursive filtering formulas for the different systems that we consider. The key tool is a simple lemma on conditional expectations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0107144","kind":"arxiv","version":1},"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":"2026-05-18T02:47:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pp6irw7fYbgFyyqOeQx3IhJSvwd73H7FV1fMDTJBUa4rR70JaYjTqTjnL0le3Zu4tM1KbAk5mGRp+bfwMQh7Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T15:37:45.116179Z"},"content_sha256":"5d436c718d41b0a7c02bd2980775a1bb895d92f96f43093772a1c62fcedd755f","schema_version":"1.0","event_id":"sha256:5d436c718d41b0a7c02bd2980775a1bb895d92f96f43093772a1c62fcedd755f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4SUJT3W6JIZG4WUGA7XJHDEPA5/bundle.json","state_url":"https://pith.science/pith/4SUJT3W6JIZG4WUGA7XJHDEPA5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4SUJT3W6JIZG4WUGA7XJHDEPA5/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":"2026-06-22T15:37:45Z","links":{"resolver":"https://pith.science/pith/4SUJT3W6JIZG4WUGA7XJHDEPA5","bundle":"https://pith.science/pith/4SUJT3W6JIZG4WUGA7XJHDEPA5/bundle.json","state":"https://pith.science/pith/4SUJT3W6JIZG4WUGA7XJHDEPA5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4SUJT3W6JIZG4WUGA7XJHDEPA5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:4SUJT3W6JIZG4WUGA7XJHDEPA5","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":"67ee31635135d1b0da104a09925c174df0b20c089efbd8ea15c9b90ddd871381","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2001-07-20T09:27:44Z","title_canon_sha256":"7e68d2faf2f312dd2a0701fb9b6f680b504f80ac581719048501d83dd059b802"},"schema_version":"1.0","source":{"id":"math/0107144","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0107144","created_at":"2026-05-18T02:47:41Z"},{"alias_kind":"arxiv_version","alias_value":"math/0107144v1","created_at":"2026-05-18T02:47:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0107144","created_at":"2026-05-18T02:47:41Z"},{"alias_kind":"pith_short_12","alias_value":"4SUJT3W6JIZG","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"4SUJT3W6JIZG4WUG","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"4SUJT3W6","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:5d436c718d41b0a7c02bd2980775a1bb895d92f96f43093772a1c62fcedd755f","target":"graph","created_at":"2026-05-18T02:47:41Z","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":"In this paper we study various properties of finite stochastic systems or hidden Markov chains as they are alternatively called. We discuss their construction following different approaches and we also derive recursive filtering formulas for the different systems that we consider. The key tool is a simple lemma on conditional expectations.","authors_text":"Peter Spreij","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2001-07-20T09:27:44Z","title":"On hidden Markov chains and finite stochastic systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0107144","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":"sha256:3c03623c5b67ca21ace456441dd88c0765ca6c8c5ecd8e05fc70bb2d677fbfa1","target":"record","created_at":"2026-05-18T02:47:41Z","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":"67ee31635135d1b0da104a09925c174df0b20c089efbd8ea15c9b90ddd871381","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2001-07-20T09:27:44Z","title_canon_sha256":"7e68d2faf2f312dd2a0701fb9b6f680b504f80ac581719048501d83dd059b802"},"schema_version":"1.0","source":{"id":"math/0107144","kind":"arxiv","version":1}},"canonical_sha256":"e4a899eede4a326e5a8607ee938c8f077cc617db522d2285d16c65db4f03074e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4a899eede4a326e5a8607ee938c8f077cc617db522d2285d16c65db4f03074e","first_computed_at":"2026-05-18T02:47:41.660004Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:41.660004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MIihb83WytkS2h086nONfeEt77w01W/sdveuUfNGgzYHJPBfY+itAVCh+/rjl02LCJii3hCud2ExCdWZa3wZDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:41.660755Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0107144","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c03623c5b67ca21ace456441dd88c0765ca6c8c5ecd8e05fc70bb2d677fbfa1","sha256:5d436c718d41b0a7c02bd2980775a1bb895d92f96f43093772a1c62fcedd755f"],"state_sha256":"8acaada4326460f1df7997735a5ab9b1eabc3694d3554684169ae6aa6616c823"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ydv6Var+uVqtTJgXGDVy2WWkba/WsWFZorV0oQYLIO2aJ/28rjl8xUa0NtYYFbGUIUGSJHXN6Tfg8Jf87axSCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T15:37:45.118122Z","bundle_sha256":"3feccaaa88049e5a506bcd9d9d60d4cfc8ab702abd6640a7562be5cf7a6415c9"}}