{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KANQYIZKCK6J5N5T3HBKP3EBW5","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":"49acb79d719dbdd102e03ad94bf2f4a8a6f9e273d885f63867d544bb3bec920d","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-03-14T19:52:04Z","title_canon_sha256":"70591372dd1361bd923e6caf05ac5e900de3afe192653c1ee0e2aedec8fa7dcb"},"schema_version":"1.0","source":{"id":"1603.04419","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04419","created_at":"2026-05-18T01:14:58Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04419v3","created_at":"2026-05-18T01:14:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04419","created_at":"2026-05-18T01:14:58Z"},{"alias_kind":"pith_short_12","alias_value":"KANQYIZKCK6J","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KANQYIZKCK6J5N5T","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KANQYIZK","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:bf286202a3404a2a8e8b97e192d8842bd9819040785f1f78cd2d485ab8ae2e2a","target":"graph","created_at":"2026-05-18T01:14:58Z","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":"Reciprocal processes are acausal generalizations of Markov processes introduced by Bernstein in 1932. In the literature, a significant amount of attention has been focused on developing dynamical models for reciprocal processes. In this paper, we provide a probabilistic graphical model for reciprocal processes. This leads to a principled solution of the smoothing problem via message passing algorithms. For the finite state space case, convergence analysis is revisited via the Hilbert metric.","authors_text":"Francesca Paola Carli","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-03-14T19:52:04Z","title":"Modeling and Estimation of Discrete-Time Reciprocal Processes via Probabilistic Graphical Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04419","kind":"arxiv","version":3},"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":"sha256:7509a93ac340e558f6633b364b5d8bfa6e7d150e5cfcd9722cf9b1d0b7bab3b4","target":"record","created_at":"2026-05-18T01:14:58Z","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":"49acb79d719dbdd102e03ad94bf2f4a8a6f9e273d885f63867d544bb3bec920d","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-03-14T19:52:04Z","title_canon_sha256":"70591372dd1361bd923e6caf05ac5e900de3afe192653c1ee0e2aedec8fa7dcb"},"schema_version":"1.0","source":{"id":"1603.04419","kind":"arxiv","version":3}},"canonical_sha256":"501b0c232a12bc9eb7b3d9c2a7ec81b755797cda7171f6818e8834a404931825","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"501b0c232a12bc9eb7b3d9c2a7ec81b755797cda7171f6818e8834a404931825","first_computed_at":"2026-05-18T01:14:58.509931Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:58.509931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vnNwg0c4uhHGiaFahbDpIVnaMDqfB45pQfBuJzFABStVyeuMTtQuXKemQkqOuGrWT16Bn+6SDXOKdm06mE2ZBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:58.510392Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.04419","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7509a93ac340e558f6633b364b5d8bfa6e7d150e5cfcd9722cf9b1d0b7bab3b4","sha256:bf286202a3404a2a8e8b97e192d8842bd9819040785f1f78cd2d485ab8ae2e2a"],"state_sha256":"e7c0ea4ae4a8e458f1d58606de4868912232bedd15a24990cad9c5bbc780f4d5"}