{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:KANQYIZKCK6J5N5T3HBKP3EBW5","short_pith_number":"pith:KANQYIZK","canonical_record":{"source":{"id":"1603.04419","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-03-14T19:52:04Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"70591372dd1361bd923e6caf05ac5e900de3afe192653c1ee0e2aedec8fa7dcb","abstract_canon_sha256":"49acb79d719dbdd102e03ad94bf2f4a8a6f9e273d885f63867d544bb3bec920d"},"schema_version":"1.0"},"canonical_sha256":"501b0c232a12bc9eb7b3d9c2a7ec81b755797cda7171f6818e8834a404931825","source":{"kind":"arxiv","id":"1603.04419","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:KANQYIZKCK6J5N5T3HBKP3EBW5","target":"record","payload":{"canonical_record":{"source":{"id":"1603.04419","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-03-14T19:52:04Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"70591372dd1361bd923e6caf05ac5e900de3afe192653c1ee0e2aedec8fa7dcb","abstract_canon_sha256":"49acb79d719dbdd102e03ad94bf2f4a8a6f9e273d885f63867d544bb3bec920d"},"schema_version":"1.0"},"canonical_sha256":"501b0c232a12bc9eb7b3d9c2a7ec81b755797cda7171f6818e8834a404931825","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:58.510392Z","signature_b64":"vnNwg0c4uhHGiaFahbDpIVnaMDqfB45pQfBuJzFABStVyeuMTtQuXKemQkqOuGrWT16Bn+6SDXOKdm06mE2ZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"501b0c232a12bc9eb7b3d9c2a7ec81b755797cda7171f6818e8834a404931825","last_reissued_at":"2026-05-18T01:14:58.509931Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:58.509931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.04419","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:14:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rOjkSz0esVvTi46rv3ZobfY9kAxKdSA/Ycu3b5Kyibf66Kyl3tfcTgXnT/i+nZ90VVTgC6BU1VJ4Qu3TjKkfDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:08:10.309913Z"},"content_sha256":"7509a93ac340e558f6633b364b5d8bfa6e7d150e5cfcd9722cf9b1d0b7bab3b4","schema_version":"1.0","event_id":"sha256:7509a93ac340e558f6633b364b5d8bfa6e7d150e5cfcd9722cf9b1d0b7bab3b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:KANQYIZKCK6J5N5T3HBKP3EBW5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modeling and Estimation of Discrete-Time Reciprocal Processes via Probabilistic Graphical Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"stat.ML","authors_text":"Francesca Paola Carli","submitted_at":"2016-03-14T19:52:04Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04419","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:14:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XMDnopkhV3BzL7fHMmYgeyEqh/O8T0wWPDth/dNvbisb6OFB2O/WiJoE8zEh/oW/j9mYStKVjWoA6UATcaW4Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:08:10.310638Z"},"content_sha256":"bf286202a3404a2a8e8b97e192d8842bd9819040785f1f78cd2d485ab8ae2e2a","schema_version":"1.0","event_id":"sha256:bf286202a3404a2a8e8b97e192d8842bd9819040785f1f78cd2d485ab8ae2e2a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KANQYIZKCK6J5N5T3HBKP3EBW5/bundle.json","state_url":"https://pith.science/pith/KANQYIZKCK6J5N5T3HBKP3EBW5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KANQYIZKCK6J5N5T3HBKP3EBW5/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":"2026-06-08T18:08:10Z","links":{"resolver":"https://pith.science/pith/KANQYIZKCK6J5N5T3HBKP3EBW5","bundle":"https://pith.science/pith/KANQYIZKCK6J5N5T3HBKP3EBW5/bundle.json","state":"https://pith.science/pith/KANQYIZKCK6J5N5T3HBKP3EBW5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KANQYIZKCK6J5N5T3HBKP3EBW5/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3lk5QfHY7OObgDhkwbZ8FQtMGGylUd/JHqs6ZtbiDMfO7g5KaDKD7ZuTYOn+aIUP0KtZb4xV0t1uWdjls49kCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T18:08:10.314651Z","bundle_sha256":"473ae37dc1dc19c51fbd81bfd9ec50e01a2b02107e5d8465f1b3c0ffbd85457b"}}