{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SWVPWYMWOQ4R3UGLGBTYP3NLQN","short_pith_number":"pith:SWVPWYMW","canonical_record":{"source":{"id":"1603.09279","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-03-30T17:15:02Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"029b0c8395b88e7ff7f242e854b9d30f9d19f6d2d2581eee1211a6f2ef3e7281","abstract_canon_sha256":"cd113d6b6c3c4c682f1ee6195f9a0dc26b6e153e6e24313cd7ddeb0b41b3024b"},"schema_version":"1.0"},"canonical_sha256":"95aafb619674391dd0cb306787edab835761b0eea8654f372dc5e5665d3ba643","source":{"kind":"arxiv","id":"1603.09279","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.09279","created_at":"2026-05-18T00:18:54Z"},{"alias_kind":"arxiv_version","alias_value":"1603.09279v2","created_at":"2026-05-18T00:18:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.09279","created_at":"2026-05-18T00:18:54Z"},{"alias_kind":"pith_short_12","alias_value":"SWVPWYMWOQ4R","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SWVPWYMWOQ4R3UGL","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SWVPWYMW","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SWVPWYMWOQ4R3UGLGBTYP3NLQN","target":"record","payload":{"canonical_record":{"source":{"id":"1603.09279","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-03-30T17:15:02Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"029b0c8395b88e7ff7f242e854b9d30f9d19f6d2d2581eee1211a6f2ef3e7281","abstract_canon_sha256":"cd113d6b6c3c4c682f1ee6195f9a0dc26b6e153e6e24313cd7ddeb0b41b3024b"},"schema_version":"1.0"},"canonical_sha256":"95aafb619674391dd0cb306787edab835761b0eea8654f372dc5e5665d3ba643","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:54.225001Z","signature_b64":"tl2uq/ZRKja4TzqLm/CmumazU8gYyE65g7A5HC/vrhRREAxHJ55hMBAqg0O6TJrUcU/weZX4nzkcURTYtvPmBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95aafb619674391dd0cb306787edab835761b0eea8654f372dc5e5665d3ba643","last_reissued_at":"2026-05-18T00:18:54.224438Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:54.224438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.09279","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":"2026-05-18T00:18:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UweVrQXUwHqc8HUtFhD7h69BuI5/Jux9m2XLBZVH6Rduu2T7a0hKdZGipl2zMjCOX6JvEIwIKs5p9BqDzHyLBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:37:51.360281Z"},"content_sha256":"8a0c822e75d4cb1a64942a031e25bdd0c4a84f0efe63885827524f2fc698df2b","schema_version":"1.0","event_id":"sha256:8a0c822e75d4cb1a64942a031e25bdd0c4a84f0efe63885827524f2fc698df2b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SWVPWYMWOQ4R3UGLGBTYP3NLQN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Geometry of Message Passing Algorithms for Gaussian Reciprocal Processes","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":"2016-03-30T17:15:02Z","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. Recently, probabilistic graphical models for reciprocal processes have been provided. This opens the way to the application of efficient inference algorithms in the machine learning literature to solve the smoothing problem for reciprocal processes. Such algorithms are known to converge if the underlying graph is a tree. This is not the case for a reciprocal process, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09279","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":"2026-05-18T00:18:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"As1NcnWcUFN6pw+BR46yXKNs+wfnh8feV/j39iegDf2W9csuWiSS1cks54zgA7VCX5nSZ4X3lhY9bt9l4Ol/Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:37:51.360994Z"},"content_sha256":"d409da027c5f5873ef674886c3aa76267a0bc73d33418cac0a1ba1e8727a16d4","schema_version":"1.0","event_id":"sha256:d409da027c5f5873ef674886c3aa76267a0bc73d33418cac0a1ba1e8727a16d4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SWVPWYMWOQ4R3UGLGBTYP3NLQN/bundle.json","state_url":"https://pith.science/pith/SWVPWYMWOQ4R3UGLGBTYP3NLQN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SWVPWYMWOQ4R3UGLGBTYP3NLQN/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":"2026-06-09T06:37:51Z","links":{"resolver":"https://pith.science/pith/SWVPWYMWOQ4R3UGLGBTYP3NLQN","bundle":"https://pith.science/pith/SWVPWYMWOQ4R3UGLGBTYP3NLQN/bundle.json","state":"https://pith.science/pith/SWVPWYMWOQ4R3UGLGBTYP3NLQN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SWVPWYMWOQ4R3UGLGBTYP3NLQN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SWVPWYMWOQ4R3UGLGBTYP3NLQN","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":"cd113d6b6c3c4c682f1ee6195f9a0dc26b6e153e6e24313cd7ddeb0b41b3024b","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-03-30T17:15:02Z","title_canon_sha256":"029b0c8395b88e7ff7f242e854b9d30f9d19f6d2d2581eee1211a6f2ef3e7281"},"schema_version":"1.0","source":{"id":"1603.09279","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.09279","created_at":"2026-05-18T00:18:54Z"},{"alias_kind":"arxiv_version","alias_value":"1603.09279v2","created_at":"2026-05-18T00:18:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.09279","created_at":"2026-05-18T00:18:54Z"},{"alias_kind":"pith_short_12","alias_value":"SWVPWYMWOQ4R","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SWVPWYMWOQ4R3UGL","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SWVPWYMW","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:d409da027c5f5873ef674886c3aa76267a0bc73d33418cac0a1ba1e8727a16d4","target":"graph","created_at":"2026-05-18T00:18:54Z","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. Recently, probabilistic graphical models for reciprocal processes have been provided. This opens the way to the application of efficient inference algorithms in the machine learning literature to solve the smoothing problem for reciprocal processes. Such algorithms are known to converge if the underlying graph is a tree. This is not the case for a reciprocal process, w","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":"2016-03-30T17:15:02Z","title":"On the Geometry of Message Passing Algorithms for Gaussian Reciprocal Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09279","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":"sha256:8a0c822e75d4cb1a64942a031e25bdd0c4a84f0efe63885827524f2fc698df2b","target":"record","created_at":"2026-05-18T00:18:54Z","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":"cd113d6b6c3c4c682f1ee6195f9a0dc26b6e153e6e24313cd7ddeb0b41b3024b","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-03-30T17:15:02Z","title_canon_sha256":"029b0c8395b88e7ff7f242e854b9d30f9d19f6d2d2581eee1211a6f2ef3e7281"},"schema_version":"1.0","source":{"id":"1603.09279","kind":"arxiv","version":2}},"canonical_sha256":"95aafb619674391dd0cb306787edab835761b0eea8654f372dc5e5665d3ba643","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95aafb619674391dd0cb306787edab835761b0eea8654f372dc5e5665d3ba643","first_computed_at":"2026-05-18T00:18:54.224438Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:54.224438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tl2uq/ZRKja4TzqLm/CmumazU8gYyE65g7A5HC/vrhRREAxHJ55hMBAqg0O6TJrUcU/weZX4nzkcURTYtvPmBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:54.225001Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.09279","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a0c822e75d4cb1a64942a031e25bdd0c4a84f0efe63885827524f2fc698df2b","sha256:d409da027c5f5873ef674886c3aa76267a0bc73d33418cac0a1ba1e8727a16d4"],"state_sha256":"5fbed30dbe9a626137fbc4e35fde4e483c9ea41ea50704ff212cb3423ce84297"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dTfC0V9xSM7Os2QZ5Jzq9uG8Fht0vhxE4gNl1YsbIvfDCh9qjbgA2MJ4QvVKgX19vpEaD2CX1RQd/w8yKn4ICA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T06:37:51.365465Z","bundle_sha256":"28c875a2ae23967e0947f77cc36294c1893dc0f8f14057769a3d57b61832d3f8"}}