{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:Z5OC3QC3RUCCYEQS4ZBS62HNBP","short_pith_number":"pith:Z5OC3QC3","canonical_record":{"source":{"id":"1604.01472","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-04-06T03:31:19Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"f86932d5a993011146fca4356db802fc60e76ce2a1b88a1d85df29ab693a82d8","abstract_canon_sha256":"56498cadc70dade3be77aacf8375a1a8b395c142c45e40c7ed9a45e220e0a76d"},"schema_version":"1.0"},"canonical_sha256":"cf5c2dc05b8d042c1212e6432f68ed0bda87b3ca7411da2ae685de5f5d5d380e","source":{"kind":"arxiv","id":"1604.01472","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.01472","created_at":"2026-05-18T00:45:04Z"},{"alias_kind":"arxiv_version","alias_value":"1604.01472v3","created_at":"2026-05-18T00:45:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.01472","created_at":"2026-05-18T00:45:04Z"},{"alias_kind":"pith_short_12","alias_value":"Z5OC3QC3RUCC","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"Z5OC3QC3RUCCYEQS","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"Z5OC3QC3","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:Z5OC3QC3RUCCYEQS4ZBS62HNBP","target":"record","payload":{"canonical_record":{"source":{"id":"1604.01472","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-04-06T03:31:19Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"f86932d5a993011146fca4356db802fc60e76ce2a1b88a1d85df29ab693a82d8","abstract_canon_sha256":"56498cadc70dade3be77aacf8375a1a8b395c142c45e40c7ed9a45e220e0a76d"},"schema_version":"1.0"},"canonical_sha256":"cf5c2dc05b8d042c1212e6432f68ed0bda87b3ca7411da2ae685de5f5d5d380e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:04.946948Z","signature_b64":"ClD0z60DQXPgWRzYFcr8E+HmkCy2nD297d2ylWjnyuuD8JcXafKw0c+bRhFkcSIL4Xt4WOIIBJ6TBXSpwS76BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf5c2dc05b8d042c1212e6432f68ed0bda87b3ca7411da2ae685de5f5d5d380e","last_reissued_at":"2026-05-18T00:45:04.946594Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:04.946594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.01472","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":"2026-05-18T00:45:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HreGxOz2ynucyGrQSmXGvJzGju3l+wkTUS6CN19wOz3BZBKl/p1LVffUry4sWO8rjEm1jV3uluzogjvePXnKCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T13:39:49.155113Z"},"content_sha256":"9b9e2e2341a1a58fa77fec100e1a2cd4173ff81f7309cd1de6c11cecade32e55","schema_version":"1.0","event_id":"sha256:9b9e2e2341a1a58fa77fec100e1a2cd4173ff81f7309cd1de6c11cecade32e55"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:Z5OC3QC3RUCCYEQS4ZBS62HNBP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conjugate Processes: Theory and Application to Risk Forecasting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Eduardo Horta, Flavio Ziegelmann","submitted_at":"2016-04-06T03:31:19Z","abstract_excerpt":"Many dynamical phenomena display a cyclic behavior, in the sense that time can be partitioned into units within which distributional aspects of a process are homogeneous. In this paper, we introduce a class of models - called conjugate processes - allowing the sequence of marginal distributions of a cyclic, continuous-time process to evolve stochastically in time. The connection between the two processes is given by a fundamental compatibility equation. Key results include Laws of Large Numbers in the presented framework. We provide a constructive example which illustrates the theory, and give"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01472","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":"2026-05-18T00:45:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mkD+k4D+6XBUbpa26QJ7Y3rDlvy/F0egCeCmMeVQUYAVrgQi+CbCopu8CM6Tii0nt4r1scEWnJ+xys5N6QdoDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T13:39:49.155898Z"},"content_sha256":"09fb9114a009d74d0f8a8b1e8d5f31508c36d3acb5390c48949aea53bf60cea0","schema_version":"1.0","event_id":"sha256:09fb9114a009d74d0f8a8b1e8d5f31508c36d3acb5390c48949aea53bf60cea0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z5OC3QC3RUCCYEQS4ZBS62HNBP/bundle.json","state_url":"https://pith.science/pith/Z5OC3QC3RUCCYEQS4ZBS62HNBP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z5OC3QC3RUCCYEQS4ZBS62HNBP/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":"2026-05-31T13:39:49Z","links":{"resolver":"https://pith.science/pith/Z5OC3QC3RUCCYEQS4ZBS62HNBP","bundle":"https://pith.science/pith/Z5OC3QC3RUCCYEQS4ZBS62HNBP/bundle.json","state":"https://pith.science/pith/Z5OC3QC3RUCCYEQS4ZBS62HNBP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z5OC3QC3RUCCYEQS4ZBS62HNBP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:Z5OC3QC3RUCCYEQS4ZBS62HNBP","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":"56498cadc70dade3be77aacf8375a1a8b395c142c45e40c7ed9a45e220e0a76d","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-04-06T03:31:19Z","title_canon_sha256":"f86932d5a993011146fca4356db802fc60e76ce2a1b88a1d85df29ab693a82d8"},"schema_version":"1.0","source":{"id":"1604.01472","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.01472","created_at":"2026-05-18T00:45:04Z"},{"alias_kind":"arxiv_version","alias_value":"1604.01472v3","created_at":"2026-05-18T00:45:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.01472","created_at":"2026-05-18T00:45:04Z"},{"alias_kind":"pith_short_12","alias_value":"Z5OC3QC3RUCC","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"Z5OC3QC3RUCCYEQS","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"Z5OC3QC3","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:09fb9114a009d74d0f8a8b1e8d5f31508c36d3acb5390c48949aea53bf60cea0","target":"graph","created_at":"2026-05-18T00:45:04Z","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":"Many dynamical phenomena display a cyclic behavior, in the sense that time can be partitioned into units within which distributional aspects of a process are homogeneous. In this paper, we introduce a class of models - called conjugate processes - allowing the sequence of marginal distributions of a cyclic, continuous-time process to evolve stochastically in time. The connection between the two processes is given by a fundamental compatibility equation. Key results include Laws of Large Numbers in the presented framework. We provide a constructive example which illustrates the theory, and give","authors_text":"Eduardo Horta, Flavio Ziegelmann","cross_cats":["math.PR","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-04-06T03:31:19Z","title":"Conjugate Processes: Theory and Application to Risk Forecasting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01472","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":"sha256:9b9e2e2341a1a58fa77fec100e1a2cd4173ff81f7309cd1de6c11cecade32e55","target":"record","created_at":"2026-05-18T00:45:04Z","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":"56498cadc70dade3be77aacf8375a1a8b395c142c45e40c7ed9a45e220e0a76d","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-04-06T03:31:19Z","title_canon_sha256":"f86932d5a993011146fca4356db802fc60e76ce2a1b88a1d85df29ab693a82d8"},"schema_version":"1.0","source":{"id":"1604.01472","kind":"arxiv","version":3}},"canonical_sha256":"cf5c2dc05b8d042c1212e6432f68ed0bda87b3ca7411da2ae685de5f5d5d380e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf5c2dc05b8d042c1212e6432f68ed0bda87b3ca7411da2ae685de5f5d5d380e","first_computed_at":"2026-05-18T00:45:04.946594Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:04.946594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ClD0z60DQXPgWRzYFcr8E+HmkCy2nD297d2ylWjnyuuD8JcXafKw0c+bRhFkcSIL4Xt4WOIIBJ6TBXSpwS76BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:04.946948Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.01472","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b9e2e2341a1a58fa77fec100e1a2cd4173ff81f7309cd1de6c11cecade32e55","sha256:09fb9114a009d74d0f8a8b1e8d5f31508c36d3acb5390c48949aea53bf60cea0"],"state_sha256":"437f33a6b5927d21a76d6d76dacaf81ed6964716e033f907affdee2631017cd0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lvS7JTAhTkgdCWcqsOfJ9di0vPh+vkXRq3GR06NXy/0bXLqymffIHNG663Q4r8423tOD8QlOC7xdb2KIn53XAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T13:39:49.160143Z","bundle_sha256":"f85ba29c9f9ac09f29dd113fa9e66a868644953150dbd8044f0b8316e8494e3a"}}