{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:KQ6KSWUKAUVYDCIVGB7JCREXJN","short_pith_number":"pith:KQ6KSWUK","canonical_record":{"source":{"id":"1205.3658","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-16T12:45:05Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"3f47005392f1309c8fe97311ddaeddc2e5489d8b469c8c50e91f452f62a6155d","abstract_canon_sha256":"a567357d8e64c5045cb02a578c14a798364f272307a83e6d8cbd55494cb5fe16"},"schema_version":"1.0"},"canonical_sha256":"543ca95a8a052b818915307e9144974b448e4a2d79bb476f91e570ea2985290e","source":{"kind":"arxiv","id":"1205.3658","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.3658","created_at":"2026-05-18T03:27:52Z"},{"alias_kind":"arxiv_version","alias_value":"1205.3658v3","created_at":"2026-05-18T03:27:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.3658","created_at":"2026-05-18T03:27:52Z"},{"alias_kind":"pith_short_12","alias_value":"KQ6KSWUKAUVY","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KQ6KSWUKAUVYDCIV","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KQ6KSWUK","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:KQ6KSWUKAUVYDCIVGB7JCREXJN","target":"record","payload":{"canonical_record":{"source":{"id":"1205.3658","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-16T12:45:05Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"3f47005392f1309c8fe97311ddaeddc2e5489d8b469c8c50e91f452f62a6155d","abstract_canon_sha256":"a567357d8e64c5045cb02a578c14a798364f272307a83e6d8cbd55494cb5fe16"},"schema_version":"1.0"},"canonical_sha256":"543ca95a8a052b818915307e9144974b448e4a2d79bb476f91e570ea2985290e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:52.376871Z","signature_b64":"Gtb72X3pQNuD4BwF9aXyKQObsgZClkRupOgwugNlIpVTgS61vvB/VWOuFVcsJX3tzAMNfV2BMhvi5RF9QNqZDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"543ca95a8a052b818915307e9144974b448e4a2d79bb476f91e570ea2985290e","last_reissued_at":"2026-05-18T03:27:52.376433Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:52.376433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.3658","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":"2026-05-18T03:27:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0aLJJVW/tzPVgi6s7s6HT8KzYYGghHR0i3NHTfCdOcj6nehDNlj7VMxiLnDYhZAl9VJv/lbuXer6gh+HzpZYDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T00:44:47.367985Z"},"content_sha256":"6812f24453955755ec19d1ee9719f2c38d8d50df2cd6271482f639365106d88c","schema_version":"1.0","event_id":"sha256:6812f24453955755ec19d1ee9719f2c38d8d50df2cd6271482f639365106d88c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:KQ6KSWUKAUVYDCIVGB7JCREXJN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random coefficients bifurcating autoregressive processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Anne G\\'egout-Petit, Beno\\^ite de Saporta, Laurence Marsalle","submitted_at":"2012-05-16T12:45:05Z","abstract_excerpt":"This paper presents a model of asymmetric bifurcating autoregressive process with random coefficients. We couple this model with a Galton Watson tree to take into account possibly missing observations. We propose least-squares estimators for the various parameters of the model and prove their consistency with a convergence rate, and their asymptotic normality. We use both the bifurcating Markov chain and martingale approaches and derive new important general results in both these frameworks."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3658","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":"2026-05-18T03:27:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jfaWFD28fKjffjASd29SJiqHrHzR0Gl7/BwegvXXg80UsuCwRo1igHMBTf4JuHZaKzdti+9fQGhwO1pDLh6tCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T00:44:47.368358Z"},"content_sha256":"108cf0fe4c09c58c4a86145e75e63923a56b7fda5aee52925edb66556f2304e0","schema_version":"1.0","event_id":"sha256:108cf0fe4c09c58c4a86145e75e63923a56b7fda5aee52925edb66556f2304e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KQ6KSWUKAUVYDCIVGB7JCREXJN/bundle.json","state_url":"https://pith.science/pith/KQ6KSWUKAUVYDCIVGB7JCREXJN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KQ6KSWUKAUVYDCIVGB7JCREXJN/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":"2026-06-02T00:44:47Z","links":{"resolver":"https://pith.science/pith/KQ6KSWUKAUVYDCIVGB7JCREXJN","bundle":"https://pith.science/pith/KQ6KSWUKAUVYDCIVGB7JCREXJN/bundle.json","state":"https://pith.science/pith/KQ6KSWUKAUVYDCIVGB7JCREXJN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KQ6KSWUKAUVYDCIVGB7JCREXJN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:KQ6KSWUKAUVYDCIVGB7JCREXJN","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":"a567357d8e64c5045cb02a578c14a798364f272307a83e6d8cbd55494cb5fe16","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-16T12:45:05Z","title_canon_sha256":"3f47005392f1309c8fe97311ddaeddc2e5489d8b469c8c50e91f452f62a6155d"},"schema_version":"1.0","source":{"id":"1205.3658","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.3658","created_at":"2026-05-18T03:27:52Z"},{"alias_kind":"arxiv_version","alias_value":"1205.3658v3","created_at":"2026-05-18T03:27:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.3658","created_at":"2026-05-18T03:27:52Z"},{"alias_kind":"pith_short_12","alias_value":"KQ6KSWUKAUVY","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KQ6KSWUKAUVYDCIV","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KQ6KSWUK","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:108cf0fe4c09c58c4a86145e75e63923a56b7fda5aee52925edb66556f2304e0","target":"graph","created_at":"2026-05-18T03:27:52Z","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":"This paper presents a model of asymmetric bifurcating autoregressive process with random coefficients. We couple this model with a Galton Watson tree to take into account possibly missing observations. We propose least-squares estimators for the various parameters of the model and prove their consistency with a convergence rate, and their asymptotic normality. We use both the bifurcating Markov chain and martingale approaches and derive new important general results in both these frameworks.","authors_text":"Anne G\\'egout-Petit, Beno\\^ite de Saporta, Laurence Marsalle","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-16T12:45:05Z","title":"Random coefficients bifurcating autoregressive processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3658","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":"sha256:6812f24453955755ec19d1ee9719f2c38d8d50df2cd6271482f639365106d88c","target":"record","created_at":"2026-05-18T03:27:52Z","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":"a567357d8e64c5045cb02a578c14a798364f272307a83e6d8cbd55494cb5fe16","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-16T12:45:05Z","title_canon_sha256":"3f47005392f1309c8fe97311ddaeddc2e5489d8b469c8c50e91f452f62a6155d"},"schema_version":"1.0","source":{"id":"1205.3658","kind":"arxiv","version":3}},"canonical_sha256":"543ca95a8a052b818915307e9144974b448e4a2d79bb476f91e570ea2985290e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"543ca95a8a052b818915307e9144974b448e4a2d79bb476f91e570ea2985290e","first_computed_at":"2026-05-18T03:27:52.376433Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:52.376433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gtb72X3pQNuD4BwF9aXyKQObsgZClkRupOgwugNlIpVTgS61vvB/VWOuFVcsJX3tzAMNfV2BMhvi5RF9QNqZDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:52.376871Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.3658","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6812f24453955755ec19d1ee9719f2c38d8d50df2cd6271482f639365106d88c","sha256:108cf0fe4c09c58c4a86145e75e63923a56b7fda5aee52925edb66556f2304e0"],"state_sha256":"816cbb49081384fb5ef89c17f5e2e5c426cd3cd50fb29aee8ba0dcc472a7866d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uNmHsrnVgK4NwT33phxyz8rqVA4C9dNBVgVBUuP8I4iyidnJyCntUrcdwfjucSOStl1oL0qCE2zBeEx0M209BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T00:44:47.370394Z","bundle_sha256":"380dbc0c318f388969121356a76b74c8f6d4b2a1a4836fedbf7442fb83092025"}}