{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:E7RSID6LUE2XAFSPMOLN6P7JIS","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":"6df11ec1f3e2e1cb54fed6db83031884b678cfc8d5d9161e8d4ab4f9514047f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-03-27T10:49:07Z","title_canon_sha256":"c49c706d7b551a3de6edd72d23b49902588c1fd9c828e0fee165adf136ab923f"},"schema_version":"1.0","source":{"id":"1903.11338","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.11338","created_at":"2026-05-17T23:50:03Z"},{"alias_kind":"arxiv_version","alias_value":"1903.11338v1","created_at":"2026-05-17T23:50:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.11338","created_at":"2026-05-17T23:50:03Z"},{"alias_kind":"pith_short_12","alias_value":"E7RSID6LUE2X","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"E7RSID6LUE2XAFSP","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"E7RSID6L","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:d13e5125d33828d4284da0bec571f1c5323f0668502e659c7d74ef476c04e528","target":"graph","created_at":"2026-05-17T23:50:03Z","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":"We consider the critical branching processes in correlated random environment which is positively associated and study the probability of survival up to the n-th generation. Moreover, when the environment is given by fractional Brownian motion, we estimate also the tail of progeny as well as the tail of width.","authors_text":"Nadine Guillotin-Plantard (ICJ), Xinxin Chen (PSPM)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-03-27T10:49:07Z","title":"Branching processes in correlated random environment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.11338","kind":"arxiv","version":1},"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":"sha256:3a6b8db37570e0678b9ff693ffc3a47219a0e99f5b8f431d4628afd5a936adb9","target":"record","created_at":"2026-05-17T23:50:03Z","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":"6df11ec1f3e2e1cb54fed6db83031884b678cfc8d5d9161e8d4ab4f9514047f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-03-27T10:49:07Z","title_canon_sha256":"c49c706d7b551a3de6edd72d23b49902588c1fd9c828e0fee165adf136ab923f"},"schema_version":"1.0","source":{"id":"1903.11338","kind":"arxiv","version":1}},"canonical_sha256":"27e3240fcba13570164f6396df3fe94488f1e99cce138448840f01f906e7d0bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27e3240fcba13570164f6396df3fe94488f1e99cce138448840f01f906e7d0bf","first_computed_at":"2026-05-17T23:50:03.545592Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:03.545592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xGY3Vu/KcEg6uNK0NNYPIqY0IxAQTU2DxvUmyRvt8douPx2689QpYhyMsWkyPVMqgR+/K4Ml4L2CvQVuJnsJCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:03.546042Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.11338","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a6b8db37570e0678b9ff693ffc3a47219a0e99f5b8f431d4628afd5a936adb9","sha256:d13e5125d33828d4284da0bec571f1c5323f0668502e659c7d74ef476c04e528"],"state_sha256":"208fe654b181e0cbdfd38de3eaa4d3b3431f3a35e1829e5f64276ce17d4f1422"}