{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:ZFCDG6EGOSJ25JSQWAYAXAHWSN","short_pith_number":"pith:ZFCDG6EG","canonical_record":{"source":{"id":"1905.03535","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-09T11:18:16Z","cross_cats_sorted":[],"title_canon_sha256":"094b956d1a83398a143a5d37ffd0bd5ee1e3f4ab0e496816998f464cb50a20ac","abstract_canon_sha256":"315923627d1aa60ff7eb8495f83d2803464ae34cfb2b695b34401f4afc8574ff"},"schema_version":"1.0"},"canonical_sha256":"c9443378867493aea650b0300b80f6934ba0d8fdad5119e09144e4be2c83691f","source":{"kind":"arxiv","id":"1905.03535","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.03535","created_at":"2026-05-17T23:46:37Z"},{"alias_kind":"arxiv_version","alias_value":"1905.03535v1","created_at":"2026-05-17T23:46:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.03535","created_at":"2026-05-17T23:46:37Z"},{"alias_kind":"pith_short_12","alias_value":"ZFCDG6EGOSJ2","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"ZFCDG6EGOSJ25JSQ","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"ZFCDG6EG","created_at":"2026-05-18T12:33:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:ZFCDG6EGOSJ25JSQWAYAXAHWSN","target":"record","payload":{"canonical_record":{"source":{"id":"1905.03535","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-09T11:18:16Z","cross_cats_sorted":[],"title_canon_sha256":"094b956d1a83398a143a5d37ffd0bd5ee1e3f4ab0e496816998f464cb50a20ac","abstract_canon_sha256":"315923627d1aa60ff7eb8495f83d2803464ae34cfb2b695b34401f4afc8574ff"},"schema_version":"1.0"},"canonical_sha256":"c9443378867493aea650b0300b80f6934ba0d8fdad5119e09144e4be2c83691f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:37.519842Z","signature_b64":"5/613IVPib4dGNv0zjsvQcpmiaqhVscb711o6r9voMNaZVhoa4KNGKb/4EdKVoSym3WnjRJg2UWqOs1ti3GpDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9443378867493aea650b0300b80f6934ba0d8fdad5119e09144e4be2c83691f","last_reissued_at":"2026-05-17T23:46:37.519149Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:37.519149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.03535","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:46:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/I9p+et2GKkbXfOdcLqEWRs5UkK14SWLg4wVJ4nKL0A0Q6y7eiy5X7pflpj130UbKcl8tJ6wt7LAudk+gdS+BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:28:40.928750Z"},"content_sha256":"730400f2d01080da1748373f08e8afe149f5c51c3d3ef3e7376dfc14be0efbb2","schema_version":"1.0","event_id":"sha256:730400f2d01080da1748373f08e8afe149f5c51c3d3ef3e7376dfc14be0efbb2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:ZFCDG6EGOSJ25JSQWAYAXAHWSN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Branching processes in random environment with immigration stopped at zero","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Doudou Li, Elena Dyakonova, Mei Zhang, Vladimir Vatutin","submitted_at":"2019-05-09T11:18:16Z","abstract_excerpt":"A critical branching process with immigration which evolve in a random environment is considered. Assuming that immigration is not allowed when there are no individuals in the aboriginal population we investigate the tail distribution of the so-called life period of the process, i.e., the length of the time interval between the moment when the process is initiated by a positive number of particles and the moment when there are no individuals in the population for the first time."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03535","kind":"arxiv","version":1},"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":"2026-05-17T23:46:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B4KZGOt837aFz4OSUxAkMdM00OEkYgqx8IVSr/xVjMDtfhwl3fgcS7227+oSvjJYWf8Q7n9y6qS6XgDtDBm0Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:28:40.929102Z"},"content_sha256":"78483d4ddfbe3359f0bdbad4c8315501284d2413a08f727812f3b70d26b3c578","schema_version":"1.0","event_id":"sha256:78483d4ddfbe3359f0bdbad4c8315501284d2413a08f727812f3b70d26b3c578"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZFCDG6EGOSJ25JSQWAYAXAHWSN/bundle.json","state_url":"https://pith.science/pith/ZFCDG6EGOSJ25JSQWAYAXAHWSN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZFCDG6EGOSJ25JSQWAYAXAHWSN/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":"2026-05-31T06:28:40Z","links":{"resolver":"https://pith.science/pith/ZFCDG6EGOSJ25JSQWAYAXAHWSN","bundle":"https://pith.science/pith/ZFCDG6EGOSJ25JSQWAYAXAHWSN/bundle.json","state":"https://pith.science/pith/ZFCDG6EGOSJ25JSQWAYAXAHWSN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZFCDG6EGOSJ25JSQWAYAXAHWSN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ZFCDG6EGOSJ25JSQWAYAXAHWSN","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":"315923627d1aa60ff7eb8495f83d2803464ae34cfb2b695b34401f4afc8574ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-09T11:18:16Z","title_canon_sha256":"094b956d1a83398a143a5d37ffd0bd5ee1e3f4ab0e496816998f464cb50a20ac"},"schema_version":"1.0","source":{"id":"1905.03535","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.03535","created_at":"2026-05-17T23:46:37Z"},{"alias_kind":"arxiv_version","alias_value":"1905.03535v1","created_at":"2026-05-17T23:46:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.03535","created_at":"2026-05-17T23:46:37Z"},{"alias_kind":"pith_short_12","alias_value":"ZFCDG6EGOSJ2","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"ZFCDG6EGOSJ25JSQ","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"ZFCDG6EG","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:78483d4ddfbe3359f0bdbad4c8315501284d2413a08f727812f3b70d26b3c578","target":"graph","created_at":"2026-05-17T23:46:37Z","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":"A critical branching process with immigration which evolve in a random environment is considered. Assuming that immigration is not allowed when there are no individuals in the aboriginal population we investigate the tail distribution of the so-called life period of the process, i.e., the length of the time interval between the moment when the process is initiated by a positive number of particles and the moment when there are no individuals in the population for the first time.","authors_text":"Doudou Li, Elena Dyakonova, Mei Zhang, Vladimir Vatutin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-09T11:18:16Z","title":"Branching processes in random environment with immigration stopped at zero"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03535","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":"sha256:730400f2d01080da1748373f08e8afe149f5c51c3d3ef3e7376dfc14be0efbb2","target":"record","created_at":"2026-05-17T23:46:37Z","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":"315923627d1aa60ff7eb8495f83d2803464ae34cfb2b695b34401f4afc8574ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-09T11:18:16Z","title_canon_sha256":"094b956d1a83398a143a5d37ffd0bd5ee1e3f4ab0e496816998f464cb50a20ac"},"schema_version":"1.0","source":{"id":"1905.03535","kind":"arxiv","version":1}},"canonical_sha256":"c9443378867493aea650b0300b80f6934ba0d8fdad5119e09144e4be2c83691f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9443378867493aea650b0300b80f6934ba0d8fdad5119e09144e4be2c83691f","first_computed_at":"2026-05-17T23:46:37.519149Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:37.519149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5/613IVPib4dGNv0zjsvQcpmiaqhVscb711o6r9voMNaZVhoa4KNGKb/4EdKVoSym3WnjRJg2UWqOs1ti3GpDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:37.519842Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.03535","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:730400f2d01080da1748373f08e8afe149f5c51c3d3ef3e7376dfc14be0efbb2","sha256:78483d4ddfbe3359f0bdbad4c8315501284d2413a08f727812f3b70d26b3c578"],"state_sha256":"09ca494a7c19ffac8fd1a7ab7492d7d158cc3afcdb0db82169b602593bb0c9ca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9ikdmpFnGIU+x9p8t6PRRRHI+ARhlDxuYqGgbEPli9wsTx9OKH8V+Fete0xATZLJna0a9do281vltbynajZeAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T06:28:40.931168Z","bundle_sha256":"edf4ac7be1db40a1503801f51a54de64db7399b3972c730fd61c905dd8c6b5fb"}}