{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3N4MHPSF4PN6SVNSJKT7A2AECU","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":"e52f36d61270ca02878b8ce12d96b9d35cd1017faee0810e5c8d0bd49f7a1597","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-07-12T00:56:36Z","title_canon_sha256":"6250da485a8c9679c38b639e59883cb296514d74774146b4490553983547b440"},"schema_version":"1.0","source":{"id":"1607.03211","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.03211","created_at":"2026-05-18T00:36:09Z"},{"alias_kind":"arxiv_version","alias_value":"1607.03211v2","created_at":"2026-05-18T00:36:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.03211","created_at":"2026-05-18T00:36:09Z"},{"alias_kind":"pith_short_12","alias_value":"3N4MHPSF4PN6","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3N4MHPSF4PN6SVNS","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3N4MHPSF","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:717f8b5b039ef4ff4637d218f53b95ed4501331639bfbd00031151ea0096b6ac","target":"graph","created_at":"2026-05-18T00:36:09Z","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 study the number of white balls in a classical P\\'olya urn model with the additional feature that, at random times, a black ball is added to the urn. The number of draws between these random times are i.i.d. and, under certain moment conditions on the inter-arrival distribution, we characterize the limiting distribution of the (properly scaled) number of white balls as the number of draws goes to infinity. The possible limiting distributions obtained in this way vary considerably depending on the inter-arrival distribution and are difficult to describe explicitly. However, we show that the ","authors_text":"Adrian R\\\"ollin, Erol Pek\\\"oz, Nathan Ross","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-07-12T00:56:36Z","title":"P\\'olya urns with immigration at random times"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03211","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":"sha256:28f17315052f8e81179e2f0dcde629bd22a6285ffefa2e6cb531397bad9dc31b","target":"record","created_at":"2026-05-18T00:36:09Z","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":"e52f36d61270ca02878b8ce12d96b9d35cd1017faee0810e5c8d0bd49f7a1597","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-07-12T00:56:36Z","title_canon_sha256":"6250da485a8c9679c38b639e59883cb296514d74774146b4490553983547b440"},"schema_version":"1.0","source":{"id":"1607.03211","kind":"arxiv","version":2}},"canonical_sha256":"db78c3be45e3dbe955b24aa7f06804153ea861b84c0b8c210ac3eea5e24c7cfd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db78c3be45e3dbe955b24aa7f06804153ea861b84c0b8c210ac3eea5e24c7cfd","first_computed_at":"2026-05-18T00:36:09.702409Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:09.702409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tp+LZYneEuCWfxNrQO8jvT6Va/WyQn1mB42GNGpcLyQdqJ/5nSXuDkkLkqIg/AJDJG/hMMDK7VE2/Ap5UKZhDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:09.702943Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.03211","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28f17315052f8e81179e2f0dcde629bd22a6285ffefa2e6cb531397bad9dc31b","sha256:717f8b5b039ef4ff4637d218f53b95ed4501331639bfbd00031151ea0096b6ac"],"state_sha256":"8a213910137eef485a5d61f71151bce67c89dc7fb3a3e282a15b77b6020ca520"}