{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JT4PDYPZBG5HOTHH4KIA7HAF4R","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":"c20a6778caeae3eca62b327d8c47fd5557a56532e23b0af464d1097e6fa334cc","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-18T11:51:34Z","title_canon_sha256":"3a43992525033646d9dcbd94b848632b76a52ffc1e62454bdd107b20f6fe06c7"},"schema_version":"1.0","source":{"id":"1306.4158","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.4158","created_at":"2026-05-18T03:11:09Z"},{"alias_kind":"arxiv_version","alias_value":"1306.4158v3","created_at":"2026-05-18T03:11:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.4158","created_at":"2026-05-18T03:11:09Z"},{"alias_kind":"pith_short_12","alias_value":"JT4PDYPZBG5H","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JT4PDYPZBG5HOTHH","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JT4PDYPZ","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:99a0a5ae41703c5a173a61420bbbc80b84769233306c6dbd579035da932653dd","target":"graph","created_at":"2026-05-18T03:11:09Z","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":"In this paper we give a historical account of the development of Poisson approximation using Stein's method and present some of the main results. We give two recent applications, one on maximal arithmetic progressions and the other on bootstrap percolation. We also discuss generalisations to compound Poisson approximation, Poisson process approximation and multivariate Poisson approximation, and state a few open problems.","authors_text":"Adrian R\\\"ollin, Louis H. Y. Chen","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-18T11:51:34Z","title":"Approximating dependent rare events"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4158","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":"sha256:4b85db94222a303fd9ec41d675d7a97b05d3fd0d1000744c38660da4d2197e15","target":"record","created_at":"2026-05-18T03:11:09Z","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":"c20a6778caeae3eca62b327d8c47fd5557a56532e23b0af464d1097e6fa334cc","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-18T11:51:34Z","title_canon_sha256":"3a43992525033646d9dcbd94b848632b76a52ffc1e62454bdd107b20f6fe06c7"},"schema_version":"1.0","source":{"id":"1306.4158","kind":"arxiv","version":3}},"canonical_sha256":"4cf8f1e1f909ba774ce7e2900f9c05e4748daef085301b4b5ac685ad9dbb3fbc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4cf8f1e1f909ba774ce7e2900f9c05e4748daef085301b4b5ac685ad9dbb3fbc","first_computed_at":"2026-05-18T03:11:09.117167Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:09.117167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0JGeOhg0Zu5m8lwuk/U+PlkBYo16Y4RCdz1YaGN4ZJOXxqfaIUexoyl/f1TQAom4KSMa0Haai00gISbg9SdJAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:09.117962Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.4158","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b85db94222a303fd9ec41d675d7a97b05d3fd0d1000744c38660da4d2197e15","sha256:99a0a5ae41703c5a173a61420bbbc80b84769233306c6dbd579035da932653dd"],"state_sha256":"f9770def4963ac9ecec6d259f63726bc96228682924e49525ab8acf22dbc7e52"}