{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:4UWETFBZH55Y25A2YTOITYRX3U","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":"caa3856f8b0129d9dde458e0d43292309c834eb00a3a709a02ac5ed6f1577fd4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-03T08:53:53Z","title_canon_sha256":"49aa54cbf6744f21b3ece2530da9694818a1fd610e85d2ce896c75bc14f2015a"},"schema_version":"1.0","source":{"id":"1904.01850","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.01850","created_at":"2026-05-17T23:49:29Z"},{"alias_kind":"arxiv_version","alias_value":"1904.01850v1","created_at":"2026-05-17T23:49:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.01850","created_at":"2026-05-17T23:49:29Z"},{"alias_kind":"pith_short_12","alias_value":"4UWETFBZH55Y","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"4UWETFBZH55Y25A2","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"4UWETFBZ","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:84696ade4d6306ebd0aa2e681c5be076d602e2f7c1da40084090a7cf56dfb2a6","target":"graph","created_at":"2026-05-17T23:49:29Z","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":"Let (X k) be a strictly stationary sequence of random variables with values in some Polish space E and common marginal $\\mu$, and (A k) k>0 be a sequence of Borel sets in E. In this paper, we give some conditions on (X k) and (A k) under which the events {X k $\\in$ A k } satisfy the Borel-Cantelli (or strong Borel-Cantelli) property. In particular we prove that, if $\\mu$(lim sup n A n) > 0, the Borel-Cantelli property holds for any absolutely regular sequence. In case where the A k 's are nested, we show, on some examples, that a rate of convergence of the mixing coefficients is needed. Finall","authors_text":"Emmanuel Rio (UVSQ), Florence Merlev\\`ede (LAMA), J\\'er\\^ome Dedecker (MAP5 - UMR 8145)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-03T08:53:53Z","title":"Criteria for Borel-Cantelli lemmas with applications to Markov chains and dynamical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.01850","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:a0007a5d7839a9cd4cad83e96decbbf6143724fe71f2df897e61668303b7c44a","target":"record","created_at":"2026-05-17T23:49:29Z","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":"caa3856f8b0129d9dde458e0d43292309c834eb00a3a709a02ac5ed6f1577fd4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-03T08:53:53Z","title_canon_sha256":"49aa54cbf6744f21b3ece2530da9694818a1fd610e85d2ce896c75bc14f2015a"},"schema_version":"1.0","source":{"id":"1904.01850","kind":"arxiv","version":1}},"canonical_sha256":"e52c4994393f7b8d741ac4dc89e237dd19765b1f50313c91e87f84c31d23279e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e52c4994393f7b8d741ac4dc89e237dd19765b1f50313c91e87f84c31d23279e","first_computed_at":"2026-05-17T23:49:29.467997Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:29.467997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7ZT++QSXu+twYM9dyFGQQicpeH2MsZAn5MCNgp3KPW65vPKQZKkXTBWnsG4/OvWiYLmDKhk7Q+RfTSvyQRs/Aw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:29.468537Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.01850","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0007a5d7839a9cd4cad83e96decbbf6143724fe71f2df897e61668303b7c44a","sha256:84696ade4d6306ebd0aa2e681c5be076d602e2f7c1da40084090a7cf56dfb2a6"],"state_sha256":"ccef9d3ccfa2e73616647b45e0a85b4d8c50a76521960bafa985782aa6f221d4"}