{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:CN4I4YSQLW3FMNT2C4EGB5CNX4","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":"11d6f22175214c49b4c5f1cf76ca3bdf065ade243fac68efa12f1cddc1581ed3","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-01-14T04:46:39Z","title_canon_sha256":"140b490ec9d3b4d4419779769e5276c4908ba54895f55d6136d35ad6176341bb"},"schema_version":"1.0","source":{"id":"1901.04127","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.04127","created_at":"2026-05-17T23:56:26Z"},{"alias_kind":"arxiv_version","alias_value":"1901.04127v1","created_at":"2026-05-17T23:56:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.04127","created_at":"2026-05-17T23:56:26Z"},{"alias_kind":"pith_short_12","alias_value":"CN4I4YSQLW3F","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"CN4I4YSQLW3FMNT2","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"CN4I4YSQ","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:b3e593ddb791e56d8e372419f33fcc7a696a7dc27bdbfaf970036e7fe969e230","target":"graph","created_at":"2026-05-17T23:56:26Z","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":"On the one hand, we investigate the Bahadur representation for sample quantiles under $\\varphi$-mixing sequence with $\\varphi(n)=O(n^{-3})$ and obtain a rate as $O(n^{-\\frac{3}{4}}\\log n)$, $a.s.$. On the other hand, by relaxing the condition of mixing coefficients to $\\sum\\nolimits_{n=1}^\\infty\\varphi^{1/2}(n)<\\infty$, a rate $O(n^{-1/2}(\\log n)^{1/2})$, $a.s.$, is also obtained.","authors_text":"Shuhe Hu, Wenzhi Yang, Xuejun Wang","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-01-14T04:46:39Z","title":"The Bahadur representation for sample quantiles under dependent sequence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.04127","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":"sha256:0d0a433fb3fcc17902429e5b7307832afc5880a5289f49ba8783f5c6e7838346","target":"record","created_at":"2026-05-17T23:56:26Z","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":"11d6f22175214c49b4c5f1cf76ca3bdf065ade243fac68efa12f1cddc1581ed3","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-01-14T04:46:39Z","title_canon_sha256":"140b490ec9d3b4d4419779769e5276c4908ba54895f55d6136d35ad6176341bb"},"schema_version":"1.0","source":{"id":"1901.04127","kind":"arxiv","version":1}},"canonical_sha256":"13788e62505db656367a170860f44dbf3419f6b97a08e21fbd42526ed3b7e6df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13788e62505db656367a170860f44dbf3419f6b97a08e21fbd42526ed3b7e6df","first_computed_at":"2026-05-17T23:56:26.240410Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:26.240410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7kNJi9ZkMjzJwTwsv1DfsqvvgthE9Zp7s70bpYyOZ6ZRKGd+rJEIAuR65//CVIeyuI0Q12y/priEFjW8gEXGAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:26.240833Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.04127","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d0a433fb3fcc17902429e5b7307832afc5880a5289f49ba8783f5c6e7838346","sha256:b3e593ddb791e56d8e372419f33fcc7a696a7dc27bdbfaf970036e7fe969e230"],"state_sha256":"ddbca91d2955e3b8957617ee1c42dfa27a9ffef78318f4758f4bd459ed7ea250"}