{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:EDVTMTGGEJTK5YDGP7VUSBVQD7","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":"adfd5d2d04f7cf615ffa44624993b252e7bc35a2701b89ed48c2bd769047c844","cross_cats_sorted":["stat.TH"],"license":"","primary_cat":"math.ST","submitted_at":"2006-07-03T12:08:57Z","title_canon_sha256":"74583051a01c38f908ff0dc6aed936dfe11eac08554758c3ab0d594fa4c4b8f5"},"schema_version":"1.0","source":{"id":"math/0607046","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0607046","created_at":"2026-05-18T01:08:50Z"},{"alias_kind":"arxiv_version","alias_value":"math/0607046v1","created_at":"2026-05-18T01:08:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0607046","created_at":"2026-05-18T01:08:50Z"},{"alias_kind":"pith_short_12","alias_value":"EDVTMTGGEJTK","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"EDVTMTGGEJTK5YDG","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"EDVTMTGG","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:bc7eabb23d743922f4d841d40209323ebf601d3fe1c3702f9d56d583b83527f4","target":"graph","created_at":"2026-05-18T01:08:50Z","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 study strong approximations (invariance principles) of the sequential uniform and general Bahadur--Kiefer processes of long-range dependent sequences. We also investigate the strong and weak asymptotic behavior of the sequential Vervaat process, that is, the integrated sequential Bahadur--Kiefer process, properly normalized, as well as that of its deviation from its limiting process, the so-called Vervaat error process. It is well known that the Bahadur--Kiefer and the Vervaat error processes cannot converge weakly in the i.i.d. case. In contrast to this, we conclude that the ","authors_text":"Barbara Szyszkowicz, Lihong Wang, Mikl\\'os Cs\\\"org\\H{o}","cross_cats":["stat.TH"],"headline":"","license":"","primary_cat":"math.ST","submitted_at":"2006-07-03T12:08:57Z","title":"Strong invariance principles for sequential Bahadur--Kiefer and Vervaat error processes of long-range dependent sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0607046","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:c066e000529fd4e401f4746214130d7dab9d8b668569bd7b9d444dd66dd80884","target":"record","created_at":"2026-05-18T01:08:50Z","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":"adfd5d2d04f7cf615ffa44624993b252e7bc35a2701b89ed48c2bd769047c844","cross_cats_sorted":["stat.TH"],"license":"","primary_cat":"math.ST","submitted_at":"2006-07-03T12:08:57Z","title_canon_sha256":"74583051a01c38f908ff0dc6aed936dfe11eac08554758c3ab0d594fa4c4b8f5"},"schema_version":"1.0","source":{"id":"math/0607046","kind":"arxiv","version":1}},"canonical_sha256":"20eb364cc62266aee0667feb4906b01fcb60f0ade5c883d8e2a055b92f075908","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20eb364cc62266aee0667feb4906b01fcb60f0ade5c883d8e2a055b92f075908","first_computed_at":"2026-05-18T01:08:50.112649Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:50.112649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hUuXizAnrR0ccIsLOs1wRX7W32OD0SQjy6ClOg6+yJXXso4Lgxhg3tQQ5x5x1CC0EMlZbNHHVTF7UCj++GWODA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:50.113269Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0607046","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c066e000529fd4e401f4746214130d7dab9d8b668569bd7b9d444dd66dd80884","sha256:bc7eabb23d743922f4d841d40209323ebf601d3fe1c3702f9d56d583b83527f4"],"state_sha256":"1be0c9e440cdfc3b4657d43aa4b251f588eb35b7cfd1fd36e888b749de82dd13"}