{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3DCBUOXINYWZASOOZMSBXNB3LU","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":"576dc2d3686fb0ef74e92f82412f2023306e9044e8f2579d130522960d9064f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-21T04:22:54Z","title_canon_sha256":"79342c6b095ac2be471eade0b5312e0af266d8f6311049be5f0c6fe663b6222f"},"schema_version":"1.0","source":{"id":"1309.5433","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5433","created_at":"2026-05-18T00:44:18Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5433v4","created_at":"2026-05-18T00:44:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5433","created_at":"2026-05-18T00:44:18Z"},{"alias_kind":"pith_short_12","alias_value":"3DCBUOXINYWZ","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3DCBUOXINYWZASOO","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3DCBUOXI","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:278968250a2a17e83ef75bad7a8ec17c5e964dcbca5d87e6f9a68afc18df98dd","target":"graph","created_at":"2026-05-18T00:44:18Z","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 the self-normalized Cram\\a'{e}r-type moderate deviations for centered independent random variables $X_1, X_2,...$ with $0<E |X_i|^3 <\\infty$. The main results refine Theorems 1.1 and 1.2 of Wang (2011), the Berry-Esseen bound (2.11) and Corollaries 2.2 and 2.3 of Jing, Shao and Wang (2003) under stronger moment conditions.","authors_text":"Hailin Sang, Lin Ge","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-21T04:22:54Z","title":"Further Refinement of Self-normalized Cram\\a'{e}r-type moderate Deviations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5433","kind":"arxiv","version":4},"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":"sha256:7c6c7720a90059cd177662056c35188934e96409d6a4469c4455765956d3639e","target":"record","created_at":"2026-05-18T00:44:18Z","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":"576dc2d3686fb0ef74e92f82412f2023306e9044e8f2579d130522960d9064f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-21T04:22:54Z","title_canon_sha256":"79342c6b095ac2be471eade0b5312e0af266d8f6311049be5f0c6fe663b6222f"},"schema_version":"1.0","source":{"id":"1309.5433","kind":"arxiv","version":4}},"canonical_sha256":"d8c41a3ae86e2d9049cecb241bb43b5d0adcdcfd348eca343a8239fff2a105d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8c41a3ae86e2d9049cecb241bb43b5d0adcdcfd348eca343a8239fff2a105d8","first_computed_at":"2026-05-18T00:44:18.209167Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:18.209167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+pMGKwXdRO7kY1D1kF1ZwGgXK1lpVgetkbAucJ1oOJMM9r173xu/7IYSAX8PlrzJQVLLwnBcFFAKhu07DyAxDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:18.209839Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.5433","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c6c7720a90059cd177662056c35188934e96409d6a4469c4455765956d3639e","sha256:278968250a2a17e83ef75bad7a8ec17c5e964dcbca5d87e6f9a68afc18df98dd"],"state_sha256":"13292b71c58c9d923d27ef34157542ce38a4ac7316ef02b17364eadba2a8d7b3"}