{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:N225UMXM7KFZ6PFRPYR5E463UU","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":"54cc647981919fb06ead0d5f7a82da4ddd3ee01ed906d877757f41048eb2f01f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-12T05:32:08Z","title_canon_sha256":"17120b9f329e356a863a179ff6cada3ac2da3a095021c70b3c72e1a8e448b8bc"},"schema_version":"1.0","source":{"id":"1707.03546","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.03546","created_at":"2026-05-18T00:29:45Z"},{"alias_kind":"arxiv_version","alias_value":"1707.03546v2","created_at":"2026-05-18T00:29:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.03546","created_at":"2026-05-18T00:29:45Z"},{"alias_kind":"pith_short_12","alias_value":"N225UMXM7KFZ","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"N225UMXM7KFZ6PFR","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"N225UMXM","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:a847b98ec182b905a26794398f73f74e12585bd10d29b073039aef906d6c4f5d","target":"graph","created_at":"2026-05-18T00:29:45Z","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":"We generalize the well-known zero bias distribution and the $\\lambda$-Stein pair to an approximate zero bias distribution and an approximate $\\lambda,R$-Stein pair, respectively. Berry Esseen type bounds to the normal, based on approximate zero bias couplings and approximate $\\lambda,R$-Stein pairs, are obtained using Stein's method. The bounds are then applied to combinatorial central limit theorems where the random permutation has the Ewens $\\mathcal{E}_\\theta$ distribution with $\\theta>0$ which can be specialized to the uniform distribution by letting $\\theta=1$. The family of the Ewens dis","authors_text":"Nathakhun Wiroonsri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-12T05:32:08Z","title":"Stein's method using approximate zero bias couplings with applications to combinatorial central limit theorems under the Ewens distribution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03546","kind":"arxiv","version":2},"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:db5d605955739ce8a6e0a4d6fa2c03aaf2b489c85d3a8cb97e7cc17b6d2ab6bf","target":"record","created_at":"2026-05-18T00:29:45Z","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":"54cc647981919fb06ead0d5f7a82da4ddd3ee01ed906d877757f41048eb2f01f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-12T05:32:08Z","title_canon_sha256":"17120b9f329e356a863a179ff6cada3ac2da3a095021c70b3c72e1a8e448b8bc"},"schema_version":"1.0","source":{"id":"1707.03546","kind":"arxiv","version":2}},"canonical_sha256":"6eb5da32ecfa8b9f3cb17e23d273dba530172a00f65726ee3acd27eab2200ac9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6eb5da32ecfa8b9f3cb17e23d273dba530172a00f65726ee3acd27eab2200ac9","first_computed_at":"2026-05-18T00:29:45.762450Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:45.762450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nabZd/uFtCXlgb6XvfT0kamtX8zM5oQFRB8WK0jdqW/er7RBzMbrByUwbXCMAkQYmRs+by17FH8lDzC+usm3BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:45.763332Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.03546","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db5d605955739ce8a6e0a4d6fa2c03aaf2b489c85d3a8cb97e7cc17b6d2ab6bf","sha256:a847b98ec182b905a26794398f73f74e12585bd10d29b073039aef906d6c4f5d"],"state_sha256":"b6e342980a2b78604857017db901868cd7b8f25608f170ee606a481c5754db57"}