{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:M4ESMZ6TEUDDUJHMTANWKN5MPI","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":"d7dc5c5939cc21b1da3086fa7c58183aca78685e8277e6b75583032bf42d79d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-23T20:40:11Z","title_canon_sha256":"2b2ba50cc30b2e2297cf11f195067b8b249692fe16f5f5f78384bc863c0a6d1b"},"schema_version":"1.0","source":{"id":"1710.08503","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.08503","created_at":"2026-05-18T00:26:24Z"},{"alias_kind":"arxiv_version","alias_value":"1710.08503v2","created_at":"2026-05-18T00:26:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.08503","created_at":"2026-05-18T00:26:24Z"},{"alias_kind":"pith_short_12","alias_value":"M4ESMZ6TEUDD","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"M4ESMZ6TEUDDUJHM","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"M4ESMZ6T","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:74a6e3a5c21458458b9add3e1fbbee08e167181198bfd740865c02d115d96d5b","target":"graph","created_at":"2026-05-18T00:26:24Z","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 prove a Berry-Esseen type inequality for approximating expectations of sufficiently smooth functions $f$, like $f=|\\cdot|^3$, with respect to standardized convolutions of laws $P_1,\\ldots, P_n$ on the real line by corresponding expectations based on symmetric two-point laws $Q_1,\\ldots,Q_n$ isoscedastic to the $P_i$. Equality is attained for every possible constellation of the Lipschitz constant $\\|f\"\\|^{}_{\\mathrm{L}}$ and the variances and the third centred absolute moments of the $P_i$. The error bound is strictly smaller than $\\frac 16$ times the Lyapunov ratio times $\\|f\"\\|^{}_{\\mathrm","authors_text":"Irina Shevtsova, Lutz Mattner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-23T20:40:11Z","title":"An optimal Berry-Esseen type theorem for integrals of smooth functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08503","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":"sha256:813ae70415f324e25d65897121914463c4fad6e7b542f668e28e0fba8a090d9b","target":"record","created_at":"2026-05-18T00:26:24Z","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":"d7dc5c5939cc21b1da3086fa7c58183aca78685e8277e6b75583032bf42d79d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-23T20:40:11Z","title_canon_sha256":"2b2ba50cc30b2e2297cf11f195067b8b249692fe16f5f5f78384bc863c0a6d1b"},"schema_version":"1.0","source":{"id":"1710.08503","kind":"arxiv","version":2}},"canonical_sha256":"67092667d325063a24ec981b6537ac7a10bde860392c350ae0c4a3be939acd26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67092667d325063a24ec981b6537ac7a10bde860392c350ae0c4a3be939acd26","first_computed_at":"2026-05-18T00:26:24.370873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:24.370873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T/PKfZw+QJ4eFEneMvTNKhp5WMFpCyDKA8REPwgkumqlBSpM4KY6bRrfkUYAscXK9+atdzNYzv46sNjOd+4xCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:24.371550Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.08503","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:813ae70415f324e25d65897121914463c4fad6e7b542f668e28e0fba8a090d9b","sha256:74a6e3a5c21458458b9add3e1fbbee08e167181198bfd740865c02d115d96d5b"],"state_sha256":"1c8d3c99ea2136cdb95a0ff1f699d8d494f90800d9d979c77c1de87db8355a0d"}