{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TVXZQ7HYTA5VQ7O3FVNKZQFYNA","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":"4e568cae49216005d82d6246c0a83fb8c739ed9581cfa02c43ad9fbb421c2f9c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-07T14:13:23Z","title_canon_sha256":"6fa5c9fd3d70d29903ce2d1bb72389afae2c82c2e219416167e6d8d0e1776377"},"schema_version":"1.0","source":{"id":"1305.1527","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1527","created_at":"2026-05-18T03:26:21Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1527v1","created_at":"2026-05-18T03:26:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1527","created_at":"2026-05-18T03:26:21Z"},{"alias_kind":"pith_short_12","alias_value":"TVXZQ7HYTA5V","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TVXZQ7HYTA5VQ7O3","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TVXZQ7HY","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:47c492f38363a85d3402868c6481230dab1861c242cfcbd9f8b0da10bc413693","target":"graph","created_at":"2026-05-18T03:26:21Z","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 compute the exact rates of convergence in total variation associated with the 'fourth moment theorem' by Nualart and Peccati (2005), stating that a sequence of random variables living in a fixed Wiener chaos verifies a central limit theorem (CLT) if and only if the sequence of the corresponding fourth cumulants converges to zero. We also provide an explicit illustration based on the Breuer-Major CLT for Gaussian-subordinated random sequences.","authors_text":"Giovanni Peccati (FSTC), Ivan Nourdin (IECN)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-07T14:13:23Z","title":"The optimal fourth moment theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1527","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:be38a5cbb5ac0f0e2ba979378abbe2f841566a9a3e0941bb5ccb751e5f2f71dd","target":"record","created_at":"2026-05-18T03:26:21Z","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":"4e568cae49216005d82d6246c0a83fb8c739ed9581cfa02c43ad9fbb421c2f9c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-07T14:13:23Z","title_canon_sha256":"6fa5c9fd3d70d29903ce2d1bb72389afae2c82c2e219416167e6d8d0e1776377"},"schema_version":"1.0","source":{"id":"1305.1527","kind":"arxiv","version":1}},"canonical_sha256":"9d6f987cf8983b587ddb2d5aacc0b86839a2abc0a07268db0378c22d75fe8242","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d6f987cf8983b587ddb2d5aacc0b86839a2abc0a07268db0378c22d75fe8242","first_computed_at":"2026-05-18T03:26:21.523234Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:21.523234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xt4yD4+lbXzt2gUyON/U6m8sdzoRs/rmJBMlEbxOAzEo/kkH8lac3eWAciNC6fjE8Rx8BZ7WRbEnWu6DEOGaAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:21.523913Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.1527","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be38a5cbb5ac0f0e2ba979378abbe2f841566a9a3e0941bb5ccb751e5f2f71dd","sha256:47c492f38363a85d3402868c6481230dab1861c242cfcbd9f8b0da10bc413693"],"state_sha256":"38a882b0632a527522c5b5641cd9f5ee85f91d5d14cab43f2dff8ab28323cc6b"}