{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:O5KFMXZ344NDH6N4XEP3R7YY6C","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":"38f6dccf8f51dbc32df369d47164f93b0c0220ad3a78df733f10a8e1336c5ffe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-24T13:55:06Z","title_canon_sha256":"de42070a78061cf5637c148ff69aebe8b5462b10fcabd7b38323dc60407a53c6"},"schema_version":"1.0","source":{"id":"1407.6584","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.6584","created_at":"2026-05-18T00:27:47Z"},{"alias_kind":"arxiv_version","alias_value":"1407.6584v1","created_at":"2026-05-18T00:27:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.6584","created_at":"2026-05-18T00:27:47Z"},{"alias_kind":"pith_short_12","alias_value":"O5KFMXZ344ND","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O5KFMXZ344NDH6N4","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O5KFMXZ3","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:6e2fc30e82e076af490e72f558f6ea6583adf4a91e6ab2c23375ca072741516d","target":"graph","created_at":"2026-05-18T00:27:47Z","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 show how it is possible to assess the rate of convergence in the Gaussian approximation of triangular arrays of $U$-statistics, built from wavelets coefficients evaluated on a homogeneous spherical Poisson field of arbitrary dimension. For this purpose, we exploit the Stein-Malliavin approach introduced in the seminal paper by Peccati, Sol\\'e, Taqqu and Utzet (2011); we focus in particular on statistical applications covering evaluation of variance in non-parametric density estimation and Sobolev tests for uniformity.","authors_text":"Claudio Durastanti (DIPMAT), Domenico Marinucci (DIPMAT), Giovanni Peccati (FSTC), Solesne Bourguin (CMU)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-24T13:55:06Z","title":"Gaussian approximations of nonlinear statistics on the sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6584","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":"sha256:9162121a2b38f995042cab19e4229507ed39c0ec98a8d1ef1c02dce2629f5b86","target":"record","created_at":"2026-05-18T00:27:47Z","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":"38f6dccf8f51dbc32df369d47164f93b0c0220ad3a78df733f10a8e1336c5ffe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-24T13:55:06Z","title_canon_sha256":"de42070a78061cf5637c148ff69aebe8b5462b10fcabd7b38323dc60407a53c6"},"schema_version":"1.0","source":{"id":"1407.6584","kind":"arxiv","version":1}},"canonical_sha256":"7754565f3be71a33f9bcb91fb8ff18f09a4576c4f50c79f6757db5579945d0e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7754565f3be71a33f9bcb91fb8ff18f09a4576c4f50c79f6757db5579945d0e0","first_computed_at":"2026-05-18T00:27:47.468982Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:47.468982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9xwY4QdiEvWDaw5r19SOUnS4Yt+wN/DdD9g/YHCGs0wknDNql91LQ4gtyASJPrnc9KQBMNX+076KXNzQ/yd9DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:47.469450Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.6584","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9162121a2b38f995042cab19e4229507ed39c0ec98a8d1ef1c02dce2629f5b86","sha256:6e2fc30e82e076af490e72f558f6ea6583adf4a91e6ab2c23375ca072741516d"],"state_sha256":"8dad03fc9f87c678b9c984a036e281c55e4d596654555676693702ccaad63a16"}