{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:R3RU3RI3FDVXBWUVDSUL5MMW2T","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":"8aafff46286c80f5488e6fa50d4ec319e34bd91a2491b2ae57b74c85861fc2e8","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-12T17:08:40Z","title_canon_sha256":"4acdc68e3ca10efb0ab79946b91ac161956e3a2dced432c33ff9271ade76cf4b"},"schema_version":"1.0","source":{"id":"1202.2545","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2545","created_at":"2026-05-18T01:58:30Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2545v1","created_at":"2026-05-18T01:58:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2545","created_at":"2026-05-18T01:58:30Z"},{"alias_kind":"pith_short_12","alias_value":"R3RU3RI3FDVX","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"R3RU3RI3FDVXBWUV","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"R3RU3RI3","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:4a8d21226ff92dc136d49f481f18e8e4573706478886edd67d8924775ccc1779","target":"graph","created_at":"2026-05-18T01:58:30Z","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 2005, Nualart and Peccati showed the so-called Fourth Moment Theorem asserting that, for a sequence of normalized multiple Wiener-It\\^o integrals to converge to the standard Gaussian law, it is necessary and sufficient that its fourth moment tends to 3. A few years later, Kemp et al. extended this theorem to a sequence of normalized multiple Wigner integrals, in the context of the free Brownian motion. The q-Brownian motion, q in (-1,1], introduced by the physicists Frisch and Bourret in 1970 and mathematically studied by Bozejko and Speicher in 1991, interpolates between the classical Brow","authors_text":"Aur\\'elien Deya (IECN), Ivan Nourdin (IECN), Salim Noreddine (LPMA)","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-12T17:08:40Z","title":"Fourth Moment Theorem and q-Brownian Chaos"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2545","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":"sha256:6f7fe86ce70b3c85aea1f2ba05083ecd052e2b2ad4f792900b1d4ef8fd010388","target":"record","created_at":"2026-05-18T01:58:30Z","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":"8aafff46286c80f5488e6fa50d4ec319e34bd91a2491b2ae57b74c85861fc2e8","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-12T17:08:40Z","title_canon_sha256":"4acdc68e3ca10efb0ab79946b91ac161956e3a2dced432c33ff9271ade76cf4b"},"schema_version":"1.0","source":{"id":"1202.2545","kind":"arxiv","version":1}},"canonical_sha256":"8ee34dc51b28eb70da951ca8beb196d4c30f260d8b8a6b70d672f8860b9130ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ee34dc51b28eb70da951ca8beb196d4c30f260d8b8a6b70d672f8860b9130ab","first_computed_at":"2026-05-18T01:58:30.902916Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:58:30.902916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cu5SvZ5LyAiGNiA2VC5zV2LyhBJ4kASzDqfzCsQ9mUl7YVkemG75rp5rn7WGW3VeY2orti7qKBm/HLfYBu3/BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:58:30.903277Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.2545","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f7fe86ce70b3c85aea1f2ba05083ecd052e2b2ad4f792900b1d4ef8fd010388","sha256:4a8d21226ff92dc136d49f481f18e8e4573706478886edd67d8924775ccc1779"],"state_sha256":"67d324994002b59d39b69f0b1a6e9acd922aee9440720cd9f5bab28c06f93007"}