{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ZBYMHOWVNW3ROXIFJRQOPAYSV2","short_pith_number":"pith:ZBYMHOWV","canonical_record":{"source":{"id":"1401.2247","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-10T08:06:57Z","cross_cats_sorted":[],"title_canon_sha256":"aac4774e1c357de4e269997321630bee5b49d65994dcf45194435b87c42f5a81","abstract_canon_sha256":"816e7c63dd567157a7a346b7e402d7657c32f398465bab81c839d1154bc81b6f"},"schema_version":"1.0"},"canonical_sha256":"c870c3bad56db7175d054c60e78312ae939c2a101d50ce4c6de805607be2dccd","source":{"kind":"arxiv","id":"1401.2247","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.2247","created_at":"2026-05-18T03:02:45Z"},{"alias_kind":"arxiv_version","alias_value":"1401.2247v1","created_at":"2026-05-18T03:02:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.2247","created_at":"2026-05-18T03:02:45Z"},{"alias_kind":"pith_short_12","alias_value":"ZBYMHOWVNW3R","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZBYMHOWVNW3ROXIF","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZBYMHOWV","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ZBYMHOWVNW3ROXIFJRQOPAYSV2","target":"record","payload":{"canonical_record":{"source":{"id":"1401.2247","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-10T08:06:57Z","cross_cats_sorted":[],"title_canon_sha256":"aac4774e1c357de4e269997321630bee5b49d65994dcf45194435b87c42f5a81","abstract_canon_sha256":"816e7c63dd567157a7a346b7e402d7657c32f398465bab81c839d1154bc81b6f"},"schema_version":"1.0"},"canonical_sha256":"c870c3bad56db7175d054c60e78312ae939c2a101d50ce4c6de805607be2dccd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:45.907932Z","signature_b64":"t0wkS+xljvpy+p8GhNFyjHWVaxdHCZ46hCni3/rgwbNP/vCShEeT5Wm03sPXwWrSmKT5fQyN/A/XdFliXRgxAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c870c3bad56db7175d054c60e78312ae939c2a101d50ce4c6de805607be2dccd","last_reissued_at":"2026-05-18T03:02:45.907325Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:45.907325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.2247","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:02:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W46e92VMEmM5rMismXoKriGj197R3N0vxNBZg/P1DnX6kKtiS4ntms+dttzjDnpMA5WfnS//k4FUiQeNM306Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T15:47:47.650793Z"},"content_sha256":"fd5841b37fdf0d09e997044b6b029254e40f0929af04796c952574039121f859","schema_version":"1.0","event_id":"sha256:fd5841b37fdf0d09e997044b6b029254e40f0929af04796c952574039121f859"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ZBYMHOWVNW3ROXIFJRQOPAYSV2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strong asymptotic independence on Wiener chaos","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Nualart, Giovanni Peccati (FSTC), Ivan Nourdin (IECL)","submitted_at":"2014-01-10T08:06:57Z","abstract_excerpt":"Let $F_n = (F_{1,n}, ....,F_{d,n})$, $n\\geq 1$, be a sequence of random vectors such that, for every $j=1,...,d$, the random variable $F_{j,n}$ belongs to a fixed Wiener chaos of a Gaussian field. We show that, as $n\\to\\infty$, the components of $F_n$ are asymptotically independent if and only if ${\\rm Cov}(F_{i,n}^2,F_{j,n}^2)\\to 0$ for every $i\\neq j$. Our findings are based on a novel inequality for vectors of multiple Wiener-It\\^o integrals, and represent a substantial refining of criteria for asymptotic independence in the sense of moments recently established by Nourdin and Rosinski."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2247","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:02:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DVznpDX61WFKu6DRHSsdE0zRDbYuxEgl7e7ma3+WYCbQ5Di2Ug7JEzA6R06gD7VHKs8NxSD0WoLnQ3eZdCgFAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T15:47:47.651136Z"},"content_sha256":"d53b1bdbaecf2cb153ace3770d91a43641f94d4f1f10306a76d799675f346358","schema_version":"1.0","event_id":"sha256:d53b1bdbaecf2cb153ace3770d91a43641f94d4f1f10306a76d799675f346358"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZBYMHOWVNW3ROXIFJRQOPAYSV2/bundle.json","state_url":"https://pith.science/pith/ZBYMHOWVNW3ROXIFJRQOPAYSV2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZBYMHOWVNW3ROXIFJRQOPAYSV2/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-20T15:47:47Z","links":{"resolver":"https://pith.science/pith/ZBYMHOWVNW3ROXIFJRQOPAYSV2","bundle":"https://pith.science/pith/ZBYMHOWVNW3ROXIFJRQOPAYSV2/bundle.json","state":"https://pith.science/pith/ZBYMHOWVNW3ROXIFJRQOPAYSV2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZBYMHOWVNW3ROXIFJRQOPAYSV2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZBYMHOWVNW3ROXIFJRQOPAYSV2","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":"816e7c63dd567157a7a346b7e402d7657c32f398465bab81c839d1154bc81b6f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-10T08:06:57Z","title_canon_sha256":"aac4774e1c357de4e269997321630bee5b49d65994dcf45194435b87c42f5a81"},"schema_version":"1.0","source":{"id":"1401.2247","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.2247","created_at":"2026-05-18T03:02:45Z"},{"alias_kind":"arxiv_version","alias_value":"1401.2247v1","created_at":"2026-05-18T03:02:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.2247","created_at":"2026-05-18T03:02:45Z"},{"alias_kind":"pith_short_12","alias_value":"ZBYMHOWVNW3R","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZBYMHOWVNW3ROXIF","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZBYMHOWV","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:d53b1bdbaecf2cb153ace3770d91a43641f94d4f1f10306a76d799675f346358","target":"graph","created_at":"2026-05-18T03:02:45Z","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":"Let $F_n = (F_{1,n}, ....,F_{d,n})$, $n\\geq 1$, be a sequence of random vectors such that, for every $j=1,...,d$, the random variable $F_{j,n}$ belongs to a fixed Wiener chaos of a Gaussian field. We show that, as $n\\to\\infty$, the components of $F_n$ are asymptotically independent if and only if ${\\rm Cov}(F_{i,n}^2,F_{j,n}^2)\\to 0$ for every $i\\neq j$. Our findings are based on a novel inequality for vectors of multiple Wiener-It\\^o integrals, and represent a substantial refining of criteria for asymptotic independence in the sense of moments recently established by Nourdin and Rosinski.","authors_text":"David Nualart, Giovanni Peccati (FSTC), Ivan Nourdin (IECL)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-10T08:06:57Z","title":"Strong asymptotic independence on Wiener chaos"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2247","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:fd5841b37fdf0d09e997044b6b029254e40f0929af04796c952574039121f859","target":"record","created_at":"2026-05-18T03:02:45Z","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":"816e7c63dd567157a7a346b7e402d7657c32f398465bab81c839d1154bc81b6f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-10T08:06:57Z","title_canon_sha256":"aac4774e1c357de4e269997321630bee5b49d65994dcf45194435b87c42f5a81"},"schema_version":"1.0","source":{"id":"1401.2247","kind":"arxiv","version":1}},"canonical_sha256":"c870c3bad56db7175d054c60e78312ae939c2a101d50ce4c6de805607be2dccd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c870c3bad56db7175d054c60e78312ae939c2a101d50ce4c6de805607be2dccd","first_computed_at":"2026-05-18T03:02:45.907325Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:45.907325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t0wkS+xljvpy+p8GhNFyjHWVaxdHCZ46hCni3/rgwbNP/vCShEeT5Wm03sPXwWrSmKT5fQyN/A/XdFliXRgxAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:45.907932Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.2247","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd5841b37fdf0d09e997044b6b029254e40f0929af04796c952574039121f859","sha256:d53b1bdbaecf2cb153ace3770d91a43641f94d4f1f10306a76d799675f346358"],"state_sha256":"b82a0c6fbe9cd1bc426691524d96a6947d1ac805a55393673a7d3a8645ee3c6b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ewytF8crpdUMZIs4GfuC6RERKAbIJ1j3heZduL+TqyLaq79ftA7kzLjgX5h9o/rkER4OcJXddzFv3T6nLB7VCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T15:47:47.653061Z","bundle_sha256":"ac66eaaa8d04aedcaf20278ef51519142d75a499998e765f0613b48856369d7c"}}