{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:3VUQACSWTA6SC6DZYJPCWPYNZ7","short_pith_number":"pith:3VUQACSW","canonical_record":{"source":{"id":"1712.03619","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.PR","submitted_at":"2017-12-11T00:43:54Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"a92e43c8426557c365991746fa5d7defc9a8df7cd449f5c471dacff75f4e77eb","abstract_canon_sha256":"4f9f482dc7e1e3863db8658f2b2f42f17348fcae21eb853295f7437fc4deecc1"},"schema_version":"1.0"},"canonical_sha256":"dd69000a56983d217879c25e2b3f0dcfde08cb8902825b2232772722744c2eb7","source":{"kind":"arxiv","id":"1712.03619","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.03619","created_at":"2026-05-18T00:28:20Z"},{"alias_kind":"arxiv_version","alias_value":"1712.03619v1","created_at":"2026-05-18T00:28:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.03619","created_at":"2026-05-18T00:28:20Z"},{"alias_kind":"pith_short_12","alias_value":"3VUQACSWTA6S","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3VUQACSWTA6SC6DZ","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3VUQACSW","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:3VUQACSWTA6SC6DZYJPCWPYNZ7","target":"record","payload":{"canonical_record":{"source":{"id":"1712.03619","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.PR","submitted_at":"2017-12-11T00:43:54Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"a92e43c8426557c365991746fa5d7defc9a8df7cd449f5c471dacff75f4e77eb","abstract_canon_sha256":"4f9f482dc7e1e3863db8658f2b2f42f17348fcae21eb853295f7437fc4deecc1"},"schema_version":"1.0"},"canonical_sha256":"dd69000a56983d217879c25e2b3f0dcfde08cb8902825b2232772722744c2eb7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:20.574530Z","signature_b64":"eewhGrjwaE5f57ua1J3QrFH3qfxBRgXhZQ1iroE5qgDX7QkTwqx+FSBF+LdeqmaQcgmJufghezKnBEgQpDilBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd69000a56983d217879c25e2b3f0dcfde08cb8902825b2232772722744c2eb7","last_reissued_at":"2026-05-18T00:28:20.573771Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:20.573771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.03619","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":"2026-05-18T00:28:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FdLPV09CAAVAJrCo+swbq0wWCyR2BG+Y7nQl0XNLGmKHK3St7cDjC0S+2Xx6Of6fijgvX6d3H/rcDIFT+rwGBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T20:42:52.461239Z"},"content_sha256":"c8c6661e149087acef74c69feef7d4d00df63335ff44e2d69c55b516e2e7be26","schema_version":"1.0","event_id":"sha256:c8c6661e149087acef74c69feef7d4d00df63335ff44e2d69c55b516e2e7be26"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:3VUQACSWTA6SC6DZYJPCWPYNZ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Central Limit Theorems for a Stationary Semicircular Sequence in Free Probability","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.PR","authors_text":"Zhichao Wang","submitted_at":"2017-12-11T00:43:54Z","abstract_excerpt":"In this paper, we focus on studying central limit theorems for functionals of some specific stationary random processes. In classical probability theory, it is well-known that for non-linear functionals of stationary Gaussian sequences, we can get a central-limit result via Hermite polynomials and the diagram formula for cumulants. In this paper, the main result is an analogous central limit theorem, in a free probability setting, for real-valued functionals of a stationary semicircular sequence with long-range dependence, namely the correlation function of the underlying time series tends to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03619","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":"2026-05-18T00:28:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3L4/ZcYbQ+qNPV+lpGiiUrzptiE++XL5exlh5RXhyBrsCgFhkx6MJDxEHHdzXanHMXg74cXCCcNrlxyENupuBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T20:42:52.461911Z"},"content_sha256":"7131e85970ceff795790eb3fdc779b5b2b8a6c1f41a31e01c317d28cdab985db","schema_version":"1.0","event_id":"sha256:7131e85970ceff795790eb3fdc779b5b2b8a6c1f41a31e01c317d28cdab985db"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3VUQACSWTA6SC6DZYJPCWPYNZ7/bundle.json","state_url":"https://pith.science/pith/3VUQACSWTA6SC6DZYJPCWPYNZ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3VUQACSWTA6SC6DZYJPCWPYNZ7/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":"2026-05-24T20:42:52Z","links":{"resolver":"https://pith.science/pith/3VUQACSWTA6SC6DZYJPCWPYNZ7","bundle":"https://pith.science/pith/3VUQACSWTA6SC6DZYJPCWPYNZ7/bundle.json","state":"https://pith.science/pith/3VUQACSWTA6SC6DZYJPCWPYNZ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3VUQACSWTA6SC6DZYJPCWPYNZ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3VUQACSWTA6SC6DZYJPCWPYNZ7","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":"4f9f482dc7e1e3863db8658f2b2f42f17348fcae21eb853295f7437fc4deecc1","cross_cats_sorted":["math.OA"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.PR","submitted_at":"2017-12-11T00:43:54Z","title_canon_sha256":"a92e43c8426557c365991746fa5d7defc9a8df7cd449f5c471dacff75f4e77eb"},"schema_version":"1.0","source":{"id":"1712.03619","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.03619","created_at":"2026-05-18T00:28:20Z"},{"alias_kind":"arxiv_version","alias_value":"1712.03619v1","created_at":"2026-05-18T00:28:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.03619","created_at":"2026-05-18T00:28:20Z"},{"alias_kind":"pith_short_12","alias_value":"3VUQACSWTA6S","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3VUQACSWTA6SC6DZ","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3VUQACSW","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:7131e85970ceff795790eb3fdc779b5b2b8a6c1f41a31e01c317d28cdab985db","target":"graph","created_at":"2026-05-18T00:28:20Z","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 this paper, we focus on studying central limit theorems for functionals of some specific stationary random processes. In classical probability theory, it is well-known that for non-linear functionals of stationary Gaussian sequences, we can get a central-limit result via Hermite polynomials and the diagram formula for cumulants. In this paper, the main result is an analogous central limit theorem, in a free probability setting, for real-valued functionals of a stationary semicircular sequence with long-range dependence, namely the correlation function of the underlying time series tends to ","authors_text":"Zhichao Wang","cross_cats":["math.OA"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.PR","submitted_at":"2017-12-11T00:43:54Z","title":"Central Limit Theorems for a Stationary Semicircular Sequence in Free Probability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03619","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:c8c6661e149087acef74c69feef7d4d00df63335ff44e2d69c55b516e2e7be26","target":"record","created_at":"2026-05-18T00:28:20Z","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":"4f9f482dc7e1e3863db8658f2b2f42f17348fcae21eb853295f7437fc4deecc1","cross_cats_sorted":["math.OA"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.PR","submitted_at":"2017-12-11T00:43:54Z","title_canon_sha256":"a92e43c8426557c365991746fa5d7defc9a8df7cd449f5c471dacff75f4e77eb"},"schema_version":"1.0","source":{"id":"1712.03619","kind":"arxiv","version":1}},"canonical_sha256":"dd69000a56983d217879c25e2b3f0dcfde08cb8902825b2232772722744c2eb7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd69000a56983d217879c25e2b3f0dcfde08cb8902825b2232772722744c2eb7","first_computed_at":"2026-05-18T00:28:20.573771Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:20.573771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eewhGrjwaE5f57ua1J3QrFH3qfxBRgXhZQ1iroE5qgDX7QkTwqx+FSBF+LdeqmaQcgmJufghezKnBEgQpDilBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:20.574530Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.03619","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8c6661e149087acef74c69feef7d4d00df63335ff44e2d69c55b516e2e7be26","sha256:7131e85970ceff795790eb3fdc779b5b2b8a6c1f41a31e01c317d28cdab985db"],"state_sha256":"657ff94c3c8cedeb83eb4147e80ffc29982a0e51927b3e4f43a54811f5f8db4b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Ems8oNk1zoR9RUTpW3ydxDcY4fOkH6zFHguvTuPwmO3n4hJBVIkxJaCcw8lNjCpfXqg/OyQHlAA/FVjoaIMAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T20:42:52.465988Z","bundle_sha256":"7323b730a0080fef0053ab1c2ea6fa51329a000cf336c0a895c6f5f58ba87658"}}