{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:3CZGRD4X65PNBB6UXIX6BATVCQ","short_pith_number":"pith:3CZGRD4X","canonical_record":{"source":{"id":"1304.6426","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-23T21:20:41Z","cross_cats_sorted":[],"title_canon_sha256":"764337432e45dbd5ef5c65ab741b030aec85c99d2d355a3b32c44febd347ef71","abstract_canon_sha256":"de60ba5450e50d92a8df61d7bde0e06b9b5fbbcbe281bed9b232c3b44d56b290"},"schema_version":"1.0"},"canonical_sha256":"d8b2688f97f75ed087d4ba2fe082751418fc7c54e993e4e52bb1cb0960071dd9","source":{"kind":"arxiv","id":"1304.6426","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.6426","created_at":"2026-05-18T03:27:13Z"},{"alias_kind":"arxiv_version","alias_value":"1304.6426v1","created_at":"2026-05-18T03:27:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6426","created_at":"2026-05-18T03:27:13Z"},{"alias_kind":"pith_short_12","alias_value":"3CZGRD4X65PN","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3CZGRD4X65PNBB6U","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3CZGRD4X","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:3CZGRD4X65PNBB6UXIX6BATVCQ","target":"record","payload":{"canonical_record":{"source":{"id":"1304.6426","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-23T21:20:41Z","cross_cats_sorted":[],"title_canon_sha256":"764337432e45dbd5ef5c65ab741b030aec85c99d2d355a3b32c44febd347ef71","abstract_canon_sha256":"de60ba5450e50d92a8df61d7bde0e06b9b5fbbcbe281bed9b232c3b44d56b290"},"schema_version":"1.0"},"canonical_sha256":"d8b2688f97f75ed087d4ba2fe082751418fc7c54e993e4e52bb1cb0960071dd9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:13.161917Z","signature_b64":"G+O8uDZPWxnIm4I96ri+N1jtvD8oLJaOTbhsJF58WTYCt4jcgwF4ohED6iAsQDPpvQZkCuFoK6IYudnW5udbCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8b2688f97f75ed087d4ba2fe082751418fc7c54e993e4e52bb1cb0960071dd9","last_reissued_at":"2026-05-18T03:27:13.161294Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:13.161294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.6426","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":"2026-05-18T03:27:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2NQ1ZmKUfxXxMm/WaYS9wXUsa7fPOEZntYBxQmk4UsCWE/odUlG/cPTEQ0jci7qhdpCGf0ZBW3crbXULAJzyBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T09:27:12.806457Z"},"content_sha256":"73519203074de04fa4122a1f63bcf87211d73c307417105511f2959c28403059","schema_version":"1.0","event_id":"sha256:73519203074de04fa4122a1f63bcf87211d73c307417105511f2959c28403059"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:3CZGRD4X65PNBB6UXIX6BATVCQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Central limit theorem for an additive functional of the fractional Brownian motion II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Nualart, Fangjun Xu","submitted_at":"2013-04-23T21:20:41Z","abstract_excerpt":"We prove a central limit theorem for an additive functional of the $d$-dimensional fractional Brownian motion with Hurst index $H\\in(\\frac{1}{2+d},\\frac{1}{d})$, using the method of moments, extending the result by Papanicolaou, Stroock and Varadhan in the case of the standard Brownian motion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6426","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":"2026-05-18T03:27:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a1ptA4AfuRhcRnrUgzb0aOkF7+UGub/1pvfedKN1HjbwZnmy42hL+Gho/FuSvU9td5CC9NFIpBykDUt/fdPdBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T09:27:12.806796Z"},"content_sha256":"6f8a4a8196b8ff077eef3fb9d77c1d3449b982afc6b1f9cc2d79231a704acc1e","schema_version":"1.0","event_id":"sha256:6f8a4a8196b8ff077eef3fb9d77c1d3449b982afc6b1f9cc2d79231a704acc1e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3CZGRD4X65PNBB6UXIX6BATVCQ/bundle.json","state_url":"https://pith.science/pith/3CZGRD4X65PNBB6UXIX6BATVCQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3CZGRD4X65PNBB6UXIX6BATVCQ/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":"2026-05-20T09:27:12Z","links":{"resolver":"https://pith.science/pith/3CZGRD4X65PNBB6UXIX6BATVCQ","bundle":"https://pith.science/pith/3CZGRD4X65PNBB6UXIX6BATVCQ/bundle.json","state":"https://pith.science/pith/3CZGRD4X65PNBB6UXIX6BATVCQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3CZGRD4X65PNBB6UXIX6BATVCQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3CZGRD4X65PNBB6UXIX6BATVCQ","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":"de60ba5450e50d92a8df61d7bde0e06b9b5fbbcbe281bed9b232c3b44d56b290","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-23T21:20:41Z","title_canon_sha256":"764337432e45dbd5ef5c65ab741b030aec85c99d2d355a3b32c44febd347ef71"},"schema_version":"1.0","source":{"id":"1304.6426","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.6426","created_at":"2026-05-18T03:27:13Z"},{"alias_kind":"arxiv_version","alias_value":"1304.6426v1","created_at":"2026-05-18T03:27:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6426","created_at":"2026-05-18T03:27:13Z"},{"alias_kind":"pith_short_12","alias_value":"3CZGRD4X65PN","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3CZGRD4X65PNBB6U","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3CZGRD4X","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:6f8a4a8196b8ff077eef3fb9d77c1d3449b982afc6b1f9cc2d79231a704acc1e","target":"graph","created_at":"2026-05-18T03:27:13Z","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 prove a central limit theorem for an additive functional of the $d$-dimensional fractional Brownian motion with Hurst index $H\\in(\\frac{1}{2+d},\\frac{1}{d})$, using the method of moments, extending the result by Papanicolaou, Stroock and Varadhan in the case of the standard Brownian motion.","authors_text":"David Nualart, Fangjun Xu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-23T21:20:41Z","title":"Central limit theorem for an additive functional of the fractional Brownian motion II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6426","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":"sha256:73519203074de04fa4122a1f63bcf87211d73c307417105511f2959c28403059","target":"record","created_at":"2026-05-18T03:27:13Z","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":"de60ba5450e50d92a8df61d7bde0e06b9b5fbbcbe281bed9b232c3b44d56b290","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-23T21:20:41Z","title_canon_sha256":"764337432e45dbd5ef5c65ab741b030aec85c99d2d355a3b32c44febd347ef71"},"schema_version":"1.0","source":{"id":"1304.6426","kind":"arxiv","version":1}},"canonical_sha256":"d8b2688f97f75ed087d4ba2fe082751418fc7c54e993e4e52bb1cb0960071dd9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8b2688f97f75ed087d4ba2fe082751418fc7c54e993e4e52bb1cb0960071dd9","first_computed_at":"2026-05-18T03:27:13.161294Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:13.161294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G+O8uDZPWxnIm4I96ri+N1jtvD8oLJaOTbhsJF58WTYCt4jcgwF4ohED6iAsQDPpvQZkCuFoK6IYudnW5udbCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:13.161917Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.6426","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73519203074de04fa4122a1f63bcf87211d73c307417105511f2959c28403059","sha256:6f8a4a8196b8ff077eef3fb9d77c1d3449b982afc6b1f9cc2d79231a704acc1e"],"state_sha256":"9752b6167e57fb1cbaa024042c7096238ee10ccd31167990ca2dc18ce8b327a0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5QQQmy/85d0QSUasR8GUPubbGH0giTUYrZhLVqV4SFHrU1m98Dy0PqAfrUxvyUuQpnfa9XTBpSklxJf2n6DXCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T09:27:12.808810Z","bundle_sha256":"4d220d206f429bb746098ff372097640f60ce9e404b3c6b36cb533d7b404e72f"}}