{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LUCOSURAA2PY73PK74PKKQHJJ6","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":"6b10fbd65a8d40241bf58ddf44a4d8fdd2bfd12aae60254c4f7f6fd3321ec5f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-18T16:43:41Z","title_canon_sha256":"e0cc3ba1aebfa26ab52951ba5a40cfda4f0d917f8b4091b83b372082274f675e"},"schema_version":"1.0","source":{"id":"1111.4419","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.4419","created_at":"2026-05-18T03:02:21Z"},{"alias_kind":"arxiv_version","alias_value":"1111.4419v2","created_at":"2026-05-18T03:02:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4419","created_at":"2026-05-18T03:02:21Z"},{"alias_kind":"pith_short_12","alias_value":"LUCOSURAA2PY","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LUCOSURAA2PY73PK","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LUCOSURA","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:2e5f70b840472003719af96c865be7b4334fa51bcf1cf908a35611a7a0d83218","target":"graph","created_at":"2026-05-18T03:02:21Z","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 $H\\in(\\frac{1}{1+d},\\frac{1}{d})$, 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, Yaozhong Hu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-18T16:43:41Z","title":"Central limit theorem for an additive functional of the fractional Brownian motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4419","kind":"arxiv","version":2},"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":"sha256:935b675104b3e4bb26cf9b9f63c68bf7eb6c9ddffba8c2631d4965af2b0c762d","target":"record","created_at":"2026-05-18T03:02:21Z","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":"6b10fbd65a8d40241bf58ddf44a4d8fdd2bfd12aae60254c4f7f6fd3321ec5f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-18T16:43:41Z","title_canon_sha256":"e0cc3ba1aebfa26ab52951ba5a40cfda4f0d917f8b4091b83b372082274f675e"},"schema_version":"1.0","source":{"id":"1111.4419","kind":"arxiv","version":2}},"canonical_sha256":"5d04e95220069f8fedeaff1ea540e94f8d8b5c5ca56be3dcaf9e66718f5f41cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d04e95220069f8fedeaff1ea540e94f8d8b5c5ca56be3dcaf9e66718f5f41cc","first_computed_at":"2026-05-18T03:02:21.493421Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:21.493421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R37UU02BfkJcuohUHlvSRgu+Ap+Bj+ZB0MznS2cCXtGQuWAnF7c9DCoxuI60rEyXzIGy2t+JY3Zm5sDNKhjODQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:21.494058Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.4419","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:935b675104b3e4bb26cf9b9f63c68bf7eb6c9ddffba8c2631d4965af2b0c762d","sha256:2e5f70b840472003719af96c865be7b4334fa51bcf1cf908a35611a7a0d83218"],"state_sha256":"23a913b0be03933464fc76125e0c462573ed22f216b6ab9b11862486c0e9d4c6"}