{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:SSNJHRI5TW7QTXCDRE34OX33WV","short_pith_number":"pith:SSNJHRI5","canonical_record":{"source":{"id":"1208.1908","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-09T13:44:34Z","cross_cats_sorted":[],"title_canon_sha256":"8e586838ecea264e51b4dd3993b351c10cb4b1f7066bc4ae27452e65c67cd6da","abstract_canon_sha256":"df3b4cc338319d5307877b817f68f9e670df8d2af179dffbd28289cca48ab4f0"},"schema_version":"1.0"},"canonical_sha256":"949a93c51d9dbf09dc438937c75f7bb57a3411c17df91f0856541364368b8546","source":{"kind":"arxiv","id":"1208.1908","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1908","created_at":"2026-05-18T03:27:03Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1908v1","created_at":"2026-05-18T03:27:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1908","created_at":"2026-05-18T03:27:03Z"},{"alias_kind":"pith_short_12","alias_value":"SSNJHRI5TW7Q","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SSNJHRI5TW7QTXCD","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SSNJHRI5","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:SSNJHRI5TW7QTXCDRE34OX33WV","target":"record","payload":{"canonical_record":{"source":{"id":"1208.1908","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-09T13:44:34Z","cross_cats_sorted":[],"title_canon_sha256":"8e586838ecea264e51b4dd3993b351c10cb4b1f7066bc4ae27452e65c67cd6da","abstract_canon_sha256":"df3b4cc338319d5307877b817f68f9e670df8d2af179dffbd28289cca48ab4f0"},"schema_version":"1.0"},"canonical_sha256":"949a93c51d9dbf09dc438937c75f7bb57a3411c17df91f0856541364368b8546","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:03.407516Z","signature_b64":"VnT2MqskZOC/ygwuNDIAHGHRalmaNn5XAX0mZwFgRDYn85mnJV9s7kmCuSRXBcIkI0bFT4fkD+qMOd29//+ADA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"949a93c51d9dbf09dc438937c75f7bb57a3411c17df91f0856541364368b8546","last_reissued_at":"2026-05-18T03:27:03.406938Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:03.406938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.1908","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":"2026-05-18T03:27:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gTYcG8GD49SXlt/7PqsHgGqcmCdNuYv1E8/M5mhMmdql7hnk1gkj9FwHrM93U1/0/+0+PBIaKfKYb54e1fxcCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T09:04:44.457461Z"},"content_sha256":"85dc9e456ecab75b00b2372146e95e2ae636b00dae53d56a07fde43b0368d215","schema_version":"1.0","event_id":"sha256:85dc9e456ecab75b00b2372146e95e2ae636b00dae53d56a07fde43b0368d215"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:SSNJHRI5TW7QTXCDRE34OX33WV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"CLT for an iterated integral with respect to fBm with H > 1/2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Daniel Harnett, David Nualart","submitted_at":"2012-08-09T13:44:34Z","abstract_excerpt":"We construct an iterated stochastic integral with fractional Brownian motion with H > 1/2. The first integrand is a deterministic function, and each successive integral is with respect to an independent fBm. We show that this symmetric stochastic integral is equal to the Malliavin divergence integral. By a version of the Fourth Moment theorem of Nualart and Peccati, we show that a family of such integrals converges in distribution to a scaled Brownian motion. An application is an approximation to the windings for a planar fBm, previously studied by Baudoin and Nualart."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1908","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":"2026-05-18T03:27:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sflfw4nTjDt+MmDDJB+k8ZD2r6TlF+qYsoCRFfTGqljgDr5ldsxyAumJLqRpnWvhuyBtoRhtf+ZDsUtXXw1yCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T09:04:44.457949Z"},"content_sha256":"bf1db2168010fa7a6d1fba2ae22d6a12296ff50acdc588fb5fcbcd000ff4cd9b","schema_version":"1.0","event_id":"sha256:bf1db2168010fa7a6d1fba2ae22d6a12296ff50acdc588fb5fcbcd000ff4cd9b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SSNJHRI5TW7QTXCDRE34OX33WV/bundle.json","state_url":"https://pith.science/pith/SSNJHRI5TW7QTXCDRE34OX33WV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SSNJHRI5TW7QTXCDRE34OX33WV/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":"2026-05-21T09:04:44Z","links":{"resolver":"https://pith.science/pith/SSNJHRI5TW7QTXCDRE34OX33WV","bundle":"https://pith.science/pith/SSNJHRI5TW7QTXCDRE34OX33WV/bundle.json","state":"https://pith.science/pith/SSNJHRI5TW7QTXCDRE34OX33WV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SSNJHRI5TW7QTXCDRE34OX33WV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SSNJHRI5TW7QTXCDRE34OX33WV","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":"df3b4cc338319d5307877b817f68f9e670df8d2af179dffbd28289cca48ab4f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-09T13:44:34Z","title_canon_sha256":"8e586838ecea264e51b4dd3993b351c10cb4b1f7066bc4ae27452e65c67cd6da"},"schema_version":"1.0","source":{"id":"1208.1908","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1908","created_at":"2026-05-18T03:27:03Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1908v1","created_at":"2026-05-18T03:27:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1908","created_at":"2026-05-18T03:27:03Z"},{"alias_kind":"pith_short_12","alias_value":"SSNJHRI5TW7Q","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SSNJHRI5TW7QTXCD","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SSNJHRI5","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:bf1db2168010fa7a6d1fba2ae22d6a12296ff50acdc588fb5fcbcd000ff4cd9b","target":"graph","created_at":"2026-05-18T03:27:03Z","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 construct an iterated stochastic integral with fractional Brownian motion with H > 1/2. The first integrand is a deterministic function, and each successive integral is with respect to an independent fBm. We show that this symmetric stochastic integral is equal to the Malliavin divergence integral. By a version of the Fourth Moment theorem of Nualart and Peccati, we show that a family of such integrals converges in distribution to a scaled Brownian motion. An application is an approximation to the windings for a planar fBm, previously studied by Baudoin and Nualart.","authors_text":"Daniel Harnett, David Nualart","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-09T13:44:34Z","title":"CLT for an iterated integral with respect to fBm with H > 1/2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1908","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":"sha256:85dc9e456ecab75b00b2372146e95e2ae636b00dae53d56a07fde43b0368d215","target":"record","created_at":"2026-05-18T03:27:03Z","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":"df3b4cc338319d5307877b817f68f9e670df8d2af179dffbd28289cca48ab4f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-09T13:44:34Z","title_canon_sha256":"8e586838ecea264e51b4dd3993b351c10cb4b1f7066bc4ae27452e65c67cd6da"},"schema_version":"1.0","source":{"id":"1208.1908","kind":"arxiv","version":1}},"canonical_sha256":"949a93c51d9dbf09dc438937c75f7bb57a3411c17df91f0856541364368b8546","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"949a93c51d9dbf09dc438937c75f7bb57a3411c17df91f0856541364368b8546","first_computed_at":"2026-05-18T03:27:03.406938Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:03.406938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VnT2MqskZOC/ygwuNDIAHGHRalmaNn5XAX0mZwFgRDYn85mnJV9s7kmCuSRXBcIkI0bFT4fkD+qMOd29//+ADA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:03.407516Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.1908","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85dc9e456ecab75b00b2372146e95e2ae636b00dae53d56a07fde43b0368d215","sha256:bf1db2168010fa7a6d1fba2ae22d6a12296ff50acdc588fb5fcbcd000ff4cd9b"],"state_sha256":"9d00703f5250ceb2e0414cbd2327736aea788f4236c3b5f455d657a064e06bfb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eZoPEbV3ItXjgH5CyP7dPQW+sl4SlTAMsJY1GJNgrxjcybtISudeec+VSq4zyBb7WiXgVpWKdkJnExThhHE7AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T09:04:44.460804Z","bundle_sha256":"c8dacdcae059fee8bf21283fa9e38b1ee30883fc99ff9789e7fcd5ace9494984"}}