{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:3XQBEBMDDKS4KOO3MOGIN3U7D5","short_pith_number":"pith:3XQBEBMD","schema_version":"1.0","canonical_sha256":"dde01205831aa5c539db638c86ee9f1f68703c3f405dccf6d088f47ca4163049","source":{"kind":"arxiv","id":"1210.1560","version":1},"attestation_state":"computed","paper":{"title":"Joint convergence along different subsequences of the signed cubic variation of fractional Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Nualart, Jason Swanson, Krzysztof Burdzy","submitted_at":"2012-10-04T19:42:59Z","abstract_excerpt":"The purpose of this paper is to study the convergence in distribution of two subsequences of the signed cubic variation of the fractional Brownian motion with Hurst parameter $H=1/6$. We prove that, under some conditions on both subsequences, the limit is a two-dimensional Brownian motion whose components may be correlated and we find explicit formulae for its covariance function."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1210.1560","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-04T19:42:59Z","cross_cats_sorted":[],"title_canon_sha256":"f3889a3d0e17cbbba373e79e63b87c8c6cc77fc09c272d5ed699420b4550d48f","abstract_canon_sha256":"d54e061f6d2700133a9a0a098e88b56fa018412359bb2a93abb961e1bea35ed2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:03.138295Z","signature_b64":"4V7FLujuLYTXFdJNfjfgFCclt06r7uuNj8/Zlue3vT9I3VDu0BGjNGJgH9gixEgu/8RJVlDVfUY4qjoTW+kFAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dde01205831aa5c539db638c86ee9f1f68703c3f405dccf6d088f47ca4163049","last_reissued_at":"2026-05-18T03:44:03.137426Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:03.137426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Joint convergence along different subsequences of the signed cubic variation of fractional Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Nualart, Jason Swanson, Krzysztof Burdzy","submitted_at":"2012-10-04T19:42:59Z","abstract_excerpt":"The purpose of this paper is to study the convergence in distribution of two subsequences of the signed cubic variation of the fractional Brownian motion with Hurst parameter $H=1/6$. We prove that, under some conditions on both subsequences, the limit is a two-dimensional Brownian motion whose components may be correlated and we find explicit formulae for its covariance function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1560","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1210.1560","created_at":"2026-05-18T03:44:03.137572+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.1560v1","created_at":"2026-05-18T03:44:03.137572+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.1560","created_at":"2026-05-18T03:44:03.137572+00:00"},{"alias_kind":"pith_short_12","alias_value":"3XQBEBMDDKS4","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"3XQBEBMDDKS4KOO3","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"3XQBEBMD","created_at":"2026-05-18T12:26:53.410803+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3XQBEBMDDKS4KOO3MOGIN3U7D5","json":"https://pith.science/pith/3XQBEBMDDKS4KOO3MOGIN3U7D5.json","graph_json":"https://pith.science/api/pith-number/3XQBEBMDDKS4KOO3MOGIN3U7D5/graph.json","events_json":"https://pith.science/api/pith-number/3XQBEBMDDKS4KOO3MOGIN3U7D5/events.json","paper":"https://pith.science/paper/3XQBEBMD"},"agent_actions":{"view_html":"https://pith.science/pith/3XQBEBMDDKS4KOO3MOGIN3U7D5","download_json":"https://pith.science/pith/3XQBEBMDDKS4KOO3MOGIN3U7D5.json","view_paper":"https://pith.science/paper/3XQBEBMD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.1560&json=true","fetch_graph":"https://pith.science/api/pith-number/3XQBEBMDDKS4KOO3MOGIN3U7D5/graph.json","fetch_events":"https://pith.science/api/pith-number/3XQBEBMDDKS4KOO3MOGIN3U7D5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3XQBEBMDDKS4KOO3MOGIN3U7D5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3XQBEBMDDKS4KOO3MOGIN3U7D5/action/storage_attestation","attest_author":"https://pith.science/pith/3XQBEBMDDKS4KOO3MOGIN3U7D5/action/author_attestation","sign_citation":"https://pith.science/pith/3XQBEBMDDKS4KOO3MOGIN3U7D5/action/citation_signature","submit_replication":"https://pith.science/pith/3XQBEBMDDKS4KOO3MOGIN3U7D5/action/replication_record"}},"created_at":"2026-05-18T03:44:03.137572+00:00","updated_at":"2026-05-18T03:44:03.137572+00:00"}