{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:EBR44ZXUIGXS4O3SJO6XVTDP2T","short_pith_number":"pith:EBR44ZXU","schema_version":"1.0","canonical_sha256":"2063ce66f441af2e3b724bbd7acc6fd4e45afc23be1ba034e5e5fbe32821faeb","source":{"kind":"arxiv","id":"1304.4838","version":1},"attestation_state":"computed","paper":{"title":"Smoothing effect of rough differential equations driven by fractional Brownian motions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Cheng Ouyang, Fabrice Baudoin, Xuejing Zhang","submitted_at":"2013-04-17T14:30:28Z","abstract_excerpt":"In this work we study the smoothing effect of rough differential equations driven by a fractional Brownian motion with parameter $H>1/4$. The regularization estimates we obtain generalize to the fractional Brownian motion previous results by Kusuoka and Stroock and can be seen as a quantitative version of the existence of smooth densities under H\\\"ormander's type conditions."},"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":"1304.4838","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-17T14:30:28Z","cross_cats_sorted":[],"title_canon_sha256":"fd74c746d63984fa35b6bd74fc6a2a3d9d5d8ab299df727ee7d336952241641c","abstract_canon_sha256":"481a1e6a01075ae596a70d32900d69f3d8ad05d2ac459ed16c5974f47630a93a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:43.538920Z","signature_b64":"6H1EDkHUX6+HtJlujGYbh1Nd4F7YwHMKfn9innG9I5wU2XVK2fsLUZqxVDEMJmdUY+C3gjOu0EA5AkMO2fDFAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2063ce66f441af2e3b724bbd7acc6fd4e45afc23be1ba034e5e5fbe32821faeb","last_reissued_at":"2026-05-18T03:27:43.538473Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:43.538473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Smoothing effect of rough differential equations driven by fractional Brownian motions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Cheng Ouyang, Fabrice Baudoin, Xuejing Zhang","submitted_at":"2013-04-17T14:30:28Z","abstract_excerpt":"In this work we study the smoothing effect of rough differential equations driven by a fractional Brownian motion with parameter $H>1/4$. The regularization estimates we obtain generalize to the fractional Brownian motion previous results by Kusuoka and Stroock and can be seen as a quantitative version of the existence of smooth densities under H\\\"ormander's type conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4838","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":"1304.4838","created_at":"2026-05-18T03:27:43.538539+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.4838v1","created_at":"2026-05-18T03:27:43.538539+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4838","created_at":"2026-05-18T03:27:43.538539+00:00"},{"alias_kind":"pith_short_12","alias_value":"EBR44ZXUIGXS","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"EBR44ZXUIGXS4O3S","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"EBR44ZXU","created_at":"2026-05-18T12:27:43.054852+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/EBR44ZXUIGXS4O3SJO6XVTDP2T","json":"https://pith.science/pith/EBR44ZXUIGXS4O3SJO6XVTDP2T.json","graph_json":"https://pith.science/api/pith-number/EBR44ZXUIGXS4O3SJO6XVTDP2T/graph.json","events_json":"https://pith.science/api/pith-number/EBR44ZXUIGXS4O3SJO6XVTDP2T/events.json","paper":"https://pith.science/paper/EBR44ZXU"},"agent_actions":{"view_html":"https://pith.science/pith/EBR44ZXUIGXS4O3SJO6XVTDP2T","download_json":"https://pith.science/pith/EBR44ZXUIGXS4O3SJO6XVTDP2T.json","view_paper":"https://pith.science/paper/EBR44ZXU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.4838&json=true","fetch_graph":"https://pith.science/api/pith-number/EBR44ZXUIGXS4O3SJO6XVTDP2T/graph.json","fetch_events":"https://pith.science/api/pith-number/EBR44ZXUIGXS4O3SJO6XVTDP2T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EBR44ZXUIGXS4O3SJO6XVTDP2T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EBR44ZXUIGXS4O3SJO6XVTDP2T/action/storage_attestation","attest_author":"https://pith.science/pith/EBR44ZXUIGXS4O3SJO6XVTDP2T/action/author_attestation","sign_citation":"https://pith.science/pith/EBR44ZXUIGXS4O3SJO6XVTDP2T/action/citation_signature","submit_replication":"https://pith.science/pith/EBR44ZXUIGXS4O3SJO6XVTDP2T/action/replication_record"}},"created_at":"2026-05-18T03:27:43.538539+00:00","updated_at":"2026-05-18T03:27:43.538539+00:00"}