{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EBR44ZXUIGXS4O3SJO6XVTDP2T","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":"481a1e6a01075ae596a70d32900d69f3d8ad05d2ac459ed16c5974f47630a93a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-17T14:30:28Z","title_canon_sha256":"fd74c746d63984fa35b6bd74fc6a2a3d9d5d8ab299df727ee7d336952241641c"},"schema_version":"1.0","source":{"id":"1304.4838","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4838","created_at":"2026-05-18T03:27:43Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4838v1","created_at":"2026-05-18T03:27:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4838","created_at":"2026-05-18T03:27:43Z"},{"alias_kind":"pith_short_12","alias_value":"EBR44ZXUIGXS","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EBR44ZXUIGXS4O3S","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EBR44ZXU","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:1c338cf499eeb7a1ad08e6223817ef028ed9701fc2fffd2898e7af829f8acc79","target":"graph","created_at":"2026-05-18T03:27:43Z","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":"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.","authors_text":"Cheng Ouyang, Fabrice Baudoin, Xuejing Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-17T14:30:28Z","title":"Smoothing effect of rough differential equations driven by fractional Brownian motions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4838","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":"sha256:3da90da9adb06dc291ffb505fd03dc6b6b09167c8bca93deaf25554cdcf9aed2","target":"record","created_at":"2026-05-18T03:27:43Z","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":"481a1e6a01075ae596a70d32900d69f3d8ad05d2ac459ed16c5974f47630a93a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-17T14:30:28Z","title_canon_sha256":"fd74c746d63984fa35b6bd74fc6a2a3d9d5d8ab299df727ee7d336952241641c"},"schema_version":"1.0","source":{"id":"1304.4838","kind":"arxiv","version":1}},"canonical_sha256":"2063ce66f441af2e3b724bbd7acc6fd4e45afc23be1ba034e5e5fbe32821faeb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2063ce66f441af2e3b724bbd7acc6fd4e45afc23be1ba034e5e5fbe32821faeb","first_computed_at":"2026-05-18T03:27:43.538473Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:43.538473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6H1EDkHUX6+HtJlujGYbh1Nd4F7YwHMKfn9innG9I5wU2XVK2fsLUZqxVDEMJmdUY+C3gjOu0EA5AkMO2fDFAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:43.538920Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.4838","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3da90da9adb06dc291ffb505fd03dc6b6b09167c8bca93deaf25554cdcf9aed2","sha256:1c338cf499eeb7a1ad08e6223817ef028ed9701fc2fffd2898e7af829f8acc79"],"state_sha256":"d4723869d096a79d0a6f8ac3f58a42e10232214e5fa4ce5060e85c2ecf63dacf"}