{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:66AAHE7HHCTHRFA25KG4JSMNOF","short_pith_number":"pith:66AAHE7H","schema_version":"1.0","canonical_sha256":"f7800393e738a678941aea8dc4c98d715d209ff130f4f65a36f315f13f47cbc2","source":{"kind":"arxiv","id":"2207.04251","version":2},"attestation_state":"computed","paper":{"title":"Regularization by noise for rough differential equations driven by Gaussian rough paths","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"R\\'emi Catellier, Romain Duboscq","submitted_at":"2022-07-09T11:21:20Z","abstract_excerpt":"We consider the rough differential equation with drift driven by a Gaussian geometric rough path. Under natural conditions on the rough path, namely non-determinism, and uniform ellipticity conditions on the diffusion coefficient, we prove path-by-path well-posedness of the equation for poorly regular drifts. In the case of the fractional Brownian motion $B^H$ for $H>\\frac14$, we prove that the drift may be taken to be $\\kappa>0$ H\\\"older continuous and bounded for $\\kappa>\\frac32 - \\frac1{2H}$. A flow transform of the equation and Malliavin calculus for Gaussian rough paths are used to achiev"},"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":"2207.04251","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2022-07-09T11:21:20Z","cross_cats_sorted":[],"title_canon_sha256":"0747ddad5596d56ba37ea8d2440df2aac40c12db5e43eecfdfb177e171b664b0","abstract_canon_sha256":"6bc954fe78d9f68af31e6edd549095e30ebda144a02ba4ccf5cf3b99b9f65783"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:44:51.420425Z","signature_b64":"3tBZnTKhTjZhBcbYxZ6K0l4vj3DPG2rSNTe8WQedzpnMVgDfq6IAr9l5Bds3/ljEPaErPt+U3iyQm7DdEBzFDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7800393e738a678941aea8dc4c98d715d209ff130f4f65a36f315f13f47cbc2","last_reissued_at":"2026-07-05T07:44:51.419966Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:44:51.419966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regularization by noise for rough differential equations driven by Gaussian rough paths","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"R\\'emi Catellier, Romain Duboscq","submitted_at":"2022-07-09T11:21:20Z","abstract_excerpt":"We consider the rough differential equation with drift driven by a Gaussian geometric rough path. Under natural conditions on the rough path, namely non-determinism, and uniform ellipticity conditions on the diffusion coefficient, we prove path-by-path well-posedness of the equation for poorly regular drifts. In the case of the fractional Brownian motion $B^H$ for $H>\\frac14$, we prove that the drift may be taken to be $\\kappa>0$ H\\\"older continuous and bounded for $\\kappa>\\frac32 - \\frac1{2H}$. A flow transform of the equation and Malliavin calculus for Gaussian rough paths are used to achiev"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.04251","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2207.04251/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2207.04251","created_at":"2026-07-05T07:44:51.420024+00:00"},{"alias_kind":"arxiv_version","alias_value":"2207.04251v2","created_at":"2026-07-05T07:44:51.420024+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.04251","created_at":"2026-07-05T07:44:51.420024+00:00"},{"alias_kind":"pith_short_12","alias_value":"66AAHE7HHCTH","created_at":"2026-07-05T07:44:51.420024+00:00"},{"alias_kind":"pith_short_16","alias_value":"66AAHE7HHCTHRFA2","created_at":"2026-07-05T07:44:51.420024+00:00"},{"alias_kind":"pith_short_8","alias_value":"66AAHE7H","created_at":"2026-07-05T07:44:51.420024+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2401.09970","citing_title":"Zero noise limit for singular ODE regularized by fractional noise","ref_index":4,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/66AAHE7HHCTHRFA25KG4JSMNOF","json":"https://pith.science/pith/66AAHE7HHCTHRFA25KG4JSMNOF.json","graph_json":"https://pith.science/api/pith-number/66AAHE7HHCTHRFA25KG4JSMNOF/graph.json","events_json":"https://pith.science/api/pith-number/66AAHE7HHCTHRFA25KG4JSMNOF/events.json","paper":"https://pith.science/paper/66AAHE7H"},"agent_actions":{"view_html":"https://pith.science/pith/66AAHE7HHCTHRFA25KG4JSMNOF","download_json":"https://pith.science/pith/66AAHE7HHCTHRFA25KG4JSMNOF.json","view_paper":"https://pith.science/paper/66AAHE7H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2207.04251&json=true","fetch_graph":"https://pith.science/api/pith-number/66AAHE7HHCTHRFA25KG4JSMNOF/graph.json","fetch_events":"https://pith.science/api/pith-number/66AAHE7HHCTHRFA25KG4JSMNOF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/66AAHE7HHCTHRFA25KG4JSMNOF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/66AAHE7HHCTHRFA25KG4JSMNOF/action/storage_attestation","attest_author":"https://pith.science/pith/66AAHE7HHCTHRFA25KG4JSMNOF/action/author_attestation","sign_citation":"https://pith.science/pith/66AAHE7HHCTHRFA25KG4JSMNOF/action/citation_signature","submit_replication":"https://pith.science/pith/66AAHE7HHCTHRFA25KG4JSMNOF/action/replication_record"}},"created_at":"2026-07-05T07:44:51.420024+00:00","updated_at":"2026-07-05T07:44:51.420024+00:00"}