{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:3YEUDRTK3ZVMJSNNQWCLX6VTMK","short_pith_number":"pith:3YEUDRTK","canonical_record":{"source":{"id":"2302.11455","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-02-22T15:43:30Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"92829676f38c291720cbc182b561460769ef48d5d4395efade94b0c3063290c3","abstract_canon_sha256":"5e420de7124677a7e59da34fd45c594916128bea3270037631c8079d7458e5ec"},"schema_version":"1.0"},"canonical_sha256":"de0941c66ade6ac4c9ad8584bbfab3629b85540889ec69597a3268bd29ffa3b5","source":{"kind":"arxiv","id":"2302.11455","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.11455","created_at":"2026-07-05T09:41:27Z"},{"alias_kind":"arxiv_version","alias_value":"2302.11455v3","created_at":"2026-07-05T09:41:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.11455","created_at":"2026-07-05T09:41:27Z"},{"alias_kind":"pith_short_12","alias_value":"3YEUDRTK3ZVM","created_at":"2026-07-05T09:41:27Z"},{"alias_kind":"pith_short_16","alias_value":"3YEUDRTK3ZVMJSNN","created_at":"2026-07-05T09:41:27Z"},{"alias_kind":"pith_short_8","alias_value":"3YEUDRTK","created_at":"2026-07-05T09:41:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:3YEUDRTK3ZVMJSNNQWCLX6VTMK","target":"record","payload":{"canonical_record":{"source":{"id":"2302.11455","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-02-22T15:43:30Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"92829676f38c291720cbc182b561460769ef48d5d4395efade94b0c3063290c3","abstract_canon_sha256":"5e420de7124677a7e59da34fd45c594916128bea3270037631c8079d7458e5ec"},"schema_version":"1.0"},"canonical_sha256":"de0941c66ade6ac4c9ad8584bbfab3629b85540889ec69597a3268bd29ffa3b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:41:27.077739Z","signature_b64":"NWg9o71Q6i2h4Y7KUeF83ytBZw0YQLHf9d7mzj11Q+ruycW8J9kUnlDY7s+pzF1CD4E8GlA4GppksIEuwmxXAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de0941c66ade6ac4c9ad8584bbfab3629b85540889ec69597a3268bd29ffa3b5","last_reissued_at":"2026-07-05T09:41:27.077267Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:41:27.077267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2302.11455","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:41:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rAmKmAD11qhN8XoH6tJv+17D5DZKYddJItB8yW2cBmk18hRHKO7sVAg0WrEeClaJK/cz/VzncImADSjcLSYMAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T11:21:37.203375Z"},"content_sha256":"457f1155382df2bc874eb97ebcfbc7d985e72f8af84b3c019a937e347a3791f6","schema_version":"1.0","event_id":"sha256:457f1155382df2bc874eb97ebcfbc7d985e72f8af84b3c019a937e347a3791f6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:3YEUDRTK3ZVMJSNNQWCLX6VTMK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical approximation of SDEs with fractional noise and distributional drift","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.PR","authors_text":"Alexandre Richard, El Mehdi Haress, Ludovic Gouden\\`ege","submitted_at":"2023-02-22T15:43:30Z","abstract_excerpt":"We study the numerical approximation of SDEs with singular drifts (including distributions) driven by a fractional Brownian motion. Under the Catellier-Gubinelli condition that imposes the regularity of the drift to be strictly greater than $1-1/(2H)$, we obtain an explicit rate of convergence of a tamed Euler scheme towards the SDE, extending results for bounded drifts. Beyond this regime, when the regularity of the drift is $1-1/(2H)$, we derive a non-explicit rate. As a byproduct, strong well-posedness for these equations is recovered. Proofs use new regularising properties of discrete-time"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.11455","kind":"arxiv","version":3},"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/2302.11455/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:41:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aKRCAxCOZHiKxSJYPK6qo+UVNR8mE3VTAFNDMS3PQ22uU0q570cGbkdu23Mq2Ny4DN7h/odktNqgIzcgQKdZAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T11:21:37.204303Z"},"content_sha256":"27bd0b4c98c6fc835d668651b4c426ecbc7f95e1137ea5a6b15a92063ab100e5","schema_version":"1.0","event_id":"sha256:27bd0b4c98c6fc835d668651b4c426ecbc7f95e1137ea5a6b15a92063ab100e5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3YEUDRTK3ZVMJSNNQWCLX6VTMK/bundle.json","state_url":"https://pith.science/pith/3YEUDRTK3ZVMJSNNQWCLX6VTMK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3YEUDRTK3ZVMJSNNQWCLX6VTMK/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":"2026-08-11T11:21:37Z","links":{"resolver":"https://pith.science/pith/3YEUDRTK3ZVMJSNNQWCLX6VTMK","bundle":"https://pith.science/pith/3YEUDRTK3ZVMJSNNQWCLX6VTMK/bundle.json","state":"https://pith.science/pith/3YEUDRTK3ZVMJSNNQWCLX6VTMK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3YEUDRTK3ZVMJSNNQWCLX6VTMK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:3YEUDRTK3ZVMJSNNQWCLX6VTMK","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":"5e420de7124677a7e59da34fd45c594916128bea3270037631c8079d7458e5ec","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-02-22T15:43:30Z","title_canon_sha256":"92829676f38c291720cbc182b561460769ef48d5d4395efade94b0c3063290c3"},"schema_version":"1.0","source":{"id":"2302.11455","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.11455","created_at":"2026-07-05T09:41:27Z"},{"alias_kind":"arxiv_version","alias_value":"2302.11455v3","created_at":"2026-07-05T09:41:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.11455","created_at":"2026-07-05T09:41:27Z"},{"alias_kind":"pith_short_12","alias_value":"3YEUDRTK3ZVM","created_at":"2026-07-05T09:41:27Z"},{"alias_kind":"pith_short_16","alias_value":"3YEUDRTK3ZVMJSNN","created_at":"2026-07-05T09:41:27Z"},{"alias_kind":"pith_short_8","alias_value":"3YEUDRTK","created_at":"2026-07-05T09:41:27Z"}],"graph_snapshots":[{"event_id":"sha256:27bd0b4c98c6fc835d668651b4c426ecbc7f95e1137ea5a6b15a92063ab100e5","target":"graph","created_at":"2026-07-05T09:41:27Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2302.11455/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the numerical approximation of SDEs with singular drifts (including distributions) driven by a fractional Brownian motion. Under the Catellier-Gubinelli condition that imposes the regularity of the drift to be strictly greater than $1-1/(2H)$, we obtain an explicit rate of convergence of a tamed Euler scheme towards the SDE, extending results for bounded drifts. Beyond this regime, when the regularity of the drift is $1-1/(2H)$, we derive a non-explicit rate. As a byproduct, strong well-posedness for these equations is recovered. Proofs use new regularising properties of discrete-time","authors_text":"Alexandre Richard, El Mehdi Haress, Ludovic Gouden\\`ege","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-02-22T15:43:30Z","title":"Numerical approximation of SDEs with fractional noise and distributional drift"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.11455","kind":"arxiv","version":3},"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":"sha256:457f1155382df2bc874eb97ebcfbc7d985e72f8af84b3c019a937e347a3791f6","target":"record","created_at":"2026-07-05T09:41:27Z","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":"5e420de7124677a7e59da34fd45c594916128bea3270037631c8079d7458e5ec","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-02-22T15:43:30Z","title_canon_sha256":"92829676f38c291720cbc182b561460769ef48d5d4395efade94b0c3063290c3"},"schema_version":"1.0","source":{"id":"2302.11455","kind":"arxiv","version":3}},"canonical_sha256":"de0941c66ade6ac4c9ad8584bbfab3629b85540889ec69597a3268bd29ffa3b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de0941c66ade6ac4c9ad8584bbfab3629b85540889ec69597a3268bd29ffa3b5","first_computed_at":"2026-07-05T09:41:27.077267Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:41:27.077267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NWg9o71Q6i2h4Y7KUeF83ytBZw0YQLHf9d7mzj11Q+ruycW8J9kUnlDY7s+pzF1CD4E8GlA4GppksIEuwmxXAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:41:27.077739Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.11455","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:457f1155382df2bc874eb97ebcfbc7d985e72f8af84b3c019a937e347a3791f6","sha256:27bd0b4c98c6fc835d668651b4c426ecbc7f95e1137ea5a6b15a92063ab100e5"],"state_sha256":"24186892a478c68521fbd3f0fea26fd5d17d234a4534647d53a0ad79c53232df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"klWWbGa2ekGzvjMmLSr4i59fB9wQHClJYjGC0TA6h2T+Qnv9IA98SkvunUMtzLn2IAfn3NL3ALsf8QDp5aYtCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T11:21:37.210070Z","bundle_sha256":"d8d0871990b23b88af4c289b0297df97215f730ba2924a052d2461f362f64fcf"}}