{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XKPMIWPXG5GNM577W3NXABODOQ","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":"9c8366c3a3ad0a17e260103d795a035dd3fac46f56fa91fc2b328db4d5481eff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-23T07:11:18Z","title_canon_sha256":"4eee7a545e589f136ae4413fa7b2c04382189c98ae64e112cc209ad81cf5a4e5"},"schema_version":"1.0","source":{"id":"1605.06911","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.06911","created_at":"2026-05-18T01:12:37Z"},{"alias_kind":"arxiv_version","alias_value":"1605.06911v2","created_at":"2026-05-18T01:12:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.06911","created_at":"2026-05-18T01:12:37Z"},{"alias_kind":"pith_short_12","alias_value":"XKPMIWPXG5GN","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XKPMIWPXG5GNM577","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XKPMIWPX","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:8c291f2f755cda72245b64cfa04fd2e6c9e8fd44e4623ac5269a35ef6ebb52d8","target":"graph","created_at":"2026-05-18T01:12:37Z","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":"We consider a multidimensional SDE with a Gaussian noise and a drift vector being a vector function of bounded variation. We prove the existence of generalized derivative of the solution with respect to the initial conditions and represent the derivative as a solution of a linear SDE with coefficients depending on the initial process. The representation obtained is a natural generalization of the expression for the derivative in the smooth case. The theory of continuous additive functionals is used.","authors_text":"Andrey Pilipenko, Olga Aryasova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-23T07:11:18Z","title":"A representation for the derivative with respect to the initial data of the solution of an SDE with a non-regular drift and a Gaussian noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06911","kind":"arxiv","version":2},"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":"sha256:37a36d031ee03430048feee0a747c6f8b09973abdd1ece5541a7372ce0f86dc7","target":"record","created_at":"2026-05-18T01:12:37Z","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":"9c8366c3a3ad0a17e260103d795a035dd3fac46f56fa91fc2b328db4d5481eff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-23T07:11:18Z","title_canon_sha256":"4eee7a545e589f136ae4413fa7b2c04382189c98ae64e112cc209ad81cf5a4e5"},"schema_version":"1.0","source":{"id":"1605.06911","kind":"arxiv","version":2}},"canonical_sha256":"ba9ec459f7374cd677ffb6db7005c3742cf4ccbcd119153a246ac343b28cbb8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba9ec459f7374cd677ffb6db7005c3742cf4ccbcd119153a246ac343b28cbb8d","first_computed_at":"2026-05-18T01:12:37.666163Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:37.666163Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"znKC96k/fGX9+mr9hvhZFMxtwLau6Z9cYI6VRv3sG9EPZkSFr5dNMF1rTjOc3Xy9xR1Gm2AaqIxxDFEu8GG2AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:37.666596Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.06911","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37a36d031ee03430048feee0a747c6f8b09973abdd1ece5541a7372ce0f86dc7","sha256:8c291f2f755cda72245b64cfa04fd2e6c9e8fd44e4623ac5269a35ef6ebb52d8"],"state_sha256":"6fd88d3c576c6bceedca0f67ff24b3e44c5621fe1990c243de769ef8c2b65a3f"}