{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:372W6KXGAQYZHLRY7UETB7CEDC","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":"63f333b3d71ab60b30b0ca72d66cdad9c5632a130f42f1df117c38acea576538","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-08-21T12:40:30Z","title_canon_sha256":"56321ab03d1bf56e876a0e3f2305d716bd8b5e79bab6a2dfbab7a1e155859168"},"schema_version":"1.0","source":{"id":"1708.06188","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.06188","created_at":"2026-05-17T23:59:25Z"},{"alias_kind":"arxiv_version","alias_value":"1708.06188v2","created_at":"2026-05-17T23:59:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.06188","created_at":"2026-05-17T23:59:25Z"},{"alias_kind":"pith_short_12","alias_value":"372W6KXGAQYZ","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"372W6KXGAQYZHLRY","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"372W6KXG","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:9a92c9764c10be0d3c74c0ef8206db111e0fef9eae01853b194988ccd829d452","target":"graph","created_at":"2026-05-17T23:59:25Z","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":"For time-homogeneous stochastic differential equations (SDEs) it is enough to know that the coefficients are Lipschitz to conclude existence and uniqueness of a solution, as well as the existence of a strongly convergent numerical method for its approximation. Here we introduce a notion of piecewise Lipschitz functions and study SDEs with a drift coefficient satisfying only this weaker regularity condition. For these SDEs we can construct a strongly convergent approximation scheme, if the set of discontinuities is a sufficiently smooth hypersurface satisfying the geometrical property of being ","authors_text":"Gunther Leobacher, Michaela Sz\\\"olgyenyi","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-08-21T12:40:30Z","title":"Numerical methods for SDEs with drift discontinuous on a set of positive reach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06188","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":"sha256:6ae1ab2c77113695d59e7de9da6ebcf59eccd7e114842207fc891146eddafe0e","target":"record","created_at":"2026-05-17T23:59:25Z","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":"63f333b3d71ab60b30b0ca72d66cdad9c5632a130f42f1df117c38acea576538","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-08-21T12:40:30Z","title_canon_sha256":"56321ab03d1bf56e876a0e3f2305d716bd8b5e79bab6a2dfbab7a1e155859168"},"schema_version":"1.0","source":{"id":"1708.06188","kind":"arxiv","version":2}},"canonical_sha256":"dff56f2ae6043193ae38fd0930fc44188696572605812f79470468566638b9de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dff56f2ae6043193ae38fd0930fc44188696572605812f79470468566638b9de","first_computed_at":"2026-05-17T23:59:25.202935Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:25.202935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QCQE05SkxM1tOC/5zwu7dqmiVD2tGpIEg1fRhCeyaClSqN4gzUE4qm3CC3/fsXisLrUNgvaWsMGvwm3LogGKCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:25.203472Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.06188","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ae1ab2c77113695d59e7de9da6ebcf59eccd7e114842207fc891146eddafe0e","sha256:9a92c9764c10be0d3c74c0ef8206db111e0fef9eae01853b194988ccd829d452"],"state_sha256":"5f896df9ca766058a2fda1c4a0c93940a737d69e324c872a6cd76b824bb4501f"}