{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:TIK4CZC2CE265NVUCWKEB3VKUD","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":"7aa9f58f0d1fc79b14a8f441558cd5951f9c24f1e4a9e673c41b70e083457f45","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-04-29T13:11:46Z","title_canon_sha256":"6630f391d21bf4e27348dc3f5b0c43cfec8d7f81889deba5663ed8f85a135eb3"},"schema_version":"1.0","source":{"id":"2504.20728","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.20728","created_at":"2026-06-05T01:15:13Z"},{"alias_kind":"arxiv_version","alias_value":"2504.20728v2","created_at":"2026-06-05T01:15:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.20728","created_at":"2026-06-05T01:15:13Z"},{"alias_kind":"pith_short_12","alias_value":"TIK4CZC2CE26","created_at":"2026-06-05T01:15:13Z"},{"alias_kind":"pith_short_16","alias_value":"TIK4CZC2CE265NVU","created_at":"2026-06-05T01:15:13Z"},{"alias_kind":"pith_short_8","alias_value":"TIK4CZC2","created_at":"2026-06-05T01:15:13Z"}],"graph_snapshots":[{"event_id":"sha256:56cf44fd09950a9b05945f219109621a90d299fc33fa7b98f47dd483c1e92089","target":"graph","created_at":"2026-06-05T01:15:13Z","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/2504.20728/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study strong approximation of solutions of SDEs with bounded $\\alpha$-H\\\"older continuous drift coefficient and constant diffusion coefficient at time point $1$. Recently, it was shown in [arXiv:1909.07961v4 (2021)] that for such SDEs the equidistant Euler scheme achieves an $L^p$-error rate of at least $(1+\\alpha)/2$, up to an arbitrary small $\\varepsilon$, for all $p\\geq 1$ and $\\alpha\\in (0,1]$, in terms of the number of evaluations of the driving Brownian motion $W$. In this article, we prove a matching lower error bound for $\\alpha\\in (0,1)$. More precisely, we show that for every $\\al","authors_text":"Larisa Yaroslavtseva, Simon Ellinger, Thomas M\\\"uller-Gronbach","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-04-29T13:11:46Z","title":"Sharp lower error bounds for strong approximation of SDEs with a drift coefficient of H\\\"older or Sobolev regularity using a Weierstra{\\ss} scale"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.20728","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:d1608e947ab7cc2b06dceb782e7a82f316b90b385cfb7cdac70a88156e58a54b","target":"record","created_at":"2026-06-05T01:15:13Z","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":"7aa9f58f0d1fc79b14a8f441558cd5951f9c24f1e4a9e673c41b70e083457f45","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-04-29T13:11:46Z","title_canon_sha256":"6630f391d21bf4e27348dc3f5b0c43cfec8d7f81889deba5663ed8f85a135eb3"},"schema_version":"1.0","source":{"id":"2504.20728","kind":"arxiv","version":2}},"canonical_sha256":"9a15c1645a1135eeb6b4159440eeaaa0ffb11477bb2c168f1271118e09b158e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a15c1645a1135eeb6b4159440eeaaa0ffb11477bb2c168f1271118e09b158e8","first_computed_at":"2026-06-05T01:15:13.462451Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-05T01:15:13.462451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5HGcjVK8sZEZjgEm88csCFHWTU0lQFabUtqzRu8Fj4Iz8oKF4l8tAPuQ3ZMkQlOQP/otvZBpuG9ArK7xA7WFDA==","signature_status":"signed_v1","signed_at":"2026-06-05T01:15:13.463141Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.20728","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1608e947ab7cc2b06dceb782e7a82f316b90b385cfb7cdac70a88156e58a54b","sha256:56cf44fd09950a9b05945f219109621a90d299fc33fa7b98f47dd483c1e92089"],"state_sha256":"31e7b8ec73c3da4413c45a3bb16c3a0b2823fafd3d0a9746979ef020d8ce2f7b"}