{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5RUPFXQXPXG7XVQANLLM35IQJL","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":"917beed53567425c546ed1d2b87fd0cd7f7fcaaae682f2052f2a2d06665e7a94","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-01T13:14:48Z","title_canon_sha256":"32d9f35ef61542fd23c53ec940f6ca3a2bf368feabbe817537a66319d5149338"},"schema_version":"1.0","source":{"id":"1109.0182","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0182","created_at":"2026-05-18T04:09:37Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0182v2","created_at":"2026-05-18T04:09:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0182","created_at":"2026-05-18T04:09:37Z"},{"alias_kind":"pith_short_12","alias_value":"5RUPFXQXPXG7","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5RUPFXQXPXG7XVQA","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5RUPFXQX","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:25841e6bb73ca63580c615a8ebf595c73f810298baeb04c723634b8d14aa20d9","target":"graph","created_at":"2026-05-18T04:09:37Z","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":"The purpose of the paper is to provide a general method for computing hitting distributions of some regular subsets D for Ornstein-Uhlenbeck type operators of the form 1/2\\Delta + F\\cdot\\nabla, with F bounded and orthogonal to the boundary of D. As an important application we obtain integral representations of the Poisson kernel for a half-space and balls for hyperbolic Brownian motion and for the classical Ornstein-Uhlenbeck process. The method developed in the paper is based on stochastic calculus and on skew product representation of multidimensional Brownian motion and yields more complete","authors_text":"Jacek Malecki, Jakub Chorowski, Piotr Graczyk, Tomasz Byczkowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-01T13:14:48Z","title":"Hitting half-spaces or spheres by the Ornstein-Uhlenbeck type diffusions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0182","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":"sha256:18aca6a1b999d7ed85c70f4eae5706a828bd889932242ef57b42c6fd324d0415","target":"record","created_at":"2026-05-18T04:09:37Z","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":"917beed53567425c546ed1d2b87fd0cd7f7fcaaae682f2052f2a2d06665e7a94","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-01T13:14:48Z","title_canon_sha256":"32d9f35ef61542fd23c53ec940f6ca3a2bf368feabbe817537a66319d5149338"},"schema_version":"1.0","source":{"id":"1109.0182","kind":"arxiv","version":2}},"canonical_sha256":"ec68f2de177dcdfbd6006ad6cdf5104aee639e77a6d25207256a987771f47ebe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec68f2de177dcdfbd6006ad6cdf5104aee639e77a6d25207256a987771f47ebe","first_computed_at":"2026-05-18T04:09:37.417669Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:37.417669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mCJjW+7UF0X7ScCzDXpOdGzAYZFklPqMNPz2nlRAUN0nCZx7zMhIblmZ02Ohjju6UEF3w9ET0mEq4+7lWe+KAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:37.418402Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.0182","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18aca6a1b999d7ed85c70f4eae5706a828bd889932242ef57b42c6fd324d0415","sha256:25841e6bb73ca63580c615a8ebf595c73f810298baeb04c723634b8d14aa20d9"],"state_sha256":"ccb92ec5e8daa19bf2a66cbcbd6cd5f13fc3290fc599ab468471e59013206450"}