{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:5RUPFXQXPXG7XVQANLLM35IQJL","short_pith_number":"pith:5RUPFXQX","schema_version":"1.0","canonical_sha256":"ec68f2de177dcdfbd6006ad6cdf5104aee639e77a6d25207256a987771f47ebe","source":{"kind":"arxiv","id":"1109.0182","version":2},"attestation_state":"computed","paper":{"title":"Hitting half-spaces or spheres by the Ornstein-Uhlenbeck type diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jacek Malecki, Jakub Chorowski, Piotr Graczyk, Tomasz Byczkowski","submitted_at":"2011-09-01T13:14:48Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1109.0182","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-01T13:14:48Z","cross_cats_sorted":[],"title_canon_sha256":"32d9f35ef61542fd23c53ec940f6ca3a2bf368feabbe817537a66319d5149338","abstract_canon_sha256":"917beed53567425c546ed1d2b87fd0cd7f7fcaaae682f2052f2a2d06665e7a94"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:37.418402Z","signature_b64":"mCJjW+7UF0X7ScCzDXpOdGzAYZFklPqMNPz2nlRAUN0nCZx7zMhIblmZ02Ohjju6UEF3w9ET0mEq4+7lWe+KAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec68f2de177dcdfbd6006ad6cdf5104aee639e77a6d25207256a987771f47ebe","last_reissued_at":"2026-05-18T04:09:37.417669Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:37.417669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hitting half-spaces or spheres by the Ornstein-Uhlenbeck type diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jacek Malecki, Jakub Chorowski, Piotr Graczyk, Tomasz Byczkowski","submitted_at":"2011-09-01T13:14:48Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0182","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1109.0182","created_at":"2026-05-18T04:09:37.417787+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.0182v2","created_at":"2026-05-18T04:09:37.417787+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0182","created_at":"2026-05-18T04:09:37.417787+00:00"},{"alias_kind":"pith_short_12","alias_value":"5RUPFXQXPXG7","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_16","alias_value":"5RUPFXQXPXG7XVQA","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_8","alias_value":"5RUPFXQX","created_at":"2026-05-18T12:26:20.644004+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5RUPFXQXPXG7XVQANLLM35IQJL","json":"https://pith.science/pith/5RUPFXQXPXG7XVQANLLM35IQJL.json","graph_json":"https://pith.science/api/pith-number/5RUPFXQXPXG7XVQANLLM35IQJL/graph.json","events_json":"https://pith.science/api/pith-number/5RUPFXQXPXG7XVQANLLM35IQJL/events.json","paper":"https://pith.science/paper/5RUPFXQX"},"agent_actions":{"view_html":"https://pith.science/pith/5RUPFXQXPXG7XVQANLLM35IQJL","download_json":"https://pith.science/pith/5RUPFXQXPXG7XVQANLLM35IQJL.json","view_paper":"https://pith.science/paper/5RUPFXQX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.0182&json=true","fetch_graph":"https://pith.science/api/pith-number/5RUPFXQXPXG7XVQANLLM35IQJL/graph.json","fetch_events":"https://pith.science/api/pith-number/5RUPFXQXPXG7XVQANLLM35IQJL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5RUPFXQXPXG7XVQANLLM35IQJL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5RUPFXQXPXG7XVQANLLM35IQJL/action/storage_attestation","attest_author":"https://pith.science/pith/5RUPFXQXPXG7XVQANLLM35IQJL/action/author_attestation","sign_citation":"https://pith.science/pith/5RUPFXQXPXG7XVQANLLM35IQJL/action/citation_signature","submit_replication":"https://pith.science/pith/5RUPFXQXPXG7XVQANLLM35IQJL/action/replication_record"}},"created_at":"2026-05-18T04:09:37.417787+00:00","updated_at":"2026-05-18T04:09:37.417787+00:00"}