{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XXJQWULCX4SLGJW4JB25GNR7ST","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":"ce3db96d99731d5754a991574dc6238484e5d94b87705899872556be61523c79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-21T09:45:44Z","title_canon_sha256":"870330a57696015cffa252219ed8eb0ebd256e372bfdffaf87b7f7a59b090af7"},"schema_version":"1.0","source":{"id":"1203.4691","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.4691","created_at":"2026-05-18T03:59:37Z"},{"alias_kind":"arxiv_version","alias_value":"1203.4691v1","created_at":"2026-05-18T03:59:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.4691","created_at":"2026-05-18T03:59:37Z"},{"alias_kind":"pith_short_12","alias_value":"XXJQWULCX4SL","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XXJQWULCX4SLGJW4","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XXJQWULC","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:09c9b41d80ec99616e78f5844d72f94126815b5cd7644303aa4f14a5246c065e","target":"graph","created_at":"2026-05-18T03:59:37Z","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 revisit a result of Uchiyama (1980): given that a certain integral test is satisfied, the rate of the probability that Brownian motion remains below the moving boundary $f$ is asymptotically the same as for the constant boundary. The integral test for $f$ is also necessary in some sense. After Uchiyama's result, a number of different proofs appeared simplifying the original arguments, which strongly rely on some known identities for Brownian motion. In particular, Novikov (1996) gives an elementary proof in the case of an increasing boundary. Here, we provide an elementary, half-page proof ","authors_text":"Frank Aurzada, Tanja Kramm","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-21T09:45:44Z","title":"First exit of Brownian motion from a one-sided moving boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4691","kind":"arxiv","version":1},"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":"sha256:868e845a1f7ae4af8ad2370246af6e97af90f175412ad486027d110e274876d4","target":"record","created_at":"2026-05-18T03:59:37Z","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":"ce3db96d99731d5754a991574dc6238484e5d94b87705899872556be61523c79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-21T09:45:44Z","title_canon_sha256":"870330a57696015cffa252219ed8eb0ebd256e372bfdffaf87b7f7a59b090af7"},"schema_version":"1.0","source":{"id":"1203.4691","kind":"arxiv","version":1}},"canonical_sha256":"bdd30b5162bf24b326dc4875d3363f94ffcc0f7c0769eadafad046687ebea1ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bdd30b5162bf24b326dc4875d3363f94ffcc0f7c0769eadafad046687ebea1ac","first_computed_at":"2026-05-18T03:59:37.444057Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:37.444057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ffn7DWh/FHK2JAKeXq6IffNj2wW9srv6KBzXWkGgyiBHpHylLCJYJPsB/hGhuQXOKFyEdEaGPihhUi77UlRUDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:37.444738Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.4691","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:868e845a1f7ae4af8ad2370246af6e97af90f175412ad486027d110e274876d4","sha256:09c9b41d80ec99616e78f5844d72f94126815b5cd7644303aa4f14a5246c065e"],"state_sha256":"af06b7224be338eaa73ff6230a15e031f784d17fed862a462918b4fed5f6ac26"}