{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:O6CHPRTV6U3MEFCPXNWZL64LQJ","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":"c8e2c8133ff92ba58b511b5dbec0b11f61f00819315c61adc7c1552632376549","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-29T16:47:54Z","title_canon_sha256":"ade867961187ae7042d93fc42fc23ab62c5aafc14d4e27a4e1a33dc1d755ccf2"},"schema_version":"1.0","source":{"id":"1309.7624","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7624","created_at":"2026-05-18T03:11:56Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7624v1","created_at":"2026-05-18T03:11:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7624","created_at":"2026-05-18T03:11:56Z"},{"alias_kind":"pith_short_12","alias_value":"O6CHPRTV6U3M","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"O6CHPRTV6U3MEFCP","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"O6CHPRTV","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:47fb688a57d61e4bb00c6e7eeda3b8e946e5606177dcc0e7ebb87a323b511332","target":"graph","created_at":"2026-05-18T03:11:56Z","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":"In this paper we investigate the boundary non-crossing probabilities of a fractional Brownian motion considering some general deterministic trend function. We derive bounds for non-crossing probabilities and discuss the case of a large trend function. As a by-product we solve a minimization problem related to the norm of the trend function.","authors_text":"Enkelejd Hashorva, Oleg Seleznjev, Yuliya Mishura","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-29T16:47:54Z","title":"Boundary non-crossing probabilities for fractional Brownian motion with trend"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7624","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":"sha256:24444d1781eda4afd1417f4272db3d986c528f2ebe53a28c5befeb0790ab2daf","target":"record","created_at":"2026-05-18T03:11:56Z","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":"c8e2c8133ff92ba58b511b5dbec0b11f61f00819315c61adc7c1552632376549","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-29T16:47:54Z","title_canon_sha256":"ade867961187ae7042d93fc42fc23ab62c5aafc14d4e27a4e1a33dc1d755ccf2"},"schema_version":"1.0","source":{"id":"1309.7624","kind":"arxiv","version":1}},"canonical_sha256":"778477c675f536c2144fbb6d95fb8b824bc9436fb5aa4a1190f74e98c45634e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"778477c675f536c2144fbb6d95fb8b824bc9436fb5aa4a1190f74e98c45634e6","first_computed_at":"2026-05-18T03:11:56.386854Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:56.386854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9LSvC0s0EaBu9EUavM8zqLNU9qvXzR5ejjNuAjHGIQf/DDIM0uVsrINZNhm6OocZ9plSe9eu0WRwT6e1oMTxAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:56.387549Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.7624","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24444d1781eda4afd1417f4272db3d986c528f2ebe53a28c5befeb0790ab2daf","sha256:47fb688a57d61e4bb00c6e7eeda3b8e946e5606177dcc0e7ebb87a323b511332"],"state_sha256":"5e8db36ad90914d3b90dd0630721114645f77592cb17999ca12bdccbe89fccab"}