{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IQ5FZTZBO45EBFRYDR52UGAOPV","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":"8916c85d7f9620c0308420b1206fbb3339d7b983ba0f46e73fa3c7ea9c918baf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-28T09:58:40Z","title_canon_sha256":"80bbd3b8b76b5a227c1ba61eca7c2abf0fcdc9715974a80bac37dbc3f8b18416"},"schema_version":"1.0","source":{"id":"1302.7128","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.7128","created_at":"2026-05-18T03:32:16Z"},{"alias_kind":"arxiv_version","alias_value":"1302.7128v1","created_at":"2026-05-18T03:32:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.7128","created_at":"2026-05-18T03:32:16Z"},{"alias_kind":"pith_short_12","alias_value":"IQ5FZTZBO45E","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IQ5FZTZBO45EBFRY","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IQ5FZTZB","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:b3e0134b113bd38fa14e770d798a7e0204a886e47c80ad68676092da3b2bb6d1","target":"graph","created_at":"2026-05-18T03:32:16Z","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":"Given a deterministically time-changed Brownian motion $Z$ starting from 1, whose time-change $V(t)$ satisfies $V(t) > t$ for all $t > 0$, we perform an explicit construction of a process $X$ which is Brownian motion in its own filtration and that hits zero for the first time at $V(\\tau)$, where $\\tau := \\inf\\{t>0: Z_t =0\\}$. We also provide the semimartingale decomposition of $X$ under the filtration jointly generated by $X$ and $Z$. Our construction relies on a combination of enlargement of filtration and filtering techniques. The resulting process $X$ may be viewed as the analogue of a 3-di","authors_text":"Albina Danilova, Luciano Campi, Umut \\c{C}etin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-28T09:58:40Z","title":"Explicit construction of a dynamic Bessel bridge of dimension 3"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.7128","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":"sha256:14dabfb6c5b30869d145e592079504f33c6bb68baf9cc2fe4266d2b1c5cb56d9","target":"record","created_at":"2026-05-18T03:32:16Z","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":"8916c85d7f9620c0308420b1206fbb3339d7b983ba0f46e73fa3c7ea9c918baf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-28T09:58:40Z","title_canon_sha256":"80bbd3b8b76b5a227c1ba61eca7c2abf0fcdc9715974a80bac37dbc3f8b18416"},"schema_version":"1.0","source":{"id":"1302.7128","kind":"arxiv","version":1}},"canonical_sha256":"443a5ccf21773a4096381c7baa180e7d7a80c903e3e93c9253bdc7694b63ed1d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"443a5ccf21773a4096381c7baa180e7d7a80c903e3e93c9253bdc7694b63ed1d","first_computed_at":"2026-05-18T03:32:16.624121Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:16.624121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EyZPbNAwQ3kBeINNpnlEbBgx8AMpaVwE++O3D/aNhTXuVVSh14HAI8uAAPteH/+DwuvO5s2eY+m2RY5q5TAVBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:16.624670Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.7128","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14dabfb6c5b30869d145e592079504f33c6bb68baf9cc2fe4266d2b1c5cb56d9","sha256:b3e0134b113bd38fa14e770d798a7e0204a886e47c80ad68676092da3b2bb6d1"],"state_sha256":"d0776e04ee7098501e72abe789e72d3d6eaa5b8749bf5f4d18d4a256660373d1"}