{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LVGFZUXOIOY33FQRLKSAEU6GGO","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":"21ceb83ab9700f2afa0aec5d032f530031005df4fb3154e225f0a720e4e1e27c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-18T15:24:28Z","title_canon_sha256":"fd9870f04cb4339f4a86a15a7c3d426d85cc8ea137b245506f0e3e7e0c299c1b"},"schema_version":"1.0","source":{"id":"1704.05394","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05394","created_at":"2026-05-18T00:16:23Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05394v2","created_at":"2026-05-18T00:16:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05394","created_at":"2026-05-18T00:16:23Z"},{"alias_kind":"pith_short_12","alias_value":"LVGFZUXOIOY3","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LVGFZUXOIOY33FQR","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LVGFZUXO","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:5880b012705569adefdcf789c0635b3c758e0350cd9c647ae7c151cd091e46a0","target":"graph","created_at":"2026-05-18T00:16:23Z","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":"Consider a negatively drifted one dimensional Brownian motion starting at positive initial position, its first hitting time to 0 has the inverse Gaussian law. Moreover, conditionally on this hitting time, the Brownian motion up to that time has the law of a 3- dimensional Bessel bridge. In this paper, we give a generalization of this result to a family of Brownian motions with interacting drifts, indexed by the vertices of a conductance network. The hitting times are equal in law to the inverse of a random potential that appears in the analysis of a self-interacting process called the Vertex R","authors_text":"Christophe Sabot, Xiaolin Zeng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-18T15:24:28Z","title":"Hitting times of interacting drifted Brownian motions and the vertex reinforced jump process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05394","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":"sha256:577ad37b6bed405d27c46e1d9d37de16b83a5d9e05df49ee23b0652b3ef5baa6","target":"record","created_at":"2026-05-18T00:16:23Z","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":"21ceb83ab9700f2afa0aec5d032f530031005df4fb3154e225f0a720e4e1e27c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-18T15:24:28Z","title_canon_sha256":"fd9870f04cb4339f4a86a15a7c3d426d85cc8ea137b245506f0e3e7e0c299c1b"},"schema_version":"1.0","source":{"id":"1704.05394","kind":"arxiv","version":2}},"canonical_sha256":"5d4c5cd2ee43b1bd96115aa40253c6338ca05e993882ed3e3af42dd5c5fe20fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d4c5cd2ee43b1bd96115aa40253c6338ca05e993882ed3e3af42dd5c5fe20fe","first_computed_at":"2026-05-18T00:16:23.860073Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:23.860073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XdU3FZgDlMganRR1WgLlZf0/s9W3NwU5uuZ3rrhrcvG5j1FsNcezFsTCBqo4FLDdVUmSe+EilaswQc9M1L6fCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:23.860636Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.05394","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:577ad37b6bed405d27c46e1d9d37de16b83a5d9e05df49ee23b0652b3ef5baa6","sha256:5880b012705569adefdcf789c0635b3c758e0350cd9c647ae7c151cd091e46a0"],"state_sha256":"29a1d864fc930a106979559c170e7ab6620465cefb4c3c53e49aa8c57d194928"}