{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:GAFOI6HBBQEJ3P77UNT4HYT6NR","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":"39c5d09bbed40ff96fddc24171bc58f37619ee331863490505fb8aeb7a6e3e96","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2007-11-05T13:16:28Z","title_canon_sha256":"142b7800e426c892cfcf0d369e310c6ae5b4af08710da86311edfdbc5f410071"},"schema_version":"1.0","source":{"id":"0711.0631","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0711.0631","created_at":"2026-05-17T23:45:57Z"},{"alias_kind":"arxiv_version","alias_value":"0711.0631v1","created_at":"2026-05-17T23:45:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.0631","created_at":"2026-05-17T23:45:57Z"},{"alias_kind":"pith_short_12","alias_value":"GAFOI6HBBQEJ","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"GAFOI6HBBQEJ3P77","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"GAFOI6HB","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:34602e987f301ffc5843d9dcb28a2ef588330e4f3a0c569d8c90d23cf1f3f9a9","target":"graph","created_at":"2026-05-17T23:45:57Z","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":"Let B(t), X(t) and Y(t) be independent standard 1d Borwnian motions. Define X^+(t) and Y^-(t) as the trajectories of the processes X(t) and Y(t) pushed upwards and, respectively, downwards by B(t), according to Skorohod-reflection. In a recent paper, Jon Warren proves inter alia that Z(t):= X^+(t)-Y^-(t) is a three-dimensional Bessel-process. In this note, we present an alternative, elementary proof of this fact.","authors_text":"Balint Toth, Balint Veto","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2007-11-05T13:16:28Z","title":"Skorohod-reflection of Brownian Paths and BES^3"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.0631","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":"sha256:4f94cf5e6ae850a6f91840f4fd4a426d2d65d6951a14e540a7f79f5511c09880","target":"record","created_at":"2026-05-17T23:45:57Z","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":"39c5d09bbed40ff96fddc24171bc58f37619ee331863490505fb8aeb7a6e3e96","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2007-11-05T13:16:28Z","title_canon_sha256":"142b7800e426c892cfcf0d369e310c6ae5b4af08710da86311edfdbc5f410071"},"schema_version":"1.0","source":{"id":"0711.0631","kind":"arxiv","version":1}},"canonical_sha256":"300ae478e10c089dbfffa367c3e27e6c4555cfbe1e84e32397de4aa5b523f88b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"300ae478e10c089dbfffa367c3e27e6c4555cfbe1e84e32397de4aa5b523f88b","first_computed_at":"2026-05-17T23:45:57.159386Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:57.159386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S3cSkHoOjkWIwMvdSBJM4m4klIAhYlDy/datlpkm1GI3dhYxxFCNLNv4CTvlNItQNRcto1X4JESONbh/WU16CQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:57.159852Z","signed_message":"canonical_sha256_bytes"},"source_id":"0711.0631","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f94cf5e6ae850a6f91840f4fd4a426d2d65d6951a14e540a7f79f5511c09880","sha256:34602e987f301ffc5843d9dcb28a2ef588330e4f3a0c569d8c90d23cf1f3f9a9"],"state_sha256":"42340a3d2c5a354a74cb0ba1d45d861fd6d472666f4e076d3db076eb2c5e4d12"}