{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:EWBTG26T2H6PREUKBIER3MJWZY","short_pith_number":"pith:EWBTG26T","canonical_record":{"source":{"id":"1312.4632","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.PR","submitted_at":"2013-12-17T04:03:56Z","cross_cats_sorted":[],"title_canon_sha256":"6761118f57fd9e5fc5c73f866f208570da124d13e24a8fecd116ec62c31d63eb","abstract_canon_sha256":"3f70c5954794dc81e4d777e6f908522236d168454607ac52d576246c34001049"},"schema_version":"1.0"},"canonical_sha256":"2583336bd3d1fcf8928a0a091db136ce1a44e2448ec9de20f3e44ddf0b18c3d7","source":{"kind":"arxiv","id":"1312.4632","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.4632","created_at":"2026-05-18T01:15:07Z"},{"alias_kind":"arxiv_version","alias_value":"1312.4632v2","created_at":"2026-05-18T01:15:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4632","created_at":"2026-05-18T01:15:07Z"},{"alias_kind":"pith_short_12","alias_value":"EWBTG26T2H6P","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EWBTG26T2H6PREUK","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EWBTG26T","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:EWBTG26T2H6PREUKBIER3MJWZY","target":"record","payload":{"canonical_record":{"source":{"id":"1312.4632","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.PR","submitted_at":"2013-12-17T04:03:56Z","cross_cats_sorted":[],"title_canon_sha256":"6761118f57fd9e5fc5c73f866f208570da124d13e24a8fecd116ec62c31d63eb","abstract_canon_sha256":"3f70c5954794dc81e4d777e6f908522236d168454607ac52d576246c34001049"},"schema_version":"1.0"},"canonical_sha256":"2583336bd3d1fcf8928a0a091db136ce1a44e2448ec9de20f3e44ddf0b18c3d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:07.178306Z","signature_b64":"Zpq1Zha9KOqdg7p8TzclNj6UJiCo16GSu5sRy/AoulxkEegzVTjc6It63kj/d+M/1vRJk6kO1R7PTxK6ZO5HBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2583336bd3d1fcf8928a0a091db136ce1a44e2448ec9de20f3e44ddf0b18c3d7","last_reissued_at":"2026-05-18T01:15:07.177681Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:07.177681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.4632","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:15:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kAs/pJBm8WsYZDU5S+uYuuDojfg2q8+lfSiuzaJ00K06quiP/jeX+AaPvwWRVqKdcP1PdhjzBsncJj40pdT3Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:47:32.484413Z"},"content_sha256":"e68e53a5862180759e441d187a0f1ac36b74948e81f7021b2add9fff92d7cf56","schema_version":"1.0","event_id":"sha256:e68e53a5862180759e441d187a0f1ac36b74948e81f7021b2add9fff92d7cf56"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:EWBTG26T2H6PREUKBIER3MJWZY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Time for Brownian Motion to Visit Every Point on a Circle","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Larry Shepp, Philip Ernst","submitted_at":"2013-12-17T04:03:56Z","abstract_excerpt":"Consider a Wiener process $W$ on a circle of circumference $L$. We prove the rather surprising result that the Laplace transform of the distribution of the first time, $\\theta_L$, when the Wiener process has visited every point of the circle can be solved in closed form using a continuous recurrence approach."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4632","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:15:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/6hS2z2Y7clMF2umsH5jqkrgajaxlTCE2VftCE49BVRhn9DjuAmk7sD2gbfrvWoQrKLgigyE27dL03BFzvWWAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:47:32.485095Z"},"content_sha256":"e5415acb31c7b39e9d4e28ed9b83ebcbf47cb101c63e5a831b3844a228560889","schema_version":"1.0","event_id":"sha256:e5415acb31c7b39e9d4e28ed9b83ebcbf47cb101c63e5a831b3844a228560889"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EWBTG26T2H6PREUKBIER3MJWZY/bundle.json","state_url":"https://pith.science/pith/EWBTG26T2H6PREUKBIER3MJWZY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EWBTG26T2H6PREUKBIER3MJWZY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T09:47:32Z","links":{"resolver":"https://pith.science/pith/EWBTG26T2H6PREUKBIER3MJWZY","bundle":"https://pith.science/pith/EWBTG26T2H6PREUKBIER3MJWZY/bundle.json","state":"https://pith.science/pith/EWBTG26T2H6PREUKBIER3MJWZY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EWBTG26T2H6PREUKBIER3MJWZY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EWBTG26T2H6PREUKBIER3MJWZY","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":"3f70c5954794dc81e4d777e6f908522236d168454607ac52d576246c34001049","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.PR","submitted_at":"2013-12-17T04:03:56Z","title_canon_sha256":"6761118f57fd9e5fc5c73f866f208570da124d13e24a8fecd116ec62c31d63eb"},"schema_version":"1.0","source":{"id":"1312.4632","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.4632","created_at":"2026-05-18T01:15:07Z"},{"alias_kind":"arxiv_version","alias_value":"1312.4632v2","created_at":"2026-05-18T01:15:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4632","created_at":"2026-05-18T01:15:07Z"},{"alias_kind":"pith_short_12","alias_value":"EWBTG26T2H6P","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EWBTG26T2H6PREUK","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EWBTG26T","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:e5415acb31c7b39e9d4e28ed9b83ebcbf47cb101c63e5a831b3844a228560889","target":"graph","created_at":"2026-05-18T01:15:07Z","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 Wiener process $W$ on a circle of circumference $L$. We prove the rather surprising result that the Laplace transform of the distribution of the first time, $\\theta_L$, when the Wiener process has visited every point of the circle can be solved in closed form using a continuous recurrence approach.","authors_text":"Larry Shepp, Philip Ernst","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.PR","submitted_at":"2013-12-17T04:03:56Z","title":"On the Time for Brownian Motion to Visit Every Point on a Circle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4632","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:e68e53a5862180759e441d187a0f1ac36b74948e81f7021b2add9fff92d7cf56","target":"record","created_at":"2026-05-18T01:15:07Z","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":"3f70c5954794dc81e4d777e6f908522236d168454607ac52d576246c34001049","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.PR","submitted_at":"2013-12-17T04:03:56Z","title_canon_sha256":"6761118f57fd9e5fc5c73f866f208570da124d13e24a8fecd116ec62c31d63eb"},"schema_version":"1.0","source":{"id":"1312.4632","kind":"arxiv","version":2}},"canonical_sha256":"2583336bd3d1fcf8928a0a091db136ce1a44e2448ec9de20f3e44ddf0b18c3d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2583336bd3d1fcf8928a0a091db136ce1a44e2448ec9de20f3e44ddf0b18c3d7","first_computed_at":"2026-05-18T01:15:07.177681Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:07.177681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zpq1Zha9KOqdg7p8TzclNj6UJiCo16GSu5sRy/AoulxkEegzVTjc6It63kj/d+M/1vRJk6kO1R7PTxK6ZO5HBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:07.178306Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.4632","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e68e53a5862180759e441d187a0f1ac36b74948e81f7021b2add9fff92d7cf56","sha256:e5415acb31c7b39e9d4e28ed9b83ebcbf47cb101c63e5a831b3844a228560889"],"state_sha256":"e867261b21b6b209599f463f57517725fbbcd5bd2459d57c2d66008da74156a6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZudEaMvZUTou7n2dZ/SODiYEjLxK3lXlimDJi6zJzPFl+AwdphImxm9fIIXep+cxMoGJEVGfsJpERLsFV0SkCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T09:47:32.489078Z","bundle_sha256":"de9098e59238fd6aacac24b9d678a463bbebbefce5b18a38221c5e66a617077a"}}