{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:OAD5FVJZ3YW6ATJVUQJY4JFGB7","short_pith_number":"pith:OAD5FVJZ","canonical_record":{"source":{"id":"1812.08355","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-20T04:10:21Z","cross_cats_sorted":[],"title_canon_sha256":"48761ad751b8f1b51cbaaddce7117a857895d79510a9e644a77f73adda618873","abstract_canon_sha256":"c6b99e0582486137ced0759c4873254f8af1c8f2e6f6039327d54f8acbfa36d6"},"schema_version":"1.0"},"canonical_sha256":"7007d2d539de2de04d35a4138e24a60fff2bfe89526f7d43f8c80d89b30cbbde","source":{"kind":"arxiv","id":"1812.08355","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.08355","created_at":"2026-05-17T23:57:51Z"},{"alias_kind":"arxiv_version","alias_value":"1812.08355v1","created_at":"2026-05-17T23:57:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.08355","created_at":"2026-05-17T23:57:51Z"},{"alias_kind":"pith_short_12","alias_value":"OAD5FVJZ3YW6","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OAD5FVJZ3YW6ATJV","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OAD5FVJZ","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:OAD5FVJZ3YW6ATJVUQJY4JFGB7","target":"record","payload":{"canonical_record":{"source":{"id":"1812.08355","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-20T04:10:21Z","cross_cats_sorted":[],"title_canon_sha256":"48761ad751b8f1b51cbaaddce7117a857895d79510a9e644a77f73adda618873","abstract_canon_sha256":"c6b99e0582486137ced0759c4873254f8af1c8f2e6f6039327d54f8acbfa36d6"},"schema_version":"1.0"},"canonical_sha256":"7007d2d539de2de04d35a4138e24a60fff2bfe89526f7d43f8c80d89b30cbbde","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:51.511910Z","signature_b64":"LkkXplZ/49BmlFNRlu0ZjlCibAOyyLL/mqpuCbVbOedjK4+bTWhPse/PQu8xFm0BKHmOqJ0qWfOLnHQpT7UjAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7007d2d539de2de04d35a4138e24a60fff2bfe89526f7d43f8c80d89b30cbbde","last_reissued_at":"2026-05-17T23:57:51.511185Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:51.511185Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.08355","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:57:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HSqSRDJiBBtsXpJIilzS/ElFgwcYe/XHd4n0UJ8Obj/6G3enXaQjtkPZx7dnbykLXDtYdfVhP0lbOb0+eBcQDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:11:34.717108Z"},"content_sha256":"250501fd11a7c85876a10939b76448cc91b77589eb5dc05b6e0ed3c2dc816b48","schema_version":"1.0","event_id":"sha256:250501fd11a7c85876a10939b76448cc91b77589eb5dc05b6e0ed3c2dc816b48"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:OAD5FVJZ3YW6ATJVUQJY4JFGB7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simultaneous boundary hitting by coupled reflected Brownian motions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Krzysztof Burdzy","submitted_at":"2018-12-20T04:10:21Z","abstract_excerpt":"(i) Uncountably many synchronized reflected Brownian motions can hit the boundary of a $C^2$ domain at the same time. (ii) Measures associated to local times of two synchronized reflected Brownian motions are mutually singular until the time when the normal vectors at the reflection locations become identical. (iii) Mirror coupled reflected Brownian motions can simultaneously hit opposite sides of a wedge at different distances from the origin."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08355","kind":"arxiv","version":1},"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":"2026-05-17T23:57:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CnoFjtpIa8G1w4ziZ8GwYlQ+6Pldn7+71+prAHTJAvkWHck8sw8tqK/D2mFfc8x9MkCoejkSWjISuhWSPcpXDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:11:34.717475Z"},"content_sha256":"ea7b6d16aeb3b0e1e609bb7fc78bb9f32bf015e25abe130a9182d97fc9516153","schema_version":"1.0","event_id":"sha256:ea7b6d16aeb3b0e1e609bb7fc78bb9f32bf015e25abe130a9182d97fc9516153"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OAD5FVJZ3YW6ATJVUQJY4JFGB7/bundle.json","state_url":"https://pith.science/pith/OAD5FVJZ3YW6ATJVUQJY4JFGB7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OAD5FVJZ3YW6ATJVUQJY4JFGB7/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":"2026-06-01T20:11:34Z","links":{"resolver":"https://pith.science/pith/OAD5FVJZ3YW6ATJVUQJY4JFGB7","bundle":"https://pith.science/pith/OAD5FVJZ3YW6ATJVUQJY4JFGB7/bundle.json","state":"https://pith.science/pith/OAD5FVJZ3YW6ATJVUQJY4JFGB7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OAD5FVJZ3YW6ATJVUQJY4JFGB7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OAD5FVJZ3YW6ATJVUQJY4JFGB7","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":"c6b99e0582486137ced0759c4873254f8af1c8f2e6f6039327d54f8acbfa36d6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-20T04:10:21Z","title_canon_sha256":"48761ad751b8f1b51cbaaddce7117a857895d79510a9e644a77f73adda618873"},"schema_version":"1.0","source":{"id":"1812.08355","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.08355","created_at":"2026-05-17T23:57:51Z"},{"alias_kind":"arxiv_version","alias_value":"1812.08355v1","created_at":"2026-05-17T23:57:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.08355","created_at":"2026-05-17T23:57:51Z"},{"alias_kind":"pith_short_12","alias_value":"OAD5FVJZ3YW6","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OAD5FVJZ3YW6ATJV","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OAD5FVJZ","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:ea7b6d16aeb3b0e1e609bb7fc78bb9f32bf015e25abe130a9182d97fc9516153","target":"graph","created_at":"2026-05-17T23:57:51Z","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":"(i) Uncountably many synchronized reflected Brownian motions can hit the boundary of a $C^2$ domain at the same time. (ii) Measures associated to local times of two synchronized reflected Brownian motions are mutually singular until the time when the normal vectors at the reflection locations become identical. (iii) Mirror coupled reflected Brownian motions can simultaneously hit opposite sides of a wedge at different distances from the origin.","authors_text":"Krzysztof Burdzy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-20T04:10:21Z","title":"Simultaneous boundary hitting by coupled reflected Brownian motions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08355","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":"sha256:250501fd11a7c85876a10939b76448cc91b77589eb5dc05b6e0ed3c2dc816b48","target":"record","created_at":"2026-05-17T23:57:51Z","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":"c6b99e0582486137ced0759c4873254f8af1c8f2e6f6039327d54f8acbfa36d6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-20T04:10:21Z","title_canon_sha256":"48761ad751b8f1b51cbaaddce7117a857895d79510a9e644a77f73adda618873"},"schema_version":"1.0","source":{"id":"1812.08355","kind":"arxiv","version":1}},"canonical_sha256":"7007d2d539de2de04d35a4138e24a60fff2bfe89526f7d43f8c80d89b30cbbde","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7007d2d539de2de04d35a4138e24a60fff2bfe89526f7d43f8c80d89b30cbbde","first_computed_at":"2026-05-17T23:57:51.511185Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:51.511185Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LkkXplZ/49BmlFNRlu0ZjlCibAOyyLL/mqpuCbVbOedjK4+bTWhPse/PQu8xFm0BKHmOqJ0qWfOLnHQpT7UjAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:51.511910Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.08355","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:250501fd11a7c85876a10939b76448cc91b77589eb5dc05b6e0ed3c2dc816b48","sha256:ea7b6d16aeb3b0e1e609bb7fc78bb9f32bf015e25abe130a9182d97fc9516153"],"state_sha256":"bc9162e08ab68da774522fd470236e5091b1a9968d05741263aa621e28f72d49"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"//UN7eHPfzKoKhfseZhI2rBmshK2xwcFfzN5XSt+GcrLAtI/RmBaaKkMs4kwTWD+8GIpQS9kAVRwrAWm7eMOBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T20:11:34.719387Z","bundle_sha256":"5c2f1e1bbfbb8bc6debd1606ce8551bc36d779ca67ecc6930d192441ddd702fa"}}