{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:U2HDZSPX4G27WXGUVCLZHCUVDU","short_pith_number":"pith:U2HDZSPX","canonical_record":{"source":{"id":"1512.02323","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-08T04:35:40Z","cross_cats_sorted":[],"title_canon_sha256":"d9b5c3fb6e77aa61507764322e16ed9b5b406db9dcc0887e0b73c905d4c5249e","abstract_canon_sha256":"f97c3a6046e565a867d6be6ba4c0fd4e042e53de0de8a30d82e9f23db388db59"},"schema_version":"1.0"},"canonical_sha256":"a68e3cc9f7e1b5fb5cd4a897938a951d13dd546a27f3dfb9e855837953e8612c","source":{"kind":"arxiv","id":"1512.02323","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.02323","created_at":"2026-05-18T01:24:45Z"},{"alias_kind":"arxiv_version","alias_value":"1512.02323v1","created_at":"2026-05-18T01:24:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02323","created_at":"2026-05-18T01:24:45Z"},{"alias_kind":"pith_short_12","alias_value":"U2HDZSPX4G27","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"U2HDZSPX4G27WXGU","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"U2HDZSPX","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:U2HDZSPX4G27WXGUVCLZHCUVDU","target":"record","payload":{"canonical_record":{"source":{"id":"1512.02323","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-08T04:35:40Z","cross_cats_sorted":[],"title_canon_sha256":"d9b5c3fb6e77aa61507764322e16ed9b5b406db9dcc0887e0b73c905d4c5249e","abstract_canon_sha256":"f97c3a6046e565a867d6be6ba4c0fd4e042e53de0de8a30d82e9f23db388db59"},"schema_version":"1.0"},"canonical_sha256":"a68e3cc9f7e1b5fb5cd4a897938a951d13dd546a27f3dfb9e855837953e8612c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:45.007073Z","signature_b64":"yPqu7EiVkvqLeV2pzuLsIoRgw6wpzifiVOvgPQ6CD0w+gvPZ5KHb+o9mN/jy3tfvsj8qZPVBR7t2wXOBUVPgBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a68e3cc9f7e1b5fb5cd4a897938a951d13dd546a27f3dfb9e855837953e8612c","last_reissued_at":"2026-05-18T01:24:45.006432Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:45.006432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.02323","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":"2026-05-18T01:24:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hqDbJ0Bw1UIg81wHdvrUIBzLUTDFhFojtLefkrF6SsQWs48uRS7Wyb9jNcqFpiFNa0/lQGtfyXrTAzLXaF4WBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T04:12:04.185807Z"},"content_sha256":"4768946f6b850eb30a83aa7df02456d5330a381d12a00b41ed7e7882f2c0825a","schema_version":"1.0","event_id":"sha256:4768946f6b850eb30a83aa7df02456d5330a381d12a00b41ed7e7882f2c0825a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:U2HDZSPX4G27WXGUVCLZHCUVDU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Obliquely reflected Brownian motion in non-smooth planar domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Donald Marshall, Kavita Ramanan, Krzysztof Burdzy, Zhen-Qing Chen","submitted_at":"2015-12-08T04:35:40Z","abstract_excerpt":"We construct obliquely reflected Brownian motions in all bounded simply connected planar domains, including non-smooth domains, with general reflection vector fields on the boundary. Conformal mappings and excursion theory are our main technical tools. A key intermediate step, which may be of independent interest, is an alternative characterization of reflected Brownian motions in smooth bounded planar domains with a given field of angles of oblique reflection on the boundary in terms of a pair of quantities, namely an integrable positive harmonic function, which represents the stationary dist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02323","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":"2026-05-18T01:24:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M5cF2tHtzHppzZVBT+gXqQ3c0NGi90QNoAcpD8Aqi2Gr+ZZXDYjpUmucTf7thGE9qztam22onPM5JZAWuJqTCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T04:12:04.186149Z"},"content_sha256":"40de08ba92f027fb81d1251e0816b24e8b1434b9d9f4ed51c2264fb0c16cc02c","schema_version":"1.0","event_id":"sha256:40de08ba92f027fb81d1251e0816b24e8b1434b9d9f4ed51c2264fb0c16cc02c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U2HDZSPX4G27WXGUVCLZHCUVDU/bundle.json","state_url":"https://pith.science/pith/U2HDZSPX4G27WXGUVCLZHCUVDU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U2HDZSPX4G27WXGUVCLZHCUVDU/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":"2026-05-20T04:12:04Z","links":{"resolver":"https://pith.science/pith/U2HDZSPX4G27WXGUVCLZHCUVDU","bundle":"https://pith.science/pith/U2HDZSPX4G27WXGUVCLZHCUVDU/bundle.json","state":"https://pith.science/pith/U2HDZSPX4G27WXGUVCLZHCUVDU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U2HDZSPX4G27WXGUVCLZHCUVDU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:U2HDZSPX4G27WXGUVCLZHCUVDU","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":"f97c3a6046e565a867d6be6ba4c0fd4e042e53de0de8a30d82e9f23db388db59","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-08T04:35:40Z","title_canon_sha256":"d9b5c3fb6e77aa61507764322e16ed9b5b406db9dcc0887e0b73c905d4c5249e"},"schema_version":"1.0","source":{"id":"1512.02323","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.02323","created_at":"2026-05-18T01:24:45Z"},{"alias_kind":"arxiv_version","alias_value":"1512.02323v1","created_at":"2026-05-18T01:24:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02323","created_at":"2026-05-18T01:24:45Z"},{"alias_kind":"pith_short_12","alias_value":"U2HDZSPX4G27","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"U2HDZSPX4G27WXGU","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"U2HDZSPX","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:40de08ba92f027fb81d1251e0816b24e8b1434b9d9f4ed51c2264fb0c16cc02c","target":"graph","created_at":"2026-05-18T01:24:45Z","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":"We construct obliquely reflected Brownian motions in all bounded simply connected planar domains, including non-smooth domains, with general reflection vector fields on the boundary. Conformal mappings and excursion theory are our main technical tools. A key intermediate step, which may be of independent interest, is an alternative characterization of reflected Brownian motions in smooth bounded planar domains with a given field of angles of oblique reflection on the boundary in terms of a pair of quantities, namely an integrable positive harmonic function, which represents the stationary dist","authors_text":"Donald Marshall, Kavita Ramanan, Krzysztof Burdzy, Zhen-Qing Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-08T04:35:40Z","title":"Obliquely reflected Brownian motion in non-smooth planar domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02323","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":"sha256:4768946f6b850eb30a83aa7df02456d5330a381d12a00b41ed7e7882f2c0825a","target":"record","created_at":"2026-05-18T01:24:45Z","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":"f97c3a6046e565a867d6be6ba4c0fd4e042e53de0de8a30d82e9f23db388db59","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-08T04:35:40Z","title_canon_sha256":"d9b5c3fb6e77aa61507764322e16ed9b5b406db9dcc0887e0b73c905d4c5249e"},"schema_version":"1.0","source":{"id":"1512.02323","kind":"arxiv","version":1}},"canonical_sha256":"a68e3cc9f7e1b5fb5cd4a897938a951d13dd546a27f3dfb9e855837953e8612c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a68e3cc9f7e1b5fb5cd4a897938a951d13dd546a27f3dfb9e855837953e8612c","first_computed_at":"2026-05-18T01:24:45.006432Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:45.006432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yPqu7EiVkvqLeV2pzuLsIoRgw6wpzifiVOvgPQ6CD0w+gvPZ5KHb+o9mN/jy3tfvsj8qZPVBR7t2wXOBUVPgBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:45.007073Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.02323","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4768946f6b850eb30a83aa7df02456d5330a381d12a00b41ed7e7882f2c0825a","sha256:40de08ba92f027fb81d1251e0816b24e8b1434b9d9f4ed51c2264fb0c16cc02c"],"state_sha256":"849290e9900a8d7d080297f423e1ce719858ecf8b31b2d330c9dfbeded313ef5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GSTCilDzfN0ct19Fa6ETIdy0YnWAHDaW1IrFpZNkzJNyP2z6qCAYI9Y4u1EuE0fKDktr3qsn7cYU8fa/8URYAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T04:12:04.188396Z","bundle_sha256":"246ba10d50292af3a61741c67bcd2e33b0cb11eb47fc5529d4c855caef426f57"}}