{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:KECMTHPG4PKPPLMULPX5QUBIG3","short_pith_number":"pith:KECMTHPG","canonical_record":{"source":{"id":"1005.1303","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-05-07T22:25:42Z","cross_cats_sorted":[],"title_canon_sha256":"e6cca38a487aa223f96742aec99d82b464e7c9edb99b66fc416cd0d080d771fe","abstract_canon_sha256":"ef247006c6bb5e46be86946f7e7a10d7b86cc501a8f947fe1acb77e533244414"},"schema_version":"1.0"},"canonical_sha256":"5104c99de6e3d4f7ad945befd8502836de1f368c9d7e6e5e9742fec0fcc1fb16","source":{"kind":"arxiv","id":"1005.1303","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.1303","created_at":"2026-05-18T04:23:35Z"},{"alias_kind":"arxiv_version","alias_value":"1005.1303v2","created_at":"2026-05-18T04:23:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.1303","created_at":"2026-05-18T04:23:35Z"},{"alias_kind":"pith_short_12","alias_value":"KECMTHPG4PKP","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KECMTHPG4PKPPLMU","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KECMTHPG","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:KECMTHPG4PKPPLMULPX5QUBIG3","target":"record","payload":{"canonical_record":{"source":{"id":"1005.1303","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-05-07T22:25:42Z","cross_cats_sorted":[],"title_canon_sha256":"e6cca38a487aa223f96742aec99d82b464e7c9edb99b66fc416cd0d080d771fe","abstract_canon_sha256":"ef247006c6bb5e46be86946f7e7a10d7b86cc501a8f947fe1acb77e533244414"},"schema_version":"1.0"},"canonical_sha256":"5104c99de6e3d4f7ad945befd8502836de1f368c9d7e6e5e9742fec0fcc1fb16","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:35.223828Z","signature_b64":"DutB5CftcX/af8ntL4H3Wov8JIrO279R7aXf2tsZ9kp1UMDo83L7NtyJOoow3I5uqKxm2NRX8tv+rnuvC8BjBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5104c99de6e3d4f7ad945befd8502836de1f368c9d7e6e5e9742fec0fcc1fb16","last_reissued_at":"2026-05-18T04:23:35.223118Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:35.223118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.1303","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":"2026-05-18T04:23:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pIfl2X4KXYBCMC+E8whg6E3vA8zEgWLwaNsixD4jvrdBn1og8RY2MKRoIDJSLkm8jJQsl5mVmkfZxOefl/QsBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:37:25.584481Z"},"content_sha256":"22b44daf04895dfdc714d50f7b96dcc7b1549675bab074400048933f3f8f0a13","schema_version":"1.0","event_id":"sha256:22b44daf04895dfdc714d50f7b96dcc7b1549675bab074400048933f3f8f0a13"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:KECMTHPG4PKPPLMULPX5QUBIG3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-intersecting Brownian motions leaving from and going to several points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Didier Vanderstichelen, Mark Adler, Pierre van Moerbeke","submitted_at":"2010-05-07T22:25:42Z","abstract_excerpt":"Consider n non-intersecting Brownian motions on $\\mathbb{R}$, depending on time $t \\in [0,1]$, with $m_i$ particles forced to leave from $a_i$ at time $t=0$, $1\\leq i\\leq q$, and $n_j$ particles forced to end up at $b_j$ at time $t=1$, $1\\leq j\\leq p$. For arbitrary $p$ and $q$, it is not known if the distribution of the positions of the non-intersecting Brownian particles at a given time $0<t<1$, is the same as the joint distribution of the eigenvalues of a matrix ensemble. This paper proves the existence, for general $p$ and $q$, of a partial differential equation (PDE) satisfied by the log "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.1303","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":"2026-05-18T04:23:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0qQT1bk9Xbwbh2ttVtY46qDoS7Ed2M6AMlkppEF6MW3JqkecIelhUSigJKuYJAA+2agMSYc2F+Uw7kqE2McpAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:37:25.584829Z"},"content_sha256":"15ca4802292c5671b1fa984208db49cf27f70ef1a2ea63fa9aefd80c938ae1e4","schema_version":"1.0","event_id":"sha256:15ca4802292c5671b1fa984208db49cf27f70ef1a2ea63fa9aefd80c938ae1e4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KECMTHPG4PKPPLMULPX5QUBIG3/bundle.json","state_url":"https://pith.science/pith/KECMTHPG4PKPPLMULPX5QUBIG3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KECMTHPG4PKPPLMULPX5QUBIG3/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":"2026-06-03T06:37:25Z","links":{"resolver":"https://pith.science/pith/KECMTHPG4PKPPLMULPX5QUBIG3","bundle":"https://pith.science/pith/KECMTHPG4PKPPLMULPX5QUBIG3/bundle.json","state":"https://pith.science/pith/KECMTHPG4PKPPLMULPX5QUBIG3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KECMTHPG4PKPPLMULPX5QUBIG3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KECMTHPG4PKPPLMULPX5QUBIG3","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":"ef247006c6bb5e46be86946f7e7a10d7b86cc501a8f947fe1acb77e533244414","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-05-07T22:25:42Z","title_canon_sha256":"e6cca38a487aa223f96742aec99d82b464e7c9edb99b66fc416cd0d080d771fe"},"schema_version":"1.0","source":{"id":"1005.1303","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.1303","created_at":"2026-05-18T04:23:35Z"},{"alias_kind":"arxiv_version","alias_value":"1005.1303v2","created_at":"2026-05-18T04:23:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.1303","created_at":"2026-05-18T04:23:35Z"},{"alias_kind":"pith_short_12","alias_value":"KECMTHPG4PKP","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KECMTHPG4PKPPLMU","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KECMTHPG","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:15ca4802292c5671b1fa984208db49cf27f70ef1a2ea63fa9aefd80c938ae1e4","target":"graph","created_at":"2026-05-18T04:23:35Z","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 n non-intersecting Brownian motions on $\\mathbb{R}$, depending on time $t \\in [0,1]$, with $m_i$ particles forced to leave from $a_i$ at time $t=0$, $1\\leq i\\leq q$, and $n_j$ particles forced to end up at $b_j$ at time $t=1$, $1\\leq j\\leq p$. For arbitrary $p$ and $q$, it is not known if the distribution of the positions of the non-intersecting Brownian particles at a given time $0<t<1$, is the same as the joint distribution of the eigenvalues of a matrix ensemble. This paper proves the existence, for general $p$ and $q$, of a partial differential equation (PDE) satisfied by the log ","authors_text":"Didier Vanderstichelen, Mark Adler, Pierre van Moerbeke","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-05-07T22:25:42Z","title":"Non-intersecting Brownian motions leaving from and going to several points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.1303","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":"sha256:22b44daf04895dfdc714d50f7b96dcc7b1549675bab074400048933f3f8f0a13","target":"record","created_at":"2026-05-18T04:23:35Z","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":"ef247006c6bb5e46be86946f7e7a10d7b86cc501a8f947fe1acb77e533244414","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-05-07T22:25:42Z","title_canon_sha256":"e6cca38a487aa223f96742aec99d82b464e7c9edb99b66fc416cd0d080d771fe"},"schema_version":"1.0","source":{"id":"1005.1303","kind":"arxiv","version":2}},"canonical_sha256":"5104c99de6e3d4f7ad945befd8502836de1f368c9d7e6e5e9742fec0fcc1fb16","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5104c99de6e3d4f7ad945befd8502836de1f368c9d7e6e5e9742fec0fcc1fb16","first_computed_at":"2026-05-18T04:23:35.223118Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:35.223118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DutB5CftcX/af8ntL4H3Wov8JIrO279R7aXf2tsZ9kp1UMDo83L7NtyJOoow3I5uqKxm2NRX8tv+rnuvC8BjBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:35.223828Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.1303","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22b44daf04895dfdc714d50f7b96dcc7b1549675bab074400048933f3f8f0a13","sha256:15ca4802292c5671b1fa984208db49cf27f70ef1a2ea63fa9aefd80c938ae1e4"],"state_sha256":"ecf8858fb553e4e9d319d82fe7cdfea2a0b0942fb8885976cec85fc2f6f56ccb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YT26M57R7r4SJKjw1hmNRH3RmzKOGFl//Hlpy5ghifp7Ut5NSlZbtU+aYnlFRKq/HWTVAaIpZCYLm1iERBwHAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T06:37:25.586759Z","bundle_sha256":"feafddab9f4c1c749d825cea6ed2635105f7b21ce1b743162671e97952f499d7"}}