{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:VNZ6XXVED6EVVJAXMTOKYSP7WC","short_pith_number":"pith:VNZ6XXVE","canonical_record":{"source":{"id":"1707.09915","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-31T15:16:14Z","cross_cats_sorted":[],"title_canon_sha256":"797ee0dfcbaf615ef482a29b664c4d160d74f8192607ab946d2b1abfeecd6464","abstract_canon_sha256":"6a09f7eddb789fc730d55a7efb1d90d74dc57f1ba9800dc5ecc0b1265afcfd3d"},"schema_version":"1.0"},"canonical_sha256":"ab73ebdea41f895aa41764dcac49ffb08eed095b92e0d60ea4e54e28b17372a5","source":{"kind":"arxiv","id":"1707.09915","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.09915","created_at":"2026-05-18T00:35:03Z"},{"alias_kind":"arxiv_version","alias_value":"1707.09915v2","created_at":"2026-05-18T00:35:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.09915","created_at":"2026-05-18T00:35:03Z"},{"alias_kind":"pith_short_12","alias_value":"VNZ6XXVED6EV","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VNZ6XXVED6EVVJAX","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VNZ6XXVE","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:VNZ6XXVED6EVVJAXMTOKYSP7WC","target":"record","payload":{"canonical_record":{"source":{"id":"1707.09915","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-31T15:16:14Z","cross_cats_sorted":[],"title_canon_sha256":"797ee0dfcbaf615ef482a29b664c4d160d74f8192607ab946d2b1abfeecd6464","abstract_canon_sha256":"6a09f7eddb789fc730d55a7efb1d90d74dc57f1ba9800dc5ecc0b1265afcfd3d"},"schema_version":"1.0"},"canonical_sha256":"ab73ebdea41f895aa41764dcac49ffb08eed095b92e0d60ea4e54e28b17372a5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:03.711935Z","signature_b64":"RjIlBkN0hyOSJgK9ZYOk7pmEg6p5vppEHKBOWxkzpBccZgL6Po36eW02hfLLLSZyBScdnPfuDtF6iiXhVWlIDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab73ebdea41f895aa41764dcac49ffb08eed095b92e0d60ea4e54e28b17372a5","last_reissued_at":"2026-05-18T00:35:03.711201Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:03.711201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.09915","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":"2026-05-18T00:35:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CsKRQCGL66Lym+3bQYVBo56jMo0/hcTMcZBcjx8znwtz3AXbAD/NzZyC7Va3QaJtXoPRX9BKbiyYykDcKMhLCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:31:12.172231Z"},"content_sha256":"263c2349e326e48157c06652e2a34397b238127c4223895e50ce720d42acd09a","schema_version":"1.0","event_id":"sha256:263c2349e326e48157c06652e2a34397b238127c4223895e50ce720d42acd09a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:VNZ6XXVED6EVVJAXMTOKYSP7WC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A matrix Bougerol identity and the Hua-Pickrell measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Theodoros Assiotis","submitted_at":"2017-07-31T15:16:14Z","abstract_excerpt":"We prove a Hermitian matrix version of Bougerol's identity. Moreover, we construct the Hua-Pickrell measures on Hermitian matrices, as stochastic integrals with respect to a drifting Hermitian Brownian motion and with an integrand involving a conjugation by an independent, matrix analogue of the exponential of a complex Brownian motion with drift."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.09915","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":"2026-05-18T00:35:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4T08oW6nCUjfGOSLTGgJb+0KEgjEQQ2Hs2b3xZTOQ+LFHObIVgODd5x4KXHu1oEvp0TLQY8y0tV9VWdS/v2hBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:31:12.172609Z"},"content_sha256":"19bbcca528a7a31056f98404a585bf26512b2095da5aac603594b354c66be65f","schema_version":"1.0","event_id":"sha256:19bbcca528a7a31056f98404a585bf26512b2095da5aac603594b354c66be65f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VNZ6XXVED6EVVJAXMTOKYSP7WC/bundle.json","state_url":"https://pith.science/pith/VNZ6XXVED6EVVJAXMTOKYSP7WC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VNZ6XXVED6EVVJAXMTOKYSP7WC/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":"2026-06-01T10:31:12Z","links":{"resolver":"https://pith.science/pith/VNZ6XXVED6EVVJAXMTOKYSP7WC","bundle":"https://pith.science/pith/VNZ6XXVED6EVVJAXMTOKYSP7WC/bundle.json","state":"https://pith.science/pith/VNZ6XXVED6EVVJAXMTOKYSP7WC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VNZ6XXVED6EVVJAXMTOKYSP7WC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VNZ6XXVED6EVVJAXMTOKYSP7WC","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":"6a09f7eddb789fc730d55a7efb1d90d74dc57f1ba9800dc5ecc0b1265afcfd3d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-31T15:16:14Z","title_canon_sha256":"797ee0dfcbaf615ef482a29b664c4d160d74f8192607ab946d2b1abfeecd6464"},"schema_version":"1.0","source":{"id":"1707.09915","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.09915","created_at":"2026-05-18T00:35:03Z"},{"alias_kind":"arxiv_version","alias_value":"1707.09915v2","created_at":"2026-05-18T00:35:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.09915","created_at":"2026-05-18T00:35:03Z"},{"alias_kind":"pith_short_12","alias_value":"VNZ6XXVED6EV","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VNZ6XXVED6EVVJAX","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VNZ6XXVE","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:19bbcca528a7a31056f98404a585bf26512b2095da5aac603594b354c66be65f","target":"graph","created_at":"2026-05-18T00:35:03Z","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 prove a Hermitian matrix version of Bougerol's identity. Moreover, we construct the Hua-Pickrell measures on Hermitian matrices, as stochastic integrals with respect to a drifting Hermitian Brownian motion and with an integrand involving a conjugation by an independent, matrix analogue of the exponential of a complex Brownian motion with drift.","authors_text":"Theodoros Assiotis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-31T15:16:14Z","title":"A matrix Bougerol identity and the Hua-Pickrell measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.09915","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":"sha256:263c2349e326e48157c06652e2a34397b238127c4223895e50ce720d42acd09a","target":"record","created_at":"2026-05-18T00:35:03Z","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":"6a09f7eddb789fc730d55a7efb1d90d74dc57f1ba9800dc5ecc0b1265afcfd3d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-31T15:16:14Z","title_canon_sha256":"797ee0dfcbaf615ef482a29b664c4d160d74f8192607ab946d2b1abfeecd6464"},"schema_version":"1.0","source":{"id":"1707.09915","kind":"arxiv","version":2}},"canonical_sha256":"ab73ebdea41f895aa41764dcac49ffb08eed095b92e0d60ea4e54e28b17372a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab73ebdea41f895aa41764dcac49ffb08eed095b92e0d60ea4e54e28b17372a5","first_computed_at":"2026-05-18T00:35:03.711201Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:03.711201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RjIlBkN0hyOSJgK9ZYOk7pmEg6p5vppEHKBOWxkzpBccZgL6Po36eW02hfLLLSZyBScdnPfuDtF6iiXhVWlIDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:03.711935Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.09915","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:263c2349e326e48157c06652e2a34397b238127c4223895e50ce720d42acd09a","sha256:19bbcca528a7a31056f98404a585bf26512b2095da5aac603594b354c66be65f"],"state_sha256":"61def5319feab3afc0f2d6a5e881216314ffb468c9dc4fabbbc8acdbd8448379"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HmSCHCxD79oK0++BXn1xLZg+kJpIZzPmosTioq5rnkhx41UhK1AjYkzO/u9e/Iufi5ms/TUEzK6ij18hgQl2CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T10:31:12.174520Z","bundle_sha256":"80ef0c6f64f6868f735ce3bf58b83f25c4cebd36c705646f97a6bfa0ceb1ce3b"}}