{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:4YZHP6MYN3FCJ57WQSOJUPFNC4","short_pith_number":"pith:4YZHP6MY","canonical_record":{"source":{"id":"1007.0220","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-01T17:15:58Z","cross_cats_sorted":[],"title_canon_sha256":"fa2bbf6002e4ea82d5eb50a30c8f99fa5c5c535bc1d0ea5e2aced8a67da2d85f","abstract_canon_sha256":"501615ce0e3e7f076213c2f7b6c002799db7bc787c23dd9bc579c5213bf1f392"},"schema_version":"1.0"},"canonical_sha256":"e63277f9986eca24f7f6849c9a3cad173ea185c4e41fcbc395290bbddffe7780","source":{"kind":"arxiv","id":"1007.0220","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.0220","created_at":"2026-05-18T03:40:14Z"},{"alias_kind":"arxiv_version","alias_value":"1007.0220v3","created_at":"2026-05-18T03:40:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0220","created_at":"2026-05-18T03:40:14Z"},{"alias_kind":"pith_short_12","alias_value":"4YZHP6MYN3FC","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"4YZHP6MYN3FCJ57W","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"4YZHP6MY","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:4YZHP6MYN3FCJ57WQSOJUPFNC4","target":"record","payload":{"canonical_record":{"source":{"id":"1007.0220","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-01T17:15:58Z","cross_cats_sorted":[],"title_canon_sha256":"fa2bbf6002e4ea82d5eb50a30c8f99fa5c5c535bc1d0ea5e2aced8a67da2d85f","abstract_canon_sha256":"501615ce0e3e7f076213c2f7b6c002799db7bc787c23dd9bc579c5213bf1f392"},"schema_version":"1.0"},"canonical_sha256":"e63277f9986eca24f7f6849c9a3cad173ea185c4e41fcbc395290bbddffe7780","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:14.672776Z","signature_b64":"L95Ayeq6hCBzBO0Z9aOsIsEV01fRYrJNi3jFT/g2fNfz312sOlgUaFa0rSzcXG0PBPOOko7bcv861T6RmXHFDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e63277f9986eca24f7f6849c9a3cad173ea185c4e41fcbc395290bbddffe7780","last_reissued_at":"2026-05-18T03:40:14.672221Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:14.672221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.0220","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:40:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lpaa2povzP+MhyplQpH0gTBDZeRULiQYrrapMv4NeYf2xo15X5CXNjQ57UEK/CwgkUiZS+eVvayt9nzbGp1qCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:35:03.082447Z"},"content_sha256":"ef6ee175d1c122f15093f72afc3199d22bdd8544d534268c54c1866b31a44b39","schema_version":"1.0","event_id":"sha256:ef6ee175d1c122f15093f72afc3199d22bdd8544d534268c54c1866b31a44b39"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:4YZHP6MYN3FCJ57WQSOJUPFNC4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Consecutive Minors for Dyson's Brownian Motions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eric Nordenstam, Mark Adler, Pierre van Moerbeke","submitted_at":"2010-07-01T17:15:58Z","abstract_excerpt":"In 1962, Dyson introduced dynamics in random matrix models, in particular into GUE (also for beta=1 and 4), by letting the entries evolve according to independent Ornstein-Uhlenbeck processes. Dyson shows the spectral points of the matrix evolve according to non-intersecting Brownian motions. The present paper shows that the interlacing spectra of two consecutive principal minors form a Markov process (diffusion) as well. This diffusion consists of two sets of Dyson non-intersecting Brownian motions, with a specific interaction respecting the interlacing. This is revealed in the form of the ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0220","kind":"arxiv","version":3},"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":"2026-05-18T03:40:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vEmpIwLsLwTyYhcLa0vSXI/IvFFZrEwEX+TJzs8WnOxcvi3PRk6E2tNa1Yzs+TwwlMlrMV6JgHC+SeB+Nh+sDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:35:03.082811Z"},"content_sha256":"30a813f7e5b35dca3f51bf86df452700e0efb495a745470bdb8b799d80326b65","schema_version":"1.0","event_id":"sha256:30a813f7e5b35dca3f51bf86df452700e0efb495a745470bdb8b799d80326b65"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4YZHP6MYN3FCJ57WQSOJUPFNC4/bundle.json","state_url":"https://pith.science/pith/4YZHP6MYN3FCJ57WQSOJUPFNC4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4YZHP6MYN3FCJ57WQSOJUPFNC4/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":"2026-06-03T01:35:03Z","links":{"resolver":"https://pith.science/pith/4YZHP6MYN3FCJ57WQSOJUPFNC4","bundle":"https://pith.science/pith/4YZHP6MYN3FCJ57WQSOJUPFNC4/bundle.json","state":"https://pith.science/pith/4YZHP6MYN3FCJ57WQSOJUPFNC4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4YZHP6MYN3FCJ57WQSOJUPFNC4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:4YZHP6MYN3FCJ57WQSOJUPFNC4","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":"501615ce0e3e7f076213c2f7b6c002799db7bc787c23dd9bc579c5213bf1f392","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-01T17:15:58Z","title_canon_sha256":"fa2bbf6002e4ea82d5eb50a30c8f99fa5c5c535bc1d0ea5e2aced8a67da2d85f"},"schema_version":"1.0","source":{"id":"1007.0220","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.0220","created_at":"2026-05-18T03:40:14Z"},{"alias_kind":"arxiv_version","alias_value":"1007.0220v3","created_at":"2026-05-18T03:40:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0220","created_at":"2026-05-18T03:40:14Z"},{"alias_kind":"pith_short_12","alias_value":"4YZHP6MYN3FC","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"4YZHP6MYN3FCJ57W","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"4YZHP6MY","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:30a813f7e5b35dca3f51bf86df452700e0efb495a745470bdb8b799d80326b65","target":"graph","created_at":"2026-05-18T03:40:14Z","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":"In 1962, Dyson introduced dynamics in random matrix models, in particular into GUE (also for beta=1 and 4), by letting the entries evolve according to independent Ornstein-Uhlenbeck processes. Dyson shows the spectral points of the matrix evolve according to non-intersecting Brownian motions. The present paper shows that the interlacing spectra of two consecutive principal minors form a Markov process (diffusion) as well. This diffusion consists of two sets of Dyson non-intersecting Brownian motions, with a specific interaction respecting the interlacing. This is revealed in the form of the ge","authors_text":"Eric Nordenstam, Mark Adler, Pierre van Moerbeke","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-01T17:15:58Z","title":"Consecutive Minors for Dyson's Brownian Motions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0220","kind":"arxiv","version":3},"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:ef6ee175d1c122f15093f72afc3199d22bdd8544d534268c54c1866b31a44b39","target":"record","created_at":"2026-05-18T03:40:14Z","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":"501615ce0e3e7f076213c2f7b6c002799db7bc787c23dd9bc579c5213bf1f392","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-01T17:15:58Z","title_canon_sha256":"fa2bbf6002e4ea82d5eb50a30c8f99fa5c5c535bc1d0ea5e2aced8a67da2d85f"},"schema_version":"1.0","source":{"id":"1007.0220","kind":"arxiv","version":3}},"canonical_sha256":"e63277f9986eca24f7f6849c9a3cad173ea185c4e41fcbc395290bbddffe7780","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e63277f9986eca24f7f6849c9a3cad173ea185c4e41fcbc395290bbddffe7780","first_computed_at":"2026-05-18T03:40:14.672221Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:14.672221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L95Ayeq6hCBzBO0Z9aOsIsEV01fRYrJNi3jFT/g2fNfz312sOlgUaFa0rSzcXG0PBPOOko7bcv861T6RmXHFDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:14.672776Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.0220","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef6ee175d1c122f15093f72afc3199d22bdd8544d534268c54c1866b31a44b39","sha256:30a813f7e5b35dca3f51bf86df452700e0efb495a745470bdb8b799d80326b65"],"state_sha256":"6f5c5cd1e19bae213cffbabc0aae373a721e6b4db00ee751c07edb8e338c10da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qLETDXwGzOseuDUcsUSLGtdiTMtW641MpaQE1AQoQcd8uJ5Vkpbs9xaGAv4PDTNlovb6zMZONFMfFDsgX1s1Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T01:35:03.084773Z","bundle_sha256":"3b05e31ce8a01fbd99784c24c4df1b6da72a791b59b4d375b3bb4f90bfcde438"}}