{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:6N7NW2AMPUWGYETLOUHYSQYERN","short_pith_number":"pith:6N7NW2AM","canonical_record":{"source":{"id":"math/0606760","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2006-06-29T14:02:18Z","cross_cats_sorted":[],"title_canon_sha256":"4e61baa823b0d0744bcbaad945e16acfaba7ddb11723ca1c3bb3944c6720f903","abstract_canon_sha256":"ed0f209833d54baf539dc2cad85631ea5de73adb2de8e3e4358a73b6414466ab"},"schema_version":"1.0"},"canonical_sha256":"f37edb680c7d2c6c126b750f8943048b5eeafaea4865f893b9ba95f2ca7f146c","source":{"kind":"arxiv","id":"math/0606760","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0606760","created_at":"2026-07-04T17:22:00Z"},{"alias_kind":"arxiv_version","alias_value":"math/0606760v2","created_at":"2026-07-04T17:22:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0606760","created_at":"2026-07-04T17:22:00Z"},{"alias_kind":"pith_short_12","alias_value":"6N7NW2AMPUWG","created_at":"2026-07-04T17:22:00Z"},{"alias_kind":"pith_short_16","alias_value":"6N7NW2AMPUWGYETL","created_at":"2026-07-04T17:22:00Z"},{"alias_kind":"pith_short_8","alias_value":"6N7NW2AM","created_at":"2026-07-04T17:22:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:6N7NW2AMPUWGYETLOUHYSQYERN","target":"record","payload":{"canonical_record":{"source":{"id":"math/0606760","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2006-06-29T14:02:18Z","cross_cats_sorted":[],"title_canon_sha256":"4e61baa823b0d0744bcbaad945e16acfaba7ddb11723ca1c3bb3944c6720f903","abstract_canon_sha256":"ed0f209833d54baf539dc2cad85631ea5de73adb2de8e3e4358a73b6414466ab"},"schema_version":"1.0"},"canonical_sha256":"f37edb680c7d2c6c126b750f8943048b5eeafaea4865f893b9ba95f2ca7f146c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:22:00.634194Z","signature_b64":"79TAtHe5auyTtvnKFzIQmsmbLuZrueKAiJrmXthPdZuHDluVR0xbV/wgnP2y3axRtE5sSqfLYwOQGxcwBICFBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f37edb680c7d2c6c126b750f8943048b5eeafaea4865f893b9ba95f2ca7f146c","last_reissued_at":"2026-07-04T17:22:00.633738Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:22:00.633738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0606760","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":"2026-07-04T17:22:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MKM9CUh/fco/NXTOj4JnCt4pn0egWb3JbTgGbbCc2SuBxLjhyUSfTNBGmKvmmtploq/nM8SENb3bphr0C4t4Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T02:34:55.125590Z"},"content_sha256":"bdb92962b526f31692456ab2dd13a5abdefc72e50c5958e8bb28e1da37a117cb","schema_version":"1.0","event_id":"sha256:bdb92962b526f31692456ab2dd13a5abdefc72e50c5958e8bb28e1da37a117cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:6N7NW2AMPUWGYETLOUHYSQYERN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eigenvalues of GUE Minors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eric Nordenstam, Kurt Johansson","submitted_at":"2006-06-29T14:02:18Z","abstract_excerpt":"Consider an infinite random matrix $H=(h_{ij})_{0<i,j}$ picked from the Gaussian Unitary Ensemble (GUE). Denote its main minors by $H_i=(h_{rs})_{1\\leq r,s\\leq i}$ and let the $j$:th largest eigenvalue of $H_i$ be $\\mu^i_j$. We show that the configuration of all these eigenvalues $(i,\\mu_j^i)$ form a determinantal point process on $\\mathbb{N}\\times\\mathbb{R}$.\n  Furthermore we show that this process can be obtained as the scaling limit in random tilings of the Aztec diamond close to the boundary. We also discuss the corresponding limit for random lozenge tilings of a hexagon."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606760","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0606760/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T17:22:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rOrnB88q2ih/fxATW+4lU0q6R9PzGzV6vmQUX7bScUs9hbKsgQer671+wsUBOseJL1gVbpMKjX0MklU3K0mzAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T02:34:55.126169Z"},"content_sha256":"56e1fc421080a852087f42475ca27997b052532a25f656bb090094c23d1ef8a8","schema_version":"1.0","event_id":"sha256:56e1fc421080a852087f42475ca27997b052532a25f656bb090094c23d1ef8a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6N7NW2AMPUWGYETLOUHYSQYERN/bundle.json","state_url":"https://pith.science/pith/6N7NW2AMPUWGYETLOUHYSQYERN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6N7NW2AMPUWGYETLOUHYSQYERN/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":"2026-08-09T02:34:55Z","links":{"resolver":"https://pith.science/pith/6N7NW2AMPUWGYETLOUHYSQYERN","bundle":"https://pith.science/pith/6N7NW2AMPUWGYETLOUHYSQYERN/bundle.json","state":"https://pith.science/pith/6N7NW2AMPUWGYETLOUHYSQYERN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6N7NW2AMPUWGYETLOUHYSQYERN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:6N7NW2AMPUWGYETLOUHYSQYERN","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":"ed0f209833d54baf539dc2cad85631ea5de73adb2de8e3e4358a73b6414466ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2006-06-29T14:02:18Z","title_canon_sha256":"4e61baa823b0d0744bcbaad945e16acfaba7ddb11723ca1c3bb3944c6720f903"},"schema_version":"1.0","source":{"id":"math/0606760","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0606760","created_at":"2026-07-04T17:22:00Z"},{"alias_kind":"arxiv_version","alias_value":"math/0606760v2","created_at":"2026-07-04T17:22:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0606760","created_at":"2026-07-04T17:22:00Z"},{"alias_kind":"pith_short_12","alias_value":"6N7NW2AMPUWG","created_at":"2026-07-04T17:22:00Z"},{"alias_kind":"pith_short_16","alias_value":"6N7NW2AMPUWGYETL","created_at":"2026-07-04T17:22:00Z"},{"alias_kind":"pith_short_8","alias_value":"6N7NW2AM","created_at":"2026-07-04T17:22:00Z"}],"graph_snapshots":[{"event_id":"sha256:56e1fc421080a852087f42475ca27997b052532a25f656bb090094c23d1ef8a8","target":"graph","created_at":"2026-07-04T17:22:00Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0606760/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Consider an infinite random matrix $H=(h_{ij})_{0<i,j}$ picked from the Gaussian Unitary Ensemble (GUE). Denote its main minors by $H_i=(h_{rs})_{1\\leq r,s\\leq i}$ and let the $j$:th largest eigenvalue of $H_i$ be $\\mu^i_j$. We show that the configuration of all these eigenvalues $(i,\\mu_j^i)$ form a determinantal point process on $\\mathbb{N}\\times\\mathbb{R}$.\n  Furthermore we show that this process can be obtained as the scaling limit in random tilings of the Aztec diamond close to the boundary. We also discuss the corresponding limit for random lozenge tilings of a hexagon.","authors_text":"Eric Nordenstam, Kurt Johansson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2006-06-29T14:02:18Z","title":"Eigenvalues of GUE Minors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606760","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:bdb92962b526f31692456ab2dd13a5abdefc72e50c5958e8bb28e1da37a117cb","target":"record","created_at":"2026-07-04T17:22:00Z","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":"ed0f209833d54baf539dc2cad85631ea5de73adb2de8e3e4358a73b6414466ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2006-06-29T14:02:18Z","title_canon_sha256":"4e61baa823b0d0744bcbaad945e16acfaba7ddb11723ca1c3bb3944c6720f903"},"schema_version":"1.0","source":{"id":"math/0606760","kind":"arxiv","version":2}},"canonical_sha256":"f37edb680c7d2c6c126b750f8943048b5eeafaea4865f893b9ba95f2ca7f146c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f37edb680c7d2c6c126b750f8943048b5eeafaea4865f893b9ba95f2ca7f146c","first_computed_at":"2026-07-04T17:22:00.633738Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:22:00.633738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"79TAtHe5auyTtvnKFzIQmsmbLuZrueKAiJrmXthPdZuHDluVR0xbV/wgnP2y3axRtE5sSqfLYwOQGxcwBICFBw==","signature_status":"signed_v1","signed_at":"2026-07-04T17:22:00.634194Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0606760","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bdb92962b526f31692456ab2dd13a5abdefc72e50c5958e8bb28e1da37a117cb","sha256:56e1fc421080a852087f42475ca27997b052532a25f656bb090094c23d1ef8a8"],"state_sha256":"fe6a175896d0d4cd87cd55d4adcbd9fe496290dcb4e5a1df5b2ca3dddfd50682"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XGtjI4GGmg9TNapMemU5RNpgAfvh7OcVPkVs7beB2wsmGEGt1/35LdrqYc2eT1MmiDs9RRMRZTKWH+or927aAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T02:34:55.129798Z","bundle_sha256":"fb4ce07f5b07d5ea4a1f68f160c7028471b67214bf4fca7d08f00336caa7a557"}}