{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:DQANVNQUJDQ6GPVTT7RVGNQIXT","short_pith_number":"pith:DQANVNQU","canonical_record":{"source":{"id":"1410.4719","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-10-17T13:33:03Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP","math.ST","stat.TH"],"title_canon_sha256":"2edfb69e190691c44739f7f6e25f1d552881fa5e4f234a529495720d9ae4765f","abstract_canon_sha256":"7bb3450302e2447b322d1a03858827dc6fc23fe8d3d90f73e7ca2df98707c912"},"schema_version":"1.0"},"canonical_sha256":"1c00dab61448e1e33eb39fe3533608bcee7c0b91f763cce984bc241e4195d484","source":{"kind":"arxiv","id":"1410.4719","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.4719","created_at":"2026-05-18T02:27:18Z"},{"alias_kind":"arxiv_version","alias_value":"1410.4719v2","created_at":"2026-05-18T02:27:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.4719","created_at":"2026-05-18T02:27:18Z"},{"alias_kind":"pith_short_12","alias_value":"DQANVNQUJDQ6","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DQANVNQUJDQ6GPVT","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DQANVNQU","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:DQANVNQUJDQ6GPVTT7RVGNQIXT","target":"record","payload":{"canonical_record":{"source":{"id":"1410.4719","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-10-17T13:33:03Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP","math.ST","stat.TH"],"title_canon_sha256":"2edfb69e190691c44739f7f6e25f1d552881fa5e4f234a529495720d9ae4765f","abstract_canon_sha256":"7bb3450302e2447b322d1a03858827dc6fc23fe8d3d90f73e7ca2df98707c912"},"schema_version":"1.0"},"canonical_sha256":"1c00dab61448e1e33eb39fe3533608bcee7c0b91f763cce984bc241e4195d484","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:18.261780Z","signature_b64":"dKdMb4j6mz9ktCtjigqj1R8Vi0KKPRSAAsd3WI/niq46HDEAEzbZKbM8OuFLDg5sNvDJPUdSsStNIGAOOBznAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c00dab61448e1e33eb39fe3533608bcee7c0b91f763cce984bc241e4195d484","last_reissued_at":"2026-05-18T02:27:18.261031Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:18.261031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.4719","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":"2026-05-18T02:27:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Qm79QLW8WIGQLChMqTPntAdUzsxi8Lo4ruTVNkrq2vNhv+1JYERuCZBNI0qVRC3ZSor3yNg2mXgDkEvJGCxCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T17:58:16.835378Z"},"content_sha256":"37587c6e29d5d49bf19ae67438715f8216e8ad5c11f03013a0d7ff55f5ae44bd","schema_version":"1.0","event_id":"sha256:37587c6e29d5d49bf19ae67438715f8216e8ad5c11f03013a0d7ff55f5ae44bd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:DQANVNQUJDQ6GPVTT7RVGNQIXT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Limiting Statistics of the Largest and Smallest Eigenvalues in the Correlated Wishart Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP","math.ST","stat.TH"],"primary_cat":"math-ph","authors_text":"Mario Kieburg, Thomas Guhr, Tim Wirtz","submitted_at":"2014-10-17T13:33:03Z","abstract_excerpt":"The correlated Wishart model provides a standard tool for the analysis of correlations in a rich variety of systems. Although much is known for complex correlation matrices, the empirically much more important real case still poses substantial challenges. We put forward a new approach, which maps arbitrary statistical quantities, depending on invariants only, to invariant Hermitian matrix models. For completeness we also include the quaternion case and deal with all three cases in a unified way. As an important application, we study the statistics of the largest eigenvalue and its limiting dis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4719","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":"2026-05-18T02:27:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XkIKFqveF0OV9W7PX+9/o5uHdtjFATb+yTZm3bAB5c+bqJw3RFptuYH/r9VI/ZuSXfgBu+G6rz+0cEj3bEH+Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T17:58:16.835821Z"},"content_sha256":"84786e348209ef499830a597f2cad8e97262424d6b2f6bc801fd1b2091f612ab","schema_version":"1.0","event_id":"sha256:84786e348209ef499830a597f2cad8e97262424d6b2f6bc801fd1b2091f612ab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DQANVNQUJDQ6GPVTT7RVGNQIXT/bundle.json","state_url":"https://pith.science/pith/DQANVNQUJDQ6GPVTT7RVGNQIXT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DQANVNQUJDQ6GPVTT7RVGNQIXT/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":"2026-05-31T17:58:16Z","links":{"resolver":"https://pith.science/pith/DQANVNQUJDQ6GPVTT7RVGNQIXT","bundle":"https://pith.science/pith/DQANVNQUJDQ6GPVTT7RVGNQIXT/bundle.json","state":"https://pith.science/pith/DQANVNQUJDQ6GPVTT7RVGNQIXT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DQANVNQUJDQ6GPVTT7RVGNQIXT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DQANVNQUJDQ6GPVTT7RVGNQIXT","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":"7bb3450302e2447b322d1a03858827dc6fc23fe8d3d90f73e7ca2df98707c912","cross_cats_sorted":["cond-mat.stat-mech","math.MP","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-10-17T13:33:03Z","title_canon_sha256":"2edfb69e190691c44739f7f6e25f1d552881fa5e4f234a529495720d9ae4765f"},"schema_version":"1.0","source":{"id":"1410.4719","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.4719","created_at":"2026-05-18T02:27:18Z"},{"alias_kind":"arxiv_version","alias_value":"1410.4719v2","created_at":"2026-05-18T02:27:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.4719","created_at":"2026-05-18T02:27:18Z"},{"alias_kind":"pith_short_12","alias_value":"DQANVNQUJDQ6","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DQANVNQUJDQ6GPVT","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DQANVNQU","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:84786e348209ef499830a597f2cad8e97262424d6b2f6bc801fd1b2091f612ab","target":"graph","created_at":"2026-05-18T02:27:18Z","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":"The correlated Wishart model provides a standard tool for the analysis of correlations in a rich variety of systems. Although much is known for complex correlation matrices, the empirically much more important real case still poses substantial challenges. We put forward a new approach, which maps arbitrary statistical quantities, depending on invariants only, to invariant Hermitian matrix models. For completeness we also include the quaternion case and deal with all three cases in a unified way. As an important application, we study the statistics of the largest eigenvalue and its limiting dis","authors_text":"Mario Kieburg, Thomas Guhr, Tim Wirtz","cross_cats":["cond-mat.stat-mech","math.MP","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-10-17T13:33:03Z","title":"Limiting Statistics of the Largest and Smallest Eigenvalues in the Correlated Wishart Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4719","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":"sha256:37587c6e29d5d49bf19ae67438715f8216e8ad5c11f03013a0d7ff55f5ae44bd","target":"record","created_at":"2026-05-18T02:27:18Z","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":"7bb3450302e2447b322d1a03858827dc6fc23fe8d3d90f73e7ca2df98707c912","cross_cats_sorted":["cond-mat.stat-mech","math.MP","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-10-17T13:33:03Z","title_canon_sha256":"2edfb69e190691c44739f7f6e25f1d552881fa5e4f234a529495720d9ae4765f"},"schema_version":"1.0","source":{"id":"1410.4719","kind":"arxiv","version":2}},"canonical_sha256":"1c00dab61448e1e33eb39fe3533608bcee7c0b91f763cce984bc241e4195d484","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c00dab61448e1e33eb39fe3533608bcee7c0b91f763cce984bc241e4195d484","first_computed_at":"2026-05-18T02:27:18.261031Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:18.261031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dKdMb4j6mz9ktCtjigqj1R8Vi0KKPRSAAsd3WI/niq46HDEAEzbZKbM8OuFLDg5sNvDJPUdSsStNIGAOOBznAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:18.261780Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.4719","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37587c6e29d5d49bf19ae67438715f8216e8ad5c11f03013a0d7ff55f5ae44bd","sha256:84786e348209ef499830a597f2cad8e97262424d6b2f6bc801fd1b2091f612ab"],"state_sha256":"a31665b63a771737a32df0316fd4516613d8b239ae575f51e669f2ca7ef8b53a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UdkTK+2CInrL7hfSdfJ5Ng73oXIrJsLmqtqSdS7DDhe/ArIOianElChVLt88eKPHAkyfDgiO8yGl+tZZTkYGCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T17:58:16.839666Z","bundle_sha256":"df359d2bb225c620a292bfd2f3903aaf5fa1662110611bf257b24b3f36dcc9ae"}}