{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LE4LDRJFRNZKVQMZBYZOFG5V2I","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":"e02e3211d257a4e805a85da1732c76da15c9c19d1421268115276e629675addb","cross_cats_sorted":["cs.CC","cs.NA","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-11-02T18:38:29Z","title_canon_sha256":"aead15c8abd81c5a7ccdbe452257aa0d0b6bdf71c4fd2e70a6f7ea4bda5c5691"},"schema_version":"1.0","source":{"id":"1211.0517","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0517","created_at":"2026-05-18T03:41:31Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0517v1","created_at":"2026-05-18T03:41:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0517","created_at":"2026-05-18T03:41:31Z"},{"alias_kind":"pith_short_12","alias_value":"LE4LDRJFRNZK","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LE4LDRJFRNZKVQMZ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LE4LDRJF","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:76f9ba6f2f0cbaaa0404d107ff4648df8531e933993b999e3ed69eeac6bee4b8","target":"graph","created_at":"2026-05-18T03:41:31Z","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 a random matrix $\\mathbf{A}\\in\\mathbb{C}^{m\\times n}$ ($m \\geq n$) containing independent complex Gaussian entries with zero mean and unit variance, and let $0<\\lambda_1\\leq \\lambda_{2}\\leq ...\\leq \\lambda_n<\\infty$ denote the eigenvalues of $\\mathbf{A}^{*}\\mathbf{A}$ where $(\\cdot)^*$ represents conjugate-transpose. This paper investigates the distribution of the random variables $\\frac{\\sum_{j=1}^n \\lambda_j}{\\lambda_k}$, for $k = 1$ and $k = 2$. These two variables are related to certain condition number metrics, including the so-called Demmel condition number, which have been show","authors_text":"Matthew McKay, Prathapasinghe Dharmawansa, Yang Chen","cross_cats":["cs.CC","cs.NA","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-11-02T18:38:29Z","title":"Distributions of Demmel and Related Condition Numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0517","kind":"arxiv","version":1},"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":"sha256:731a09abd7976cc717aa6e7f8c29deca57262312706210a3473c5cb42081754f","target":"record","created_at":"2026-05-18T03:41:31Z","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":"e02e3211d257a4e805a85da1732c76da15c9c19d1421268115276e629675addb","cross_cats_sorted":["cs.CC","cs.NA","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-11-02T18:38:29Z","title_canon_sha256":"aead15c8abd81c5a7ccdbe452257aa0d0b6bdf71c4fd2e70a6f7ea4bda5c5691"},"schema_version":"1.0","source":{"id":"1211.0517","kind":"arxiv","version":1}},"canonical_sha256":"5938b1c5258b72aac1990e32e29bb5d218c701627a5313914441337bea5c57a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5938b1c5258b72aac1990e32e29bb5d218c701627a5313914441337bea5c57a6","first_computed_at":"2026-05-18T03:41:31.753656Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:31.753656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eLjp50LOTkJ0A/jGqFmSCaoEjWbUj30NXdtKwNaij4eJIlatLuuH2/suOT0gk9xy/LnlC84gJbSEEY803zemAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:31.754344Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.0517","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:731a09abd7976cc717aa6e7f8c29deca57262312706210a3473c5cb42081754f","sha256:76f9ba6f2f0cbaaa0404d107ff4648df8531e933993b999e3ed69eeac6bee4b8"],"state_sha256":"6bc75ead557325127b996afecf353d6ca34d57dcce74e515d21fe89d044cacb3"}