{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VJP6YY6DJ2OML7WATTJ6NZXKJ2","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":"53c9c84b0444144307bdceb61e74bfde6f421064e631b6e9b37466a76aa274e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-10T11:45:46Z","title_canon_sha256":"c6d45e4e721123e796f56b4052a8c271f633ad25a4829aa48cdcfdf6f87ec6e8"},"schema_version":"1.0","source":{"id":"1801.03319","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.03319","created_at":"2026-05-18T00:26:17Z"},{"alias_kind":"arxiv_version","alias_value":"1801.03319v1","created_at":"2026-05-18T00:26:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.03319","created_at":"2026-05-18T00:26:17Z"},{"alias_kind":"pith_short_12","alias_value":"VJP6YY6DJ2OM","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VJP6YY6DJ2OML7WA","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VJP6YY6D","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:d53b699594b60bd7ad721b917efca73674d77635528ab7142a9d0fed516cfde2","target":"graph","created_at":"2026-05-18T00:26:17Z","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":"This paper is to investigate the spectral properties of sample covariance matrices under a more general population. We consider a class of matrices of the form $\\mathbf S_n=\\frac1n\\mathbf B_n\\mathbf X_n\\mathbf X_n^*\\mathbf B_n^*$, where $\\mathbf B_n$ is a $p\\times m$ non-random matrix and $\\mathbf X_n$ is an $m\\times n$ matrix consisting of i.i.d standard complex entries. $p/n\\to c\\in (0,\\infty)$ as $n\\to \\infty$ while $m$ can be arbitrary. We proved that under some mild assumptions, with probability 1, there will be no eigenvalues in any closed interval contained in an open interval outside t","authors_text":"Yanqing Yin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-10T11:45:46Z","title":"No eigenvalues outside the limiting support of the spectral distribution of general sample covariance matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.03319","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:b6bda8cb52b9c2f85453a1c27e8d7c77835bf4919e73801a5fb359ee1e63a84d","target":"record","created_at":"2026-05-18T00:26:17Z","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":"53c9c84b0444144307bdceb61e74bfde6f421064e631b6e9b37466a76aa274e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-10T11:45:46Z","title_canon_sha256":"c6d45e4e721123e796f56b4052a8c271f633ad25a4829aa48cdcfdf6f87ec6e8"},"schema_version":"1.0","source":{"id":"1801.03319","kind":"arxiv","version":1}},"canonical_sha256":"aa5fec63c34e9cc5fec09cd3e6e6ea4eb4344a531aba3cae0b27006e47366b36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa5fec63c34e9cc5fec09cd3e6e6ea4eb4344a531aba3cae0b27006e47366b36","first_computed_at":"2026-05-18T00:26:17.405450Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:17.405450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HPI5+UiAhzmNI3dYUIbgqSGnFHp2kmJklD/tAyJgmasY28koFpAfCxs6N/CiRpaakD73q46iVU5TymEaRpuwBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:17.406366Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.03319","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6bda8cb52b9c2f85453a1c27e8d7c77835bf4919e73801a5fb359ee1e63a84d","sha256:d53b699594b60bd7ad721b917efca73674d77635528ab7142a9d0fed516cfde2"],"state_sha256":"9e6a6e13f553f2ef57e37584d733c48ce08258f102c1c4fa347aafc583c4f61c"}