{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:H7OTK5HAJ7RTWN3V4NET3RER7L","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":"df891de474cc1036c8ec754971d4a28fb643d073e9cd9b5166521595edf10497","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-09-16T00:56:31Z","title_canon_sha256":"7c2a62d2c5b41581a9e8a2764a1319f436b1ff9fa860a3c5e5de2df8393247ec"},"schema_version":"1.0","source":{"id":"1709.05441","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.05441","created_at":"2026-05-18T00:35:00Z"},{"alias_kind":"arxiv_version","alias_value":"1709.05441v1","created_at":"2026-05-18T00:35:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.05441","created_at":"2026-05-18T00:35:00Z"},{"alias_kind":"pith_short_12","alias_value":"H7OTK5HAJ7RT","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"H7OTK5HAJ7RTWN3V","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"H7OTK5HA","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:8e56db302e2ef45bbd1f6cdb57bad0f8f013aab7da674bd17493766e16271cf9","target":"graph","created_at":"2026-05-18T00:35:00Z","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"},"paper":{"abstract_excerpt":"Consider a truncated circular unitary matrix which is a $p_n$ by $p_n$ submatrix of an $n$ by $n$ circular unitary matrix by deleting the last $n-p_n$ columns and rows. Jiang and Qi (2017) proved that the maximum absolute value of the eigenvalues (known as spectral radius) of the truncated matrix, after properly normalized, converges in distribution to the Gumbel distribution if $p_n/n$ is bounded away from $0$ and $1$. In this paper we investigate the limiting distribution of the spectral radius under one of the following four conditions: (1). $p_n\\to\\infty$ and $p_n/n\\to 0$ as $n\\to\\infty$; ","authors_text":"Wenhao Gui, Yongcheng Qi","cross_cats":["math.PR","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-09-16T00:56:31Z","title":"Spectral Radii of Truncated Circular Unitary Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05441","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:fd8ec766f02759d7db7ab1ada2a7fcea6757b134eff7c6ad5211c9e3009db95e","target":"record","created_at":"2026-05-18T00:35:00Z","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":"df891de474cc1036c8ec754971d4a28fb643d073e9cd9b5166521595edf10497","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-09-16T00:56:31Z","title_canon_sha256":"7c2a62d2c5b41581a9e8a2764a1319f436b1ff9fa860a3c5e5de2df8393247ec"},"schema_version":"1.0","source":{"id":"1709.05441","kind":"arxiv","version":1}},"canonical_sha256":"3fdd3574e04fe33b3775e3493dc491faed2e997cad8fdd6f3df3ed1c48293936","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3fdd3574e04fe33b3775e3493dc491faed2e997cad8fdd6f3df3ed1c48293936","first_computed_at":"2026-05-18T00:35:00.759053Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:00.759053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y1RUt67o9LcJIUR94scLJq7d1UXE/4DsyRccMrSMhiI9z4HP3DhLO2zkIg7/v0rKaWIPfVdkNOfjhcOcQ1pABA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:00.760143Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.05441","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd8ec766f02759d7db7ab1ada2a7fcea6757b134eff7c6ad5211c9e3009db95e","sha256:8e56db302e2ef45bbd1f6cdb57bad0f8f013aab7da674bd17493766e16271cf9"],"state_sha256":"866711b41939b61bbc8d31d17d81be9a22e98f51c93fbbc2ce769f480a4cce83"}