{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:DFEJS2DUOY5BYSLEUHT6Q2OXS5","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":"cea0c2dbf036622b23beee97178cba4a24507705a97a8d61f5b6999ed2f5c38d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-06-20T12:58:18Z","title_canon_sha256":"4e217a7473cd5fa8aec9de9fef10593d006b32010c5ed25d770a2da8e3e66ac6"},"schema_version":"1.0","source":{"id":"2506.16967","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.16967","created_at":"2026-07-05T11:24:46Z"},{"alias_kind":"arxiv_version","alias_value":"2506.16967v1","created_at":"2026-07-05T11:24:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.16967","created_at":"2026-07-05T11:24:46Z"},{"alias_kind":"pith_short_12","alias_value":"DFEJS2DUOY5B","created_at":"2026-07-05T11:24:46Z"},{"alias_kind":"pith_short_16","alias_value":"DFEJS2DUOY5BYSLE","created_at":"2026-07-05T11:24:46Z"},{"alias_kind":"pith_short_8","alias_value":"DFEJS2DU","created_at":"2026-07-05T11:24:46Z"}],"graph_snapshots":[{"event_id":"sha256:9f22e6b581d9875bdb9193d82c431f43b6e908ac67de4b4bc299e4091f7a2b70","target":"graph","created_at":"2026-07-05T11:24:46Z","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/2506.16967/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $z_1, \\cdots, z_p$ be the eigenvalues of $A,$ which is the left-top $p\\times p$ submatrix of an $n\\times n$ Haar-invariant unitary matrix. Suppose there exist two constants $0<h_1<h_2<1$ such that $h_1<\\frac pn<h_2.$ Then,\n  $$\\sup_{x\\in \\mathbb{R}}|\\mathbb{P}(X_n\\le x)-e^{-e^{-x}}|=\\frac{(\\log \\log n)^{2}}{2e\\log n}(1+o(1))$$ and further\n  $$ W_{1}\\left(\\mathcal{L}(X_n),\\Lambda\\right)=\\frac{(\\log\\log n)^2}{2\\log n}(1+o(1))$$\n  for $n$ large enough. Here, $\\Lambda$ is the Gumbel distribution and $\\mathcal{L}(X_n)$ is the distribution of $X_n$ with $X_n$ being some rescaled version of $\\max","authors_text":"Xujia Meng, Yutao ma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-06-20T12:58:18Z","title":"How fast does spectral radius of truncated circular unitary ensemble converge?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.16967","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":"sha256:24d81ce035123cb46c2b99e251043e795ccc53ea7eafa5c660b5e900eb25de7a","target":"record","created_at":"2026-07-05T11:24:46Z","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":"cea0c2dbf036622b23beee97178cba4a24507705a97a8d61f5b6999ed2f5c38d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-06-20T12:58:18Z","title_canon_sha256":"4e217a7473cd5fa8aec9de9fef10593d006b32010c5ed25d770a2da8e3e66ac6"},"schema_version":"1.0","source":{"id":"2506.16967","kind":"arxiv","version":1}},"canonical_sha256":"1948996874763a1c4964a1e7e869d7977aaefc725cd971a543a1f5ef4164d323","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1948996874763a1c4964a1e7e869d7977aaefc725cd971a543a1f5ef4164d323","first_computed_at":"2026-07-05T11:24:46.215232Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:24:46.215232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rMmUa1o8eXpcTC6tOzKabGRRFCcAcfQkwop6rruY0C3OIElTb6JoI+PZ1q1zag7Wpws853+MmCjX3JPL0QRyDw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:24:46.215716Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.16967","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24d81ce035123cb46c2b99e251043e795ccc53ea7eafa5c660b5e900eb25de7a","sha256:9f22e6b581d9875bdb9193d82c431f43b6e908ac67de4b4bc299e4091f7a2b70"],"state_sha256":"afd5cbfbbf55086a4c1dc5195e65012e97c1f7b275f80c60e6e59070d18554f2"}