{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VYLFUT64XPGXU6J3XUZQIEYS7I","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":"15ee0e39836153417d2ee7c8c13a9280b60fbd932723523f3dd6344abb7de2df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-18T00:24:54Z","title_canon_sha256":"80e895792759e8a43260285ef26c4d9c88fda8f7122c9bf7cdf671a9d98ccdd2"},"schema_version":"1.0","source":{"id":"1207.4240","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.4240","created_at":"2026-05-18T03:50:47Z"},{"alias_kind":"arxiv_version","alias_value":"1207.4240v1","created_at":"2026-05-18T03:50:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.4240","created_at":"2026-05-18T03:50:47Z"},{"alias_kind":"pith_short_12","alias_value":"VYLFUT64XPGX","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VYLFUT64XPGXU6J3","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VYLFUT64","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:76e53a1a55ce93cfc999f067063b6ba55632a79c3cb2c5308db6e7efbf03aaaa","target":"graph","created_at":"2026-05-18T03:50:47Z","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":"In this paper we study the limiting distribution of the $k$ smallest gaps between eigenvalues of three kinds of random matrices -- the Ginibre ensemble, the Wishart ensemble and the universal unitary ensemble. All of them follow a Poissonian ansatz. More precisely, for the Ginibre ensemble we have a global result in which the $k$-th smallest gap has typical length $n^{-3/4}$ with density $x^{4k-1}e^{-x^4}$ after normalization. For the Wishart and the universal unitary ensemble, it has typical length $n^{-4/3}$ and has density $x^{3k-1}e^{-x^3}$ after normalization.","authors_text":"Dai Shi, Yunjiang Jiang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-18T00:24:54Z","title":"Smallest Gaps Between Eigenvalues of Random Matrices With Complex Ginibre, Wishart and Universal Unitary Ensembles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4240","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":"sha256:30d0e8115f26a95dd2e1d98847ca884cab93174933dbb894c9f01b083329562e","target":"record","created_at":"2026-05-18T03:50:47Z","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":"15ee0e39836153417d2ee7c8c13a9280b60fbd932723523f3dd6344abb7de2df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-18T00:24:54Z","title_canon_sha256":"80e895792759e8a43260285ef26c4d9c88fda8f7122c9bf7cdf671a9d98ccdd2"},"schema_version":"1.0","source":{"id":"1207.4240","kind":"arxiv","version":1}},"canonical_sha256":"ae165a4fdcbbcd7a793bbd33041312fa30a4f9bfbc47d116fe98f9da0f6bef05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae165a4fdcbbcd7a793bbd33041312fa30a4f9bfbc47d116fe98f9da0f6bef05","first_computed_at":"2026-05-18T03:50:47.286237Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:47.286237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E52Ci6e1FqI3Zhgc9s0JMLl40eKlwGzCO8gDIF+g32UQ1U2WNGXWYYWDTS4kpSYDQvx82q/gL3xqdrNAjIfkAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:47.286954Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.4240","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30d0e8115f26a95dd2e1d98847ca884cab93174933dbb894c9f01b083329562e","sha256:76e53a1a55ce93cfc999f067063b6ba55632a79c3cb2c5308db6e7efbf03aaaa"],"state_sha256":"b27445c69b49d258e5a6273a6ff8ebb32e5daa8bda87d7d96b21360061cd9a35"}