{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NLVLH6IHCFWD4V3V22JQZXN3Z5","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":"5a2e1eae5afeb19912eb98e2db79e34c2db848dbe98d5962b8dfe894c67176ad","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-04-01T00:25:30Z","title_canon_sha256":"9fc9fcdd05ab967136d85d72f78477597e144d6dfdfa6dad60aea8f1d5813fcf"},"schema_version":"1.0","source":{"id":"1404.0071","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.0071","created_at":"2026-05-18T02:55:05Z"},{"alias_kind":"arxiv_version","alias_value":"1404.0071v1","created_at":"2026-05-18T02:55:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.0071","created_at":"2026-05-18T02:55:05Z"},{"alias_kind":"pith_short_12","alias_value":"NLVLH6IHCFWD","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NLVLH6IHCFWD4V3V","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NLVLH6IH","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:8cc799965f4c2e4d21a69e588b3a3b9f173e8ec3c5f36b40fe8a0095b1129cf9","target":"graph","created_at":"2026-05-18T02:55:05Z","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":"We develop an algorithm for sampling from the unitary invariant random matrix ensembles. The algorithm is based on the representation of their eigenvalues as a determinantal point process whose kernel is given in terms of orthogonal polynomials. Using this algorithm, statistics beyond those known through analysis are calculable through Monte Carlo simulation. Unexpected phenomena are observed in the simulations.","authors_text":"Raj Rao Nadakuditi, Sheehan Olver, Thomas Trogdon","cross_cats":["math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-04-01T00:25:30Z","title":"Sampling unitary invariant ensembles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0071","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":"sha256:4a64b2fd88eeb3fe145e99f197f7ddb760770b52012c4cc9c21af8e7289a189c","target":"record","created_at":"2026-05-18T02:55:05Z","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":"5a2e1eae5afeb19912eb98e2db79e34c2db848dbe98d5962b8dfe894c67176ad","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-04-01T00:25:30Z","title_canon_sha256":"9fc9fcdd05ab967136d85d72f78477597e144d6dfdfa6dad60aea8f1d5813fcf"},"schema_version":"1.0","source":{"id":"1404.0071","kind":"arxiv","version":1}},"canonical_sha256":"6aeab3f907116c3e5775d6930cddbbcf74bcdd3f8d8ee15db402af1886e2ff1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6aeab3f907116c3e5775d6930cddbbcf74bcdd3f8d8ee15db402af1886e2ff1e","first_computed_at":"2026-05-18T02:55:05.254862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:05.254862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8luaYmtyRTKetL01ykKJ/W7T/R59Dtqk8tWcZf3Fqv7VwFRvFq+IOe0uURibxx041HWPzVyLnmEe2Mb+ri1GCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:05.255241Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.0071","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a64b2fd88eeb3fe145e99f197f7ddb760770b52012c4cc9c21af8e7289a189c","sha256:8cc799965f4c2e4d21a69e588b3a3b9f173e8ec3c5f36b40fe8a0095b1129cf9"],"state_sha256":"a36aec25c294df7290f3ad990a1887e88b303b97120c14e38b822365c04cfd29"}