{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6SPLRJCXM56GZWDFUIWQPE6YGN","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":"9981abc8893d1783dcc1ad395bb46081db01f26ce9d56b572a5be98a192fb076","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-24T15:48:16Z","title_canon_sha256":"99478c7e2f6ae7438e06e9708de0774e6d04c3ef1fc220c77277eddf2e415d8c"},"schema_version":"1.0","source":{"id":"1309.6224","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.6224","created_at":"2026-05-18T03:11:00Z"},{"alias_kind":"arxiv_version","alias_value":"1309.6224v2","created_at":"2026-05-18T03:11:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6224","created_at":"2026-05-18T03:11:00Z"},{"alias_kind":"pith_short_12","alias_value":"6SPLRJCXM56G","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6SPLRJCXM56GZWDF","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6SPLRJCX","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:efc01bf864f7b3446acdbc95d8a4c56413278bc0f1add8e8eba94f451cdcf4b9","target":"graph","created_at":"2026-05-18T03:11:00Z","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":"We study fluctuations of linear statistics corresponding to smooth functions for certain biorthogonal ensembles. We study those biorthogonal ensembles for which the underlying biorthogonal family satisfies a finite term recurrence and describe the asymptotic fluctuations using right limits of the recurrence matrix. As a consequence, we show that whenever the right limit is a Laurent matrix, a Central Limit Theorem holds. We will also discuss the implications for orthogonal polynomial ensembles. In particular, we obtain a Central limit theorem for the orthogonal polynomial ensemble associated w","authors_text":"Jonathan Breuer, Maurice Duits","cross_cats":["math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-24T15:48:16Z","title":"Central Limit Theorems for Biorthogonal Ensembles and Asymptotics of Recurrence Coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6224","kind":"arxiv","version":2},"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":"sha256:8865056e6f556d37cc3f816f57c47b956876ac16a2d80e82a51a0c8e4e10e3a7","target":"record","created_at":"2026-05-18T03:11:00Z","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":"9981abc8893d1783dcc1ad395bb46081db01f26ce9d56b572a5be98a192fb076","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-24T15:48:16Z","title_canon_sha256":"99478c7e2f6ae7438e06e9708de0774e6d04c3ef1fc220c77277eddf2e415d8c"},"schema_version":"1.0","source":{"id":"1309.6224","kind":"arxiv","version":2}},"canonical_sha256":"f49eb8a457677c6cd865a22d0793d833666169975cab3d28a98a4498cbd46cd1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f49eb8a457677c6cd865a22d0793d833666169975cab3d28a98a4498cbd46cd1","first_computed_at":"2026-05-18T03:11:00.094689Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:00.094689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8j8ZqdANXmFTPXUQNxHuVXPQMhTo0NyVrAbGXhXUfsULnid/MiV3FGUeJU7YnX5LelwZ1WDv1s4oWvy9tEZ6DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:00.095409Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.6224","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8865056e6f556d37cc3f816f57c47b956876ac16a2d80e82a51a0c8e4e10e3a7","sha256:efc01bf864f7b3446acdbc95d8a4c56413278bc0f1add8e8eba94f451cdcf4b9"],"state_sha256":"928a9b0e9dedbc5c3a28a8565437f7d1deed86a21e291b511de7459600249bc6"}