{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UI3U6QEAGMF4PHADRQZHIY4NCL","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":"6ec641d938c5f47192304224e569d0b719fe3881efe98359e6c9626fbf4b7a28","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-17T13:50:50Z","title_canon_sha256":"519702a4553235f2a4851d159f779fd1ffe093f49562a828660a48283f5472fa"},"schema_version":"1.0","source":{"id":"1108.3479","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.3479","created_at":"2026-05-18T02:25:11Z"},{"alias_kind":"arxiv_version","alias_value":"1108.3479v2","created_at":"2026-05-18T02:25:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3479","created_at":"2026-05-18T02:25:11Z"},{"alias_kind":"pith_short_12","alias_value":"UI3U6QEAGMF4","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UI3U6QEAGMF4PHAD","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UI3U6QEA","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:2c22312eb6d135047297cb053b65a2e75024761d6978954afa7418df84e1e47e","target":"graph","created_at":"2026-05-18T02:25:11Z","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 investigate the spectral distribution of random matrix ensembles with correlated entries. We consider symmetric matrices with real valued entries and stochastically independent diagonals. Along the diagonals the entries may be correlated. We show that under sufficiently nice moment conditions the empirical eigenvalue distribution converges almost surely weakly to the semi-circle law.","authors_text":"Matthias L\\\"owe, Olga Friesen","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-17T13:50:50Z","title":"The semicircle law for matrices with independent diagonals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3479","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":"sha256:8e0e72fc4473a78312b70b5edf81f2ed411eb69c58cee13ec68f9fbed288c7f8","target":"record","created_at":"2026-05-18T02:25:11Z","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":"6ec641d938c5f47192304224e569d0b719fe3881efe98359e6c9626fbf4b7a28","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-17T13:50:50Z","title_canon_sha256":"519702a4553235f2a4851d159f779fd1ffe093f49562a828660a48283f5472fa"},"schema_version":"1.0","source":{"id":"1108.3479","kind":"arxiv","version":2}},"canonical_sha256":"a2374f4080330bc79c038c3274638d12ebe12fb0c28b69a211613bf8ead14858","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2374f4080330bc79c038c3274638d12ebe12fb0c28b69a211613bf8ead14858","first_computed_at":"2026-05-18T02:25:11.881178Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:11.881178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+0GreYYw2+zubB00+h5hbRTMukTqxz5JWNRX46x8WDn2NSsfRwsE/5B6Nf5Sd9CexpdZmJm77+ZfEJNnxWcWAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:11.881583Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.3479","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e0e72fc4473a78312b70b5edf81f2ed411eb69c58cee13ec68f9fbed288c7f8","sha256:2c22312eb6d135047297cb053b65a2e75024761d6978954afa7418df84e1e47e"],"state_sha256":"2ebb3e0b0e9910e3f3919e9a10c91e424f819e7b43338ca265eef8c778ab5ede"}