{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3OLD53LBIF4PHUX2GWXDTBQX5P","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":"a7d0847ad2a4edceb7162189c0701c0eff2e2cbc5bb2f0e2f904e06161cf7687","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-07-04T17:24:32Z","title_canon_sha256":"21c310aee2d33deb51ad5821ed7d818c6fec1eeef0813949b9ca41fdd2f7049c"},"schema_version":"1.0","source":{"id":"1407.1282","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.1282","created_at":"2026-05-18T01:36:51Z"},{"alias_kind":"arxiv_version","alias_value":"1407.1282v4","created_at":"2026-05-18T01:36:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1282","created_at":"2026-05-18T01:36:51Z"},{"alias_kind":"pith_short_12","alias_value":"3OLD53LBIF4P","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3OLD53LBIF4PHUX2","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3OLD53LB","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:133b42b3a523e2745b3c58d26b75f87c930138a40357afbe39e2317e2db49fa0","target":"graph","created_at":"2026-05-18T01:36:51Z","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 level density for several ensembles of positive random matrices of a Wishart--like structure, $W=XX^{\\dagger}$, where $X$ stands for a nonhermitian random matrix. In particular, making use of the Cauchy transform, we study free multiplicative powers of the Marchenko-Pastur (MP) distribution, ${\\rm MP}^{\\boxtimes s}$, which for an integer $s$ yield Fuss-Catalan distributions corresponding to a product of $s$ independent square random matrices, $X=X_1\\cdots X_s$. New formulae for the level densities are derived for $s=3$ and $s=1/3$. Moreover, the level density corresponding t","authors_text":"Karol A. Penson, Karol Zyczkowski, Maciej A. Nowak, Wojciech Mlotkowski","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-07-04T17:24:32Z","title":"Spectral density of generalized Wishart matrices and free multiplicative convolution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1282","kind":"arxiv","version":4},"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:e068a4e9aad993cc0ec3c8eb55fbe6d9eaeb383cce2dd419d9b4b383df7bcc7f","target":"record","created_at":"2026-05-18T01:36:51Z","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":"a7d0847ad2a4edceb7162189c0701c0eff2e2cbc5bb2f0e2f904e06161cf7687","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-07-04T17:24:32Z","title_canon_sha256":"21c310aee2d33deb51ad5821ed7d818c6fec1eeef0813949b9ca41fdd2f7049c"},"schema_version":"1.0","source":{"id":"1407.1282","kind":"arxiv","version":4}},"canonical_sha256":"db963eed614178f3d2fa35ae398617ebd1248417749e9c4142d7ef73780bef53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db963eed614178f3d2fa35ae398617ebd1248417749e9c4142d7ef73780bef53","first_computed_at":"2026-05-18T01:36:51.681437Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:51.681437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IGeDBt8XcLF/Ne9R57P9jH/6CSoxqynZdhYvCjp78TCBwHkIPQOn9FK9nEH8CdhyT1RTUwyQCVFo21sXeklvDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:51.682062Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.1282","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e068a4e9aad993cc0ec3c8eb55fbe6d9eaeb383cce2dd419d9b4b383df7bcc7f","sha256:133b42b3a523e2745b3c58d26b75f87c930138a40357afbe39e2317e2db49fa0"],"state_sha256":"c70717c38ae63b12e3209d8516a62dd2cc7644ecddaa8539fc87d892cf24c392"}