{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:3M2GFPKSXGGG25RIYAHB7T2GQV","short_pith_number":"pith:3M2GFPKS","schema_version":"1.0","canonical_sha256":"db3462bd52b98c6d7628c00e1fcf4685451a9cc4351575377c87f9afd9f71575","source":{"kind":"arxiv","id":"1303.5694","version":5},"attestation_state":"computed","paper":{"title":"Singular value correlation functions for products of Wishart random matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.IT","math.IT","math.MP"],"primary_cat":"math-ph","authors_text":"Gernot Akemann, Lu wei, Mario Kieburg","submitted_at":"2013-03-22T19:24:35Z","abstract_excerpt":"Consider the product of $M$ quadratic random matrices with complex elements and no further symmetry, where all matrix elements of each factor have a Gaussian distribution. This generalises the classical Wishart-Laguerre Gaussian Unitary Ensemble with M=1. In this paper we first compute the joint probability distribution for the singular values of the product matrix when the matrix size $N$ and the number $M$ are fixed but arbitrary. This leads to a determinantal point process which can be realised in two different ways. First, it can be written as a one-matrix singular value model with a non-s"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1303.5694","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-22T19:24:35Z","cross_cats_sorted":["cond-mat.stat-mech","cs.IT","math.IT","math.MP"],"title_canon_sha256":"1c21cba62bbdd5bb0407d7f1143ad68f32715a2e39e0fd1ef11680cca6eaf699","abstract_canon_sha256":"ee0c033f8aec9932424ce9418212dba3c0b84de3a80c5663c726f2c079e33d9e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:45.503104Z","signature_b64":"J9Vu8vPlldS56Xt0CgF1Hqxqbdlj6suBlsG6maebt8RmhZBGmhRzihTcf30dF/5U5IuKZ7SX3rk2uYGy57I7Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db3462bd52b98c6d7628c00e1fcf4685451a9cc4351575377c87f9afd9f71575","last_reissued_at":"2026-05-18T03:19:45.502517Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:45.502517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Singular value correlation functions for products of Wishart random matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.IT","math.IT","math.MP"],"primary_cat":"math-ph","authors_text":"Gernot Akemann, Lu wei, Mario Kieburg","submitted_at":"2013-03-22T19:24:35Z","abstract_excerpt":"Consider the product of $M$ quadratic random matrices with complex elements and no further symmetry, where all matrix elements of each factor have a Gaussian distribution. This generalises the classical Wishart-Laguerre Gaussian Unitary Ensemble with M=1. In this paper we first compute the joint probability distribution for the singular values of the product matrix when the matrix size $N$ and the number $M$ are fixed but arbitrary. This leads to a determinantal point process which can be realised in two different ways. First, it can be written as a one-matrix singular value model with a non-s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5694","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1303.5694","created_at":"2026-05-18T03:19:45.502620+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.5694v5","created_at":"2026-05-18T03:19:45.502620+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.5694","created_at":"2026-05-18T03:19:45.502620+00:00"},{"alias_kind":"pith_short_12","alias_value":"3M2GFPKSXGGG","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"3M2GFPKSXGGG25RI","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"3M2GFPKS","created_at":"2026-05-18T12:27:32.513160+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.12141","citing_title":"Quantum chaotic systems: a random-matrix approach","ref_index":38,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3M2GFPKSXGGG25RIYAHB7T2GQV","json":"https://pith.science/pith/3M2GFPKSXGGG25RIYAHB7T2GQV.json","graph_json":"https://pith.science/api/pith-number/3M2GFPKSXGGG25RIYAHB7T2GQV/graph.json","events_json":"https://pith.science/api/pith-number/3M2GFPKSXGGG25RIYAHB7T2GQV/events.json","paper":"https://pith.science/paper/3M2GFPKS"},"agent_actions":{"view_html":"https://pith.science/pith/3M2GFPKSXGGG25RIYAHB7T2GQV","download_json":"https://pith.science/pith/3M2GFPKSXGGG25RIYAHB7T2GQV.json","view_paper":"https://pith.science/paper/3M2GFPKS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.5694&json=true","fetch_graph":"https://pith.science/api/pith-number/3M2GFPKSXGGG25RIYAHB7T2GQV/graph.json","fetch_events":"https://pith.science/api/pith-number/3M2GFPKSXGGG25RIYAHB7T2GQV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3M2GFPKSXGGG25RIYAHB7T2GQV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3M2GFPKSXGGG25RIYAHB7T2GQV/action/storage_attestation","attest_author":"https://pith.science/pith/3M2GFPKSXGGG25RIYAHB7T2GQV/action/author_attestation","sign_citation":"https://pith.science/pith/3M2GFPKSXGGG25RIYAHB7T2GQV/action/citation_signature","submit_replication":"https://pith.science/pith/3M2GFPKSXGGG25RIYAHB7T2GQV/action/replication_record"}},"created_at":"2026-05-18T03:19:45.502620+00:00","updated_at":"2026-05-18T03:19:45.502620+00:00"}