{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:V3OU6KQ3S64ABUXUEOTTK3HKDU","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":"444420ecd5911b3e9de32ad9c2deeb8e592f6ce7bfa9f445bcbafa9304f7b556","cross_cats_sorted":["math.CA","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-02-25T12:19:39Z","title_canon_sha256":"2a32efeba241bc5cd5b373af82a7b06afa633cd6f1f623df93943c39431ed925"},"schema_version":"1.0","source":{"id":"1502.07147","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.07147","created_at":"2026-05-18T00:44:39Z"},{"alias_kind":"arxiv_version","alias_value":"1502.07147v4","created_at":"2026-05-18T00:44:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.07147","created_at":"2026-05-18T00:44:39Z"},{"alias_kind":"pith_short_12","alias_value":"V3OU6KQ3S64A","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"V3OU6KQ3S64ABUXU","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"V3OU6KQ3","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:74a2f4cb215636bc2c8daa39787f0693ec20b7865aeabea83d75ea5f90a4022c","target":"graph","created_at":"2026-05-18T00:44:39Z","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":"Muttalib--Borodin ensembles are characterised by the pair interaction term in the eigenvalue probability density function being of the form $\\prod_{1 \\le j < k \\le N}(\\lambda_k - \\lambda_j) (\\lambda_k^\\theta - \\lambda_j^\\theta)$. We study the Laguerre and Jacobi versions of this model --- so named by the form of the one-body interaction terms --- and show that for $\\theta \\in \\mathbb Z^+$ they can be realised as the eigenvalue PDF of certain random matrices with Gaussian entries. For general $\\theta > 0$, realisations in terms of the eigenvalue PDF of ensembles involving triangular matrices ar","authors_text":"Dong Wang, Peter J. Forrester","cross_cats":["math.CA","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-02-25T12:19:39Z","title":"Muttalib--Borodin ensembles in random matrix theory --- realisations and correlation functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07147","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:f0a9749867d883c517f0e0123ae12843ba6575f402b2d4bd0d3b7c1fd7a241aa","target":"record","created_at":"2026-05-18T00:44:39Z","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":"444420ecd5911b3e9de32ad9c2deeb8e592f6ce7bfa9f445bcbafa9304f7b556","cross_cats_sorted":["math.CA","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-02-25T12:19:39Z","title_canon_sha256":"2a32efeba241bc5cd5b373af82a7b06afa633cd6f1f623df93943c39431ed925"},"schema_version":"1.0","source":{"id":"1502.07147","kind":"arxiv","version":4}},"canonical_sha256":"aedd4f2a1b97b800d2f423a7356cea1d114efc4046df3b7c081ea9db7dc0bb7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aedd4f2a1b97b800d2f423a7356cea1d114efc4046df3b7c081ea9db7dc0bb7f","first_computed_at":"2026-05-18T00:44:39.123161Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:39.123161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QrmHBGQaESQzP+ShbEUNNsTAyVdzdK4TBR6Y6GIvpcohGrZ/KKMbJMVRpGxUOgOM3EOhOyXu/fcl3+FIcd9FBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:39.123560Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.07147","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0a9749867d883c517f0e0123ae12843ba6575f402b2d4bd0d3b7c1fd7a241aa","sha256:74a2f4cb215636bc2c8daa39787f0693ec20b7865aeabea83d75ea5f90a4022c"],"state_sha256":"35029773669eaa1d7b83913e4914d513d3c2d5d6ba68782e9edb54744168adf0"}