{"paper":{"title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Christopher D. Sinclair, Jonathan M. Wells","submitted_at":"2025-09-05T20:28:29Z","abstract_excerpt":"We give a hyperpfaffian formulation for correlation functions in $\\beta$-ensembles of $M \\times M$ random matrices when $\\beta = L^2$ is an even square integer. More specifically, to the $m$th correlation function $R_m : \\R^m \\rightarrow [0, \\infty)$ we associate the $L$-vector valued function $\\omega_m : \\R^m \\rightarrow \\Lambda^L \\R^{L(M-m)}$ such that $R_m(\\mathbf y)$ is given by the Vandermonde determinant in $y_1, \\ldots, y_M$ times the hyperpfaffian of $\\omega_m.$ The partition function of the ensemble was previously shown to be the hyperpfaffian of a {\\it Gram} $L$-form $\\omega$ in $\\La"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.05487","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.05487/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}