{"paper":{"title":"Pal's permanent conjecture: proof for block uniform matrices","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.CO","authors_text":"Andrea Ottolini, Shannon Starr","submitted_at":"2026-05-24T22:02:13Z","abstract_excerpt":"Consider a symmetric function $\\mathcal{C}(x,y)$ on $[0,1]\\times[0,1]$ which is twice continuously differentiable up to the boundary, and which satisfies $ \\mathcal{C}(x,y)=\\mathcal{C}(1-x,1-y)$. Let $A^{(n)} = \\big(a^{(n)}_{i,j}\\, :\\, i,j \\in [n]\\big)$ be the matrix with entries $a^{(n)}_{i,j}\\, =\\, \\exp(-\\mathcal{C}(i/n,j/n))$. Soumik Pal conjectured the asymptotics $$\\operatorname{perm}\\big(A^{(n)}\\big)/n!\\sim \\exp\\big(n \\Lambda[\\mathcal{C}]\\big)/ \\sqrt{\\mathcal{D}[\\mathcal{C}]}$$ as $n \\to \\infty$ for known functionals that arise naturally in the context of entropy regularized optimal tran"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25274","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/2605.25274/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"}