{"paper":{"title":"Classification of indecomposable states on the infinite symmetric inverse semigroup invariant under the infinite symmetric group. Semifinite case","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Artem Dudko, Nikolay I. Nessonov","submitted_at":"2025-08-19T11:57:29Z","abstract_excerpt":"Let $\\mathbb{N}$ be a set of the natural numbers.\n  Symmetric inverse semigroup $R_\\infty$ is the semigroup of all infinite 0-1 matrices $[g_{ij}]$ with at most one 1 in each row and each column such that $g_{ii}=1$ on the complement of a finite set. The binary operation in $R_\\infty$ is the ordinary matrix multiplication. It is clear that infinite symmetric group $\\mathfrak{S}_\\infty$ is a subgroup of $R_\\infty$. The map $\\star:\\left[ g_{ij}\\right]\\mapsto\\left[ g_{ji}\\right]$ is an involution on $R_\\infty$. We call a function $f$ on $R_\\infty$ positive definite if for all $r_1, r_2, \\ldots, r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.13760","kind":"arxiv","version":2},"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/2508.13760/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"}