{"paper":{"title":"Existential Inclusions of Bi-exact Groups are Conjugacy Representation Rigid","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.LO","math.OA"],"primary_cat":"math.GR","authors_text":"Connor MacMahon","submitted_at":"2026-06-17T17:49:15Z","abstract_excerpt":"If $\\Lambda$ is a non-amenable bi-exact group and $\\Lambda \\hookrightarrow \\Gamma$ is an existential embedding, then each of the intersections $\\Lambda \\cap g \\Lambda g^{-1}$ for $g$ a member of $\\Gamma \\backslash \\Lambda$ is amenable. This in conjunction with work of Bekka and Kalantar demonstrates that in this situation, the weak equivalence class of the quasi-regular representation $\\lambda_{\\Gamma/\\Lambda}$ determines $\\Lambda$ up to conjugacy among the self-commensurating subgroups of $\\Gamma$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19322","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/2606.19322/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"}