{"paper":{"title":"Homogeneous hypersurfaces of the four-dimensional Thurston geometries $\\mathrm{Sol}_1^4$, $\\mathrm{Sol}_{m,n}^4$ and $\\mathrm{Nil}^4$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Xiaoge Lu, Xi Zhang, Zeke Yao","submitted_at":"2026-06-29T13:06:11Z","abstract_excerpt":"In this paper, we focus on the four-dimensional Thurston geometries whose isometry groups are four-dimensional, namely $\\mathrm{Sol}_1^4$, $\\mathrm{Sol}_{m,n}^4$ and $\\mathrm{Nil}^4$. We classify homogeneous hypersurfaces in the above three manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30257","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/2606.30257/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"}