{"paper":{"title":"Periodic quasiflats in hierarchically hyperbolic spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GT","math.MG"],"primary_cat":"math.GR","authors_text":"Mark Hagen, P\\'en\\'elope Azuelos","submitted_at":"2026-08-02T21:50:50Z","abstract_excerpt":"We prove a quasiflat closing theorem and a coarse flat torus theorem for hierarchically hyperbolic groups (HHGs). Namely, given an HHG $G$, we prove that $G$ is hyperbolic if and only if it contains no $\\mathbb Z^2$ subgroups and, if $A\\leq G$ is virtually $\\mathbb Z^n$, then there is an $A$--invariant $n$--dimensional uniform quality quasiflat $F$ such that any two points in $F$ are joined by a uniform-quality hierarchy path lying in $F$. The later is a consequence of a more detailed theorem describing a ``coarse minset'' for $A$ in $G$, which has various applications, including an ascending "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.01513","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/2608.01513/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"}