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As a consequence, the distortion dimension of an irreducible $\\mathbb{Q}$--rank-$1$ lattice $\\Gamma$ in a linear, semisimple Lie group $G$ of $\\mathbb R$--rank $k$ is $k-1$. That is, given $m< k-1$, a Lipschitz $m$--sphere $S$ in (a polyhedral complex quasi-isometric to) $\\Gamma$, and a $(m+1)$--ball $B$ in $X$ (or $G$) filling $S$, there is a $(m+1)$--bal"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1509.09224","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-09-30T15:33:23Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"04fc92d6f0b048d7dcb1f705d2cfb4a9e8c281e55aa26653c2a0d96d5146ed9a","abstract_canon_sha256":"7e0dac2049f3094b03a30e97af6fb768b168425712a4be071e8c03b2b701ea33"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:26.792666Z","signature_b64":"P6sON6EQpaR1TK2hrDtmD4/M4MC/MDiDmy44q0AfaGm1GxU6kVIzL9OLcv2eRheB5aP1bnfZvzSevaWSDU5iCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0900151f254681b7e91d5f2a3a8d42a0f9d0b5b7df5bfa8d4cc0f50b5ce4d84","last_reissued_at":"2026-05-18T01:31:26.792040Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:26.792040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The distortion dimension of $\\mathbb Q$--rank $1$ lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Enrico Leuzinger, Robert Young","submitted_at":"2015-09-30T15:33:23Z","abstract_excerpt":"Let $X=G/K$ be a symmetric space of noncompact type and rank $k\\ge 2$. 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