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A corollary of this is that there are, for all $n\\geq 2$, non-arithmetic lattices in PO(n,1) that are not commensurable with the Gromov--Piatetski-Shapiro lattices."},"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":"1412.4961","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-12-16T11:46:48Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"e0a7b338f539de282ad3c950309dd9a3b1634e9d0a3f2275586fca23a45ecf74","abstract_canon_sha256":"8004582f66d647ccacb7c53c7df55836f9c63ce0145ab1deee00e52e60456a3b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:46:13.781176Z","signature_b64":"H/XDhS/ARYOPSZYB2qCrOtlazwJS2VeQeHnVVQI8V/C83jvdPv6RTRkJHarhU8D9NqWroEZVdyDmkbMPG1rUAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3599dbe31940441fcf6aae3a659bc054be9e86a94ed2352507235599359f6ec","last_reissued_at":"2026-05-18T01:46:13.780534Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:46:13.780534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quasi-arithmeticity of lattices in PO(n,1)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Scott Thomson","submitted_at":"2014-12-16T11:46:48Z","abstract_excerpt":"We show that the non-arithmetic lattices in PO(n,1) of Belolipetsky and Thomson (2011), obtained as fundamental groups of closed hyperbolic manifolds with short systole, are quasi-arithmetic in the sense of Vinberg, and, by contrast, the well-known non-arithmetic lattices of Gromov and Piatetski-Shapiro are not quasi-arithmetic. 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