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It is proved in this paper that for $p\\in[1,4/3)\\cup (4,\\infty]$ neither the group $G$ nor its lattices have the property of approximation by Schur multipliers on Schatten $p$ class ($AP_{pcb}^{Schur}$) of Lafforgue and de la Salle. As a consequence, for any lattice $\\Gamma$ in $G,$ the associated non-commutative $L^p$ space $L^p(L\\Gamma)$ of its von Neumann algebra $L(\\Gamma)$ fails the operator space approximation property (OAP) and completely bounded approximation property (CBAP) for $p\\in[1,4/3"},"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":"1509.04814","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-09-16T05:48:03Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"3e183b9c58e1b9cdd471a337941b79e17fbac54544bf09859ffd297d6a760ad7","abstract_canon_sha256":"f2beacf313c96aa8b764ff9d472ff883e449721b6c697f087c12bbe54dac67c5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:51.656377Z","signature_b64":"lXkZPvZDhH+TOZoF6EjlpCm87hUdm4dRvsFccNbKTUoYaENJwvn4fPQ1qy4OaEJRKws5fAb51aRC8h2CFCVFBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"711f6bbead72b0ba90a86298dd47f055d58d57b8739ec5e4e14afb9f321b4d1f","last_reissued_at":"2026-05-18T01:32:51.655711Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:51.655711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximation properties for $p$-adic symplectic groups and lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.OA","authors_text":"Benben Liao","submitted_at":"2015-09-16T05:48:03Z","abstract_excerpt":"Let $G$ be the symplectic group $Sp_4$ over a non Archimedean local field of any characteristic. 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