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This provides a counterexample to Connes' rigidity conjecture for ICC property (T) groups. This result was obtained with assistance from GPT-5.6 Sol, independently of and concurrently with work by OpenAI."},"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":"2608.02327","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2026-08-03T14:50:28Z","cross_cats_sorted":["math.DS","math.GR"],"title_canon_sha256":"fd378a4ea5bcfe92dba38ba52d4cf2660557769d8ca8516f497fcf6416388ee9","abstract_canon_sha256":"be0cc727c296980f0e6f878de8dde2d70e3932ae07c1de9e5f63349258d906af"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-04T02:11:49.349262Z","signature_b64":"jQwscPNzwCte5rs9bp6s0g1lU9txmNCYnykToEnJTZRaNzQhbkcjepwG9s/4z+GnwdmtldaCRJCifoaOt7t9DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6ba6b16a4efdeedf490a1321bc702b1fc54e8b4ccc9c40163f8beb3ffb2715c","last_reissued_at":"2026-08-04T02:11:49.347790Z","signature_status":"signed_v1","first_computed_at":"2026-08-04T02:11:49.347790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"ICC property(T) groups without W$^*$-superrigidity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GR"],"primary_cat":"math.OA","authors_text":"Shuoxing Zhou","submitted_at":"2026-08-03T14:50:28Z","abstract_excerpt":"We construct two explicit countable discrete groups $\\Gamma_1$ and $\\Gamma_2$ that are both ICC and have Kazhdan's property (T). Although $\\Gamma_1$ and $\\Gamma_2$ are not isomorphic as groups, their group von Neumann algebras are isomorphic: $L(\\Gamma_1)\\cong L(\\Gamma_2)$. This provides a counterexample to Connes' rigidity conjecture for ICC property (T) groups. 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