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We deduce that if T_n denotes the group of upper triangular matrices in PSL(n,Z), then any free, mixing p.m.p. action of the amalgamated free product of PSL(n,Z) with itself over T_n, is W*-superrigid, i.e. any isomorphism betwe"},"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":"0906.2765","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2009-06-15T19:04:54Z","cross_cats_sorted":["math.DS","math.GR"],"title_canon_sha256":"15ebadc5a390e4ea30c64922ae34c46cce32edea143efb2b2bdbeb7d944f7e67","abstract_canon_sha256":"b9f0e9c477cdc774ebce398ea3f6448f4527224928dd9abc1d52e065651ade91"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:13:19.989828Z","signature_b64":"voDBDkuIEZnFBbW6xskJar99UPFP2hgRxUQikkf0d5Pe7VrZz2aQmwVV9J9uE/xB56t97rVVHEU4AhRbz47+Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b39c214b1b4bb7d5a4187c8ec1054040aa22402851bf23cdea645b6ef8bd7b7","last_reissued_at":"2026-05-18T02:13:19.989189Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:13:19.989189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Group measure space decomposition of II_1 factors and W*-superrigidity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GR"],"primary_cat":"math.OA","authors_text":"Sorin Popa, Stefaan Vaes","submitted_at":"2009-06-15T19:04:54Z","abstract_excerpt":"We prove a \"unique crossed product decomposition\" result for group measure space II_1 factors arising from arbitrary free ergodic probability measure preserving (p.m.p.) actions of groups \\Gamma in a fairly large family G, which contains all free products of a Kazhdan group and a non-trivial group, as well as certain amalgamated free products over an amenable subgroup. 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