{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:L4GKNEBNQFGEMDA5D2E4YTZIHZ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4a3c89c61d13c300bf5d6196ea940c77a6d14ed4f1d5c75ef05b83ef6c647e8b","cross_cats_sorted":["math.DS","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-11-07T18:42:19Z","title_canon_sha256":"af805815aa047de06360e9fb4285db138a43918b1500e5f3c89cc03bc27094a1"},"schema_version":"1.0","source":{"id":"1611.02209","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.02209","created_at":"2026-05-18T00:33:44Z"},{"alias_kind":"arxiv_version","alias_value":"1611.02209v2","created_at":"2026-05-18T00:33:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02209","created_at":"2026-05-18T00:33:44Z"},{"alias_kind":"pith_short_12","alias_value":"L4GKNEBNQFGE","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"L4GKNEBNQFGEMDA5","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"L4GKNEBN","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:765dd80c0981b61eb7768e8d87483487879cb6a65e9f1c7e4a2ff197572ff2af","target":"graph","created_at":"2026-05-18T00:33:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove that if $\\Gamma$ is an icc irreducible lattice in a product of connected non-compact rank one simple Lie groups with finite center, then the II$_1$ factor $L(\\Gamma)$ is prime. In particular, we deduce that the II$_1$ factors associated to the arithmetic groups $\\text{PSL}_2(\\mathbb Z[\\sqrt{d}])$ and $\\text{PSL}_2(\\mathbb Z[S^{-1}])$ are prime, for any square-free integer $d\\geq 2$ with $d\\not\\equiv 1 mod{4}$ and any finite non-empty set of primes $S$. This provides the first examples of prime II$_1$ factors arising from lattices in higher rank semisimple Lie groups. More generally, w","authors_text":"Adrian Ioana, Daniel Drimbe, Daniel Hoff","cross_cats":["math.DS","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-11-07T18:42:19Z","title":"Prime II$_1$ factors arising from irreducible lattices in products of rank one simple Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02209","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:52ca4f3bde505043f57bdd055a500022441807b6743684b31ee59c15a0727477","target":"record","created_at":"2026-05-18T00:33:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4a3c89c61d13c300bf5d6196ea940c77a6d14ed4f1d5c75ef05b83ef6c647e8b","cross_cats_sorted":["math.DS","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-11-07T18:42:19Z","title_canon_sha256":"af805815aa047de06360e9fb4285db138a43918b1500e5f3c89cc03bc27094a1"},"schema_version":"1.0","source":{"id":"1611.02209","kind":"arxiv","version":2}},"canonical_sha256":"5f0ca6902d814c460c1d1e89cc4f283e41d18a14b033f014b498153817ea2375","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f0ca6902d814c460c1d1e89cc4f283e41d18a14b033f014b498153817ea2375","first_computed_at":"2026-05-18T00:33:44.032963Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:44.032963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qSEwC5sb7wggeUB2yE2BZ33/67/1OMF9szjqwtDXQQk9b+vbCrB6nJjNib5ugEXotaXmQ4+JJZXupRnqLd5oAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:44.033470Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.02209","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52ca4f3bde505043f57bdd055a500022441807b6743684b31ee59c15a0727477","sha256:765dd80c0981b61eb7768e8d87483487879cb6a65e9f1c7e4a2ff197572ff2af"],"state_sha256":"eedde8d84dcb6a4b4e11dfd95336a70d32a8ecdabaaa3912df4c2b9ccd12b9d7"}