{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:VJGGT2MQZQNE2FZ3BXNNWQWP5H","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":"e65d0d5ae0b9dbbb3fac791c413f9c560d04b0638587872e53d9745eb0c88dbf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2009-12-31T18:42:36Z","title_canon_sha256":"a969168a8466617e2fd25f5a33086bc4da7c16a04706ba4e9965e12e32d08268"},"schema_version":"1.0","source":{"id":"1001.0169","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.0169","created_at":"2026-05-18T04:16:51Z"},{"alias_kind":"arxiv_version","alias_value":"1001.0169v3","created_at":"2026-05-18T04:16:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.0169","created_at":"2026-05-18T04:16:51Z"},{"alias_kind":"pith_short_12","alias_value":"VJGGT2MQZQNE","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"VJGGT2MQZQNE2FZ3","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"VJGGT2MQ","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:a7b465f77eb8dc88f2ba61db02d53162f4a37d16c0f16853ccf93c294a5951f2","target":"graph","created_at":"2026-05-18T04:16:51Z","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":"Jolissaint and Stalder introduced definitions of mixing and weak mixing for von Neumann subalgebras of finite von Neumann algebras. In this note, we study various algebraic and analytical properties of subalgebras with these mixing properties. We prove some basic results about mixing inclusions of von Neumann algebras and establish a connection between mixing properties and normalizers of von Neumann subalgebras. The special case of mixing subalgebras arising from inclusions of countable discrete groups finds applications to ergodic theory, in particular, a new generalization of a classical th","authors_text":"Jan Cameron, Junsheng Fang, Kunal Mukherjee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2009-12-31T18:42:36Z","title":"Mixing subalgebras of finite von Neumann algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.0169","kind":"arxiv","version":3},"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":"sha256:766c82b94362dd1b5126f04cd08db1ed7c858bee2f6640a146e513b8a971318a","target":"record","created_at":"2026-05-18T04:16:51Z","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":"e65d0d5ae0b9dbbb3fac791c413f9c560d04b0638587872e53d9745eb0c88dbf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2009-12-31T18:42:36Z","title_canon_sha256":"a969168a8466617e2fd25f5a33086bc4da7c16a04706ba4e9965e12e32d08268"},"schema_version":"1.0","source":{"id":"1001.0169","kind":"arxiv","version":3}},"canonical_sha256":"aa4c69e990cc1a4d173b0ddadb42cfe9e775eb48a7a4d0e604f4dc5400f7a21a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa4c69e990cc1a4d173b0ddadb42cfe9e775eb48a7a4d0e604f4dc5400f7a21a","first_computed_at":"2026-05-18T04:16:51.843606Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:51.843606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h7A6YLKIOdSSuYAaImAEEsGyLWwRbtyhzeW1vkmxDhwmlPM12tjNT/hqfXQRs0WdC3oBXKRkMSs3sLQXMCJRAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:51.844280Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.0169","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:766c82b94362dd1b5126f04cd08db1ed7c858bee2f6640a146e513b8a971318a","sha256:a7b465f77eb8dc88f2ba61db02d53162f4a37d16c0f16853ccf93c294a5951f2"],"state_sha256":"7c9d62aa9e4954113b42cbca5cd9a58f01b0b7dad855fcfcc6ca1adcfa6dec1e"}