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Consider the group measure space von Neumann algebra $\\mathscr M = \\operatorname{L}(\\Gamma \\curvearrowright G/H)$ associated with the nonsingular action $\\Gamma \\curvearrowright G/H$ and regard the group von Neumann algebra $M = \\operatorname{L}(\\Gamma)$ as a von Neumann subalgebra $M \\subset \\mathscr M$. We show that the group $\\operatorname{Aut}_M(\\mathscr M)$ of all unital normal $\\ast$-automorphisms of $\\mathsc"},"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":"2508.08194","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2025-08-11T17:13:09Z","cross_cats_sorted":["math.DS","math.GR"],"title_canon_sha256":"da2f30fe4e62176035ecc7bb90efbfdbb0006303a0770e9fc2595aedb26cb620","abstract_canon_sha256":"29b7ef93e6c09859cb7ee8b2cb3e0583195bc9b694670526c5949ceff7163a20"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:04:15.797954Z","signature_b64":"cOfEJ7/JefFtE0uTWztUzODp/skjSrNBD2FBKvgP0RpV0KCXdcy6otBylnkB6OgCty59MvWqXlyOsrES2XHZCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6da06f1bc695491da4e001a6f7802428fc4e7f8971f15381f6170f9a0723dfb1","last_reissued_at":"2026-05-21T01:04:15.797220Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:04:15.797220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weyl groups and rigidity of von Neumann algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS","math.GR"],"primary_cat":"math.OA","authors_text":"Adrian Ioana, Cyril Houdayer","submitted_at":"2025-08-11T17:13:09Z","abstract_excerpt":"Let $G$ be a noncompact semisimple algebraic group with trivial center, $S < G$ a maximal split torus, $H < G$ the centralizer of $S$ in $G$ and $\\Gamma < G$ an irreducible lattice. Consider the group measure space von Neumann algebra $\\mathscr M = \\operatorname{L}(\\Gamma \\curvearrowright G/H)$ associated with the nonsingular action $\\Gamma \\curvearrowright G/H$ and regard the group von Neumann algebra $M = \\operatorname{L}(\\Gamma)$ as a von Neumann subalgebra $M \\subset \\mathscr M$. We show that the group $\\operatorname{Aut}_M(\\mathscr M)$ of all unital normal $\\ast$-automorphisms of $\\mathsc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.08194","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.08194/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2508.08194","created_at":"2026-05-21T01:04:15.797305+00:00"},{"alias_kind":"arxiv_version","alias_value":"2508.08194v3","created_at":"2026-05-21T01:04:15.797305+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.08194","created_at":"2026-05-21T01:04:15.797305+00:00"},{"alias_kind":"pith_short_12","alias_value":"NWQG6G6GSVER","created_at":"2026-05-21T01:04:15.797305+00:00"},{"alias_kind":"pith_short_16","alias_value":"NWQG6G6GSVER3JHA","created_at":"2026-05-21T01:04:15.797305+00:00"},{"alias_kind":"pith_short_8","alias_value":"NWQG6G6G","created_at":"2026-05-21T01:04:15.797305+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NWQG6G6GSVER3JHAAGTPPABEFD","json":"https://pith.science/pith/NWQG6G6GSVER3JHAAGTPPABEFD.json","graph_json":"https://pith.science/api/pith-number/NWQG6G6GSVER3JHAAGTPPABEFD/graph.json","events_json":"https://pith.science/api/pith-number/NWQG6G6GSVER3JHAAGTPPABEFD/events.json","paper":"https://pith.science/paper/NWQG6G6G"},"agent_actions":{"view_html":"https://pith.science/pith/NWQG6G6GSVER3JHAAGTPPABEFD","download_json":"https://pith.science/pith/NWQG6G6GSVER3JHAAGTPPABEFD.json","view_paper":"https://pith.science/paper/NWQG6G6G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2508.08194&json=true","fetch_graph":"https://pith.science/api/pith-number/NWQG6G6GSVER3JHAAGTPPABEFD/graph.json","fetch_events":"https://pith.science/api/pith-number/NWQG6G6GSVER3JHAAGTPPABEFD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NWQG6G6GSVER3JHAAGTPPABEFD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NWQG6G6GSVER3JHAAGTPPABEFD/action/storage_attestation","attest_author":"https://pith.science/pith/NWQG6G6GSVER3JHAAGTPPABEFD/action/author_attestation","sign_citation":"https://pith.science/pith/NWQG6G6GSVER3JHAAGTPPABEFD/action/citation_signature","submit_replication":"https://pith.science/pith/NWQG6G6GSVER3JHAAGTPPABEFD/action/replication_record"}},"created_at":"2026-05-21T01:04:15.797305+00:00","updated_at":"2026-05-21T01:04:15.797305+00:00"}