{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:COCNSEFK7SEIGUFD74TRPCX7CE","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":"6555f8f3a8816a65a416497998d1e6a915f4067190ae379011696e716a316dc3","cross_cats_sorted":["math.DS","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2026-07-02T17:20:11Z","title_canon_sha256":"0ff689cec16873e3c878dcdf2c14e52323c13bb772406c7b2034350d2ca26446"},"schema_version":"1.0","source":{"id":"2607.02450","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.02450","created_at":"2026-07-03T01:17:59Z"},{"alias_kind":"arxiv_version","alias_value":"2607.02450v1","created_at":"2026-07-03T01:17:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.02450","created_at":"2026-07-03T01:17:59Z"},{"alias_kind":"pith_short_12","alias_value":"COCNSEFK7SEI","created_at":"2026-07-03T01:17:59Z"},{"alias_kind":"pith_short_16","alias_value":"COCNSEFK7SEIGUFD","created_at":"2026-07-03T01:17:59Z"},{"alias_kind":"pith_short_8","alias_value":"COCNSEFK","created_at":"2026-07-03T01:17:59Z"}],"graph_snapshots":[{"event_id":"sha256:9205f6cdf18ec1fa74d9120c465b5237c587e6fc3d67f72fdf5a20f712cf6a3c","target":"graph","created_at":"2026-07-03T01:17:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.02450/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $G$ be a real connected semisimple Lie group with trivial center, no non-trivial compact factors, and all simple factors of real rank at least two. Let $\\Gamma<G$ be an irreducible lattice, let $P<G$ be a minimal parabolic subgroup, and consider the crossed product $L^\\infty(G/P,\\nu_P)\\rtimes \\Gamma$. We prove that every $\\Gamma$-invariant von Neumann subalgebra of $L^\\infty(G/P,\\nu_P)\\rtimes \\Gamma$ is of the form $L^\\infty(G/Q,\\nu_Q)\\rtimes \\Lambda$, where $P\\leq Q\\leq G$ and $\\Lambda\\lhd\\Gamma$. This confirms a conjecture of Amrutam--Hartman.","authors_text":"Shuoxing Zhou","cross_cats":["math.DS","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2026-07-02T17:20:11Z","title":"On invariant subalgebras of noncommutative Poisson boundaries for higher rank lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02450","kind":"arxiv","version":1},"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":"sha256:51a5351f1b9e797b75caa5409d08e93d62446587fe33d983ca832ff5082a8fb9","target":"record","created_at":"2026-07-03T01:17:59Z","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":"6555f8f3a8816a65a416497998d1e6a915f4067190ae379011696e716a316dc3","cross_cats_sorted":["math.DS","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2026-07-02T17:20:11Z","title_canon_sha256":"0ff689cec16873e3c878dcdf2c14e52323c13bb772406c7b2034350d2ca26446"},"schema_version":"1.0","source":{"id":"2607.02450","kind":"arxiv","version":1}},"canonical_sha256":"1384d910aafc888350a3ff27178aff110b21dfb53026197cb7e2e1312b686452","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1384d910aafc888350a3ff27178aff110b21dfb53026197cb7e2e1312b686452","first_computed_at":"2026-07-03T01:17:59.512291Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-03T01:17:59.512291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xsvbE8VBCcWMdw6yg3fbYZnkwKXVynC8Dcc4FNB1HK1uE5+7JvXBMAYDWkvCLWx6OIBKNbRQc83+eajUQa6IBQ==","signature_status":"signed_v1","signed_at":"2026-07-03T01:17:59.512719Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.02450","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51a5351f1b9e797b75caa5409d08e93d62446587fe33d983ca832ff5082a8fb9","sha256:9205f6cdf18ec1fa74d9120c465b5237c587e6fc3d67f72fdf5a20f712cf6a3c"],"state_sha256":"95a058c114205efb74bfd7ade7fd8fcc2da68dea34ef791081598786066415b1"}