{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:GIXHYAPVI4MOMTXOORRZQZQKHZ","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":"6d3b61d5ceb167339b3e2a5643c5faaf009d718d6936cafe710aea2b16fbbd2b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-11-03T23:06:59Z","title_canon_sha256":"42739592bd18a0467c5cf58f8012553341fe63c41ed148496b30a44e0e493675"},"schema_version":"1.0","source":{"id":"1011.1032","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.1032","created_at":"2026-05-18T04:35:36Z"},{"alias_kind":"arxiv_version","alias_value":"1011.1032v3","created_at":"2026-05-18T04:35:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1032","created_at":"2026-05-18T04:35:36Z"},{"alias_kind":"pith_short_12","alias_value":"GIXHYAPVI4MO","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GIXHYAPVI4MOMTXO","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GIXHYAPV","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:8973f2edb6c9f3ab689747b64d84dd6834f654a98b81e85cd6e5956367182c53","target":"graph","created_at":"2026-05-18T04:35:36Z","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 provide a direct and elementary proof of the equivalence between the weak asymptotic homomorphism property for the pair of group von Neumann algebras $L(H)\\subset L(G)$ and the embedding into $H$ of the one sided quasi-normalizer of the pair $H<G$, as it is stated by J. Fang, M. Gao and R. R. Smith in a recent article, and we extend the result to triples of groups $H<K<G$.","authors_text":"Paul Jolissaint","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-11-03T23:06:59Z","title":"On the Relative Weak Asymptotic Homomorphism Property for Triples of Groups von Neumann Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1032","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:a58762f658e972afe7aa249e56453dbd9ad45423b6d11a3a4b3b2a4ad660257c","target":"record","created_at":"2026-05-18T04:35:36Z","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":"6d3b61d5ceb167339b3e2a5643c5faaf009d718d6936cafe710aea2b16fbbd2b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-11-03T23:06:59Z","title_canon_sha256":"42739592bd18a0467c5cf58f8012553341fe63c41ed148496b30a44e0e493675"},"schema_version":"1.0","source":{"id":"1011.1032","kind":"arxiv","version":3}},"canonical_sha256":"322e7c01f54718e64eee746398660a3e69b85b7b66b5bfdcd9bd887ad15c3dd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"322e7c01f54718e64eee746398660a3e69b85b7b66b5bfdcd9bd887ad15c3dd4","first_computed_at":"2026-05-18T04:35:36.314389Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:36.314389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AiJPuZZcPIEUh+l/iBVqMGdxR3vxOix9hey8WMEvn47B5Xq/w207H8r/qsw5J/a6oH/ow2zc/MUChkV/3lR5Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:36.314998Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.1032","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a58762f658e972afe7aa249e56453dbd9ad45423b6d11a3a4b3b2a4ad660257c","sha256:8973f2edb6c9f3ab689747b64d84dd6834f654a98b81e85cd6e5956367182c53"],"state_sha256":"25a4312874a8992e74864e7014c8d18ede99337c4a9ddbc1b26e1a44ac61f503"}