{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3Z6FPA2SAEKSEZPVKCLJQI2VPH","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":"acd25685288ab457f997f8084ec6c9d0af1b4812f3ac9a5fbee1fdc6a3d6213f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-06-02T19:06:47Z","title_canon_sha256":"1a42d686e9ca2f872186f50506b4a86bc06e094a168b4483f000a4c46650dd8e"},"schema_version":"1.0","source":{"id":"1606.00808","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.00808","created_at":"2026-05-17T23:56:48Z"},{"alias_kind":"arxiv_version","alias_value":"1606.00808v3","created_at":"2026-05-17T23:56:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00808","created_at":"2026-05-17T23:56:48Z"},{"alias_kind":"pith_short_12","alias_value":"3Z6FPA2SAEKS","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"3Z6FPA2SAEKSEZPV","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"3Z6FPA2S","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:a46c4aa00d7bfd9def3414979c1895195d66559ad21378807be8261701262aac","target":"graph","created_at":"2026-05-17T23:56:48Z","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 investigate the position of amenable subalgebras in arbitrary amalgamated free product von Neumann algebras $M = M_1 \\ast_B M_2$. Our main result states that under natural analytic assumptions, any amenable subalgebra of $M$ that has a large intersection with $M_1$ is actually contained in $M_1$. The proof does not rely on Popa's asymptotic orthogonality property but on the study of non normal conditional expectations.","authors_text":"Cyril Houdayer, R\\'emi Boutonnet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-06-02T19:06:47Z","title":"Amenable absorption in amalgamated free product von Neumann algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00808","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:adb048e169f5fa3ffd402a89576e179b0914d645fc92768ceff7bf7abb777fd5","target":"record","created_at":"2026-05-17T23:56:48Z","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":"acd25685288ab457f997f8084ec6c9d0af1b4812f3ac9a5fbee1fdc6a3d6213f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-06-02T19:06:47Z","title_canon_sha256":"1a42d686e9ca2f872186f50506b4a86bc06e094a168b4483f000a4c46650dd8e"},"schema_version":"1.0","source":{"id":"1606.00808","kind":"arxiv","version":3}},"canonical_sha256":"de7c57835201152265f5509698235579fa3ecb029ebe963378c6d7300467cfea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de7c57835201152265f5509698235579fa3ecb029ebe963378c6d7300467cfea","first_computed_at":"2026-05-17T23:56:48.839753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:48.839753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MwYWIwpcIvtS8rBWaqkWPWfm2Yr0lJWViLoa+Srf6eD3Wmff5tGzBbyENh7AyYhdvTUYu6M3HR1Ll8kp818DBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:48.840140Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.00808","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:adb048e169f5fa3ffd402a89576e179b0914d645fc92768ceff7bf7abb777fd5","sha256:a46c4aa00d7bfd9def3414979c1895195d66559ad21378807be8261701262aac"],"state_sha256":"49d9faa460cb62b429daf72f80fe4d031b54af5dda6067888811f315f72fc68d"}