{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:I7OJMTHM4FVPRVX7VSV5XYJS6Z","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":"38b6b20f250da9a9919b09263fe6bd998d1fcb45217b78924c144c77fbd79e98","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-02-06T00:22:02Z","title_canon_sha256":"15013e0e178a3776e5bb9470939f5f0646c60b086207f46f8a561b30d7bcf300"},"schema_version":"1.0","source":{"id":"1204.6343","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.6343","created_at":"2026-05-18T03:07:32Z"},{"alias_kind":"arxiv_version","alias_value":"1204.6343v3","created_at":"2026-05-18T03:07:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.6343","created_at":"2026-05-18T03:07:32Z"},{"alias_kind":"pith_short_12","alias_value":"I7OJMTHM4FVP","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"I7OJMTHM4FVPRVX7","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"I7OJMTHM","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:ed3fbd897e6eb1e3d2ac235fe688a8cf982505521811966f90761ebc284557ce","target":"graph","created_at":"2026-05-18T03:07:32Z","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 construct a singly generated subalgebra of ${\\mathcal K}({\\mathcal H})$ which is non-amenable, yet is boundedly approximately contractible. The example embeds into a homogeneous von Neumann algebra. We also observe that there are singly generated, biflat subalgebras of finite Type I von Neumann algebras, which are not amenable (and hence are not isomorphic to C*-algebras). Such an example can be used to show that a certain extension property for commutative operator algebras, which is shown in arXiv:1012.4259 to follow from amenability, does not necessarily imply amenability.","authors_text":"Yemon Choi","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-02-06T00:22:02Z","title":"Singly generated operator algebras satisfying weakened versions of amenability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.6343","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:d9d76605b2a632a3eedab4cbc8fd0a230c32a8866c1027deac1b011452b41afe","target":"record","created_at":"2026-05-18T03:07:32Z","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":"38b6b20f250da9a9919b09263fe6bd998d1fcb45217b78924c144c77fbd79e98","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-02-06T00:22:02Z","title_canon_sha256":"15013e0e178a3776e5bb9470939f5f0646c60b086207f46f8a561b30d7bcf300"},"schema_version":"1.0","source":{"id":"1204.6343","kind":"arxiv","version":3}},"canonical_sha256":"47dc964cece16af8d6ffacabdbe132f66fed26617cee1ba9f45b0fe9f7e77839","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47dc964cece16af8d6ffacabdbe132f66fed26617cee1ba9f45b0fe9f7e77839","first_computed_at":"2026-05-18T03:07:32.081517Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:32.081517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OtJnL9g9EiAvGpTQPTC9+rStsK+/Pn6Foi44Q36Ju7sdpLPyHUyDIpR7sxQeXEf/TLFvy7sMRnzGcWOUDUOhBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:32.081903Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.6343","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9d76605b2a632a3eedab4cbc8fd0a230c32a8866c1027deac1b011452b41afe","sha256:ed3fbd897e6eb1e3d2ac235fe688a8cf982505521811966f90761ebc284557ce"],"state_sha256":"a7cc4a10acfd3206adf92f4076efd3f542b21b9bd1d6f0cf63d1a0ca5ec39ba6"}