{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:KDYFBQ6UJZIY3LUESNPL56Q2EC","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":"6e7dd328887a5eb36b7fb4c21ae20edbf7437668ffdb1c8ca6cab24d2d3282ad","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-03-16T15:29:10Z","title_canon_sha256":"5a48370ab68465662ffc0fbba4aded2da68db4f7697c2294ae28c6e257578069"},"schema_version":"1.0","source":{"id":"1203.3737","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3737","created_at":"2026-05-18T02:27:41Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3737v3","created_at":"2026-05-18T02:27:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3737","created_at":"2026-05-18T02:27:41Z"},{"alias_kind":"pith_short_12","alias_value":"KDYFBQ6UJZIY","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KDYFBQ6UJZIY3LUE","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KDYFBQ6U","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:10c57283830879e5cba50bb6100ffa10c07ddd999d5d5c409821446e5492f193","target":"graph","created_at":"2026-05-18T02:27:41Z","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":"Let ${\\cal A}_1$ be the class of all unital separable simple $C^*$-algebras $A$ such that $A\\otimes U$ has tracial rank at most one for all UHF-algebras of infinite type. It has been shown that amenable ${\\cal Z}$-stable $C^*$-algebras in ${\\cal A}_1$ which satisfy the Universal Coefficient Theorem can be classified up to isomorphism by the Elliott invariant. We show that $A\\in {\\cal A}_1$ if and only if $A\\otimes B$ has tracial rank at most one for one of unital simple infinite dimensional AF-algebra $B.$ In fact, we show that $A\\in {\\cal A}_1$ if and only if $A\\otimes B\\in {\\cal A}_1$ for so","authors_text":"Huaxin Lin, Wei Sun","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-03-16T15:29:10Z","title":"Tensor Products of Classifiable C*-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3737","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:e40d3521ba83f0439feb176f5c2ed001a5bf3916dae985515673567dd63e78f7","target":"record","created_at":"2026-05-18T02:27:41Z","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":"6e7dd328887a5eb36b7fb4c21ae20edbf7437668ffdb1c8ca6cab24d2d3282ad","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-03-16T15:29:10Z","title_canon_sha256":"5a48370ab68465662ffc0fbba4aded2da68db4f7697c2294ae28c6e257578069"},"schema_version":"1.0","source":{"id":"1203.3737","kind":"arxiv","version":3}},"canonical_sha256":"50f050c3d44e518dae84935ebefa1a20bd2fbfc91fc0ab9eb48a0e35c937acbc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50f050c3d44e518dae84935ebefa1a20bd2fbfc91fc0ab9eb48a0e35c937acbc","first_computed_at":"2026-05-18T02:27:41.316915Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:41.316915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VFwS4XuFxcV3Do735WF6FJvw4aqe6fI5HgoY41Lf6vNDe4y7Gpm7RpI3OpZ1N9pYqqkkOpMQRwkNUYxGgDAkDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:41.317858Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.3737","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e40d3521ba83f0439feb176f5c2ed001a5bf3916dae985515673567dd63e78f7","sha256:10c57283830879e5cba50bb6100ffa10c07ddd999d5d5c409821446e5492f193"],"state_sha256":"074dccedc9f690852d3502acd982dfd64fed9e733aedc62731eac70451c93aea"}