{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:JWBOZR3LYU42RNX5LREA5JXWUW","short_pith_number":"pith:JWBOZR3L","canonical_record":{"source":{"id":"1210.6015","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-10-22T19:39:26Z","cross_cats_sorted":[],"title_canon_sha256":"7a91abfe22abb6a81181908ec15db0e629105fbdf837678c25a647e8afaaf763","abstract_canon_sha256":"bee881c66dd93b802703be35b154210746a2e731bffa8c5ce25389035987406f"},"schema_version":"1.0"},"canonical_sha256":"4d82ecc76bc539a8b6fd5c480ea6f6a595ee800959c41af41564a2cb8cb27d7c","source":{"kind":"arxiv","id":"1210.6015","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.6015","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"arxiv_version","alias_value":"1210.6015v1","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6015","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"pith_short_12","alias_value":"JWBOZR3LYU42","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JWBOZR3LYU42RNX5","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JWBOZR3L","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:JWBOZR3LYU42RNX5LREA5JXWUW","target":"record","payload":{"canonical_record":{"source":{"id":"1210.6015","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-10-22T19:39:26Z","cross_cats_sorted":[],"title_canon_sha256":"7a91abfe22abb6a81181908ec15db0e629105fbdf837678c25a647e8afaaf763","abstract_canon_sha256":"bee881c66dd93b802703be35b154210746a2e731bffa8c5ce25389035987406f"},"schema_version":"1.0"},"canonical_sha256":"4d82ecc76bc539a8b6fd5c480ea6f6a595ee800959c41af41564a2cb8cb27d7c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:18.378435Z","signature_b64":"O/qkrpMaRB/m8sh4P8a1/YBlOs8ly6LFtAUfzrdbutiHVASgFmwUqi6iQtUu1EDp/d3B7d5fw/3+gktdgifUCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d82ecc76bc539a8b6fd5c480ea6f6a595ee800959c41af41564a2cb8cb27d7c","last_reissued_at":"2026-05-17T23:53:18.377813Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:18.377813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.6015","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"efd732CLs4bV22ClfFxrf3Udm6OrYZRxgIduYnm6naiDAchbNLxSOHoTbzxf2QlfL3b/sLqjSzxNy3Q42VcBCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T09:56:43.152481Z"},"content_sha256":"0ea85c1b78670cfd9f960021c5a28a1bb70efb66998096a185c5258f04232a09","schema_version":"1.0","event_id":"sha256:0ea85c1b78670cfd9f960021c5a28a1bb70efb66998096a185c5258f04232a09"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:JWBOZR3LYU42RNX5LREA5JXWUW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Similarity Degree of Some C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Don Hadwin, Weihua Li","submitted_at":"2012-10-22T19:39:26Z","abstract_excerpt":"We define the class of weakly approximately divisible unital C*-algebras and show that this class is closed under direct sums, direct limits, any tensor product with any C*-algebra, and quotients. A nuclear C*-algebra is weakly approximately divisible if and only if it has no finite-dimensional representations. We also show that Pisier's similarity degree of a weakly approximately divisible C*-algebra is at most 5."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6015","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+u3wV6RDDfGgCS2Jic7DdcK6QON0KbDfeKGB1XtV4fjn/z+T7T7nVjYkegAlDKttAi/0yFpi9TyPRtgQmSp2Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T09:56:43.152825Z"},"content_sha256":"394879c7b64a1cf577f382b348bcb341656e956ba157de78f414d470b60ae0ae","schema_version":"1.0","event_id":"sha256:394879c7b64a1cf577f382b348bcb341656e956ba157de78f414d470b60ae0ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JWBOZR3LYU42RNX5LREA5JXWUW/bundle.json","state_url":"https://pith.science/pith/JWBOZR3LYU42RNX5LREA5JXWUW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JWBOZR3LYU42RNX5LREA5JXWUW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T09:56:43Z","links":{"resolver":"https://pith.science/pith/JWBOZR3LYU42RNX5LREA5JXWUW","bundle":"https://pith.science/pith/JWBOZR3LYU42RNX5LREA5JXWUW/bundle.json","state":"https://pith.science/pith/JWBOZR3LYU42RNX5LREA5JXWUW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JWBOZR3LYU42RNX5LREA5JXWUW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JWBOZR3LYU42RNX5LREA5JXWUW","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":"bee881c66dd93b802703be35b154210746a2e731bffa8c5ce25389035987406f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-10-22T19:39:26Z","title_canon_sha256":"7a91abfe22abb6a81181908ec15db0e629105fbdf837678c25a647e8afaaf763"},"schema_version":"1.0","source":{"id":"1210.6015","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.6015","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"arxiv_version","alias_value":"1210.6015v1","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6015","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"pith_short_12","alias_value":"JWBOZR3LYU42","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JWBOZR3LYU42RNX5","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JWBOZR3L","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:394879c7b64a1cf577f382b348bcb341656e956ba157de78f414d470b60ae0ae","target":"graph","created_at":"2026-05-17T23:53:18Z","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 define the class of weakly approximately divisible unital C*-algebras and show that this class is closed under direct sums, direct limits, any tensor product with any C*-algebra, and quotients. A nuclear C*-algebra is weakly approximately divisible if and only if it has no finite-dimensional representations. We also show that Pisier's similarity degree of a weakly approximately divisible C*-algebra is at most 5.","authors_text":"Don Hadwin, Weihua Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-10-22T19:39:26Z","title":"The Similarity Degree of Some C*-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6015","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":"sha256:0ea85c1b78670cfd9f960021c5a28a1bb70efb66998096a185c5258f04232a09","target":"record","created_at":"2026-05-17T23:53:18Z","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":"bee881c66dd93b802703be35b154210746a2e731bffa8c5ce25389035987406f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-10-22T19:39:26Z","title_canon_sha256":"7a91abfe22abb6a81181908ec15db0e629105fbdf837678c25a647e8afaaf763"},"schema_version":"1.0","source":{"id":"1210.6015","kind":"arxiv","version":1}},"canonical_sha256":"4d82ecc76bc539a8b6fd5c480ea6f6a595ee800959c41af41564a2cb8cb27d7c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d82ecc76bc539a8b6fd5c480ea6f6a595ee800959c41af41564a2cb8cb27d7c","first_computed_at":"2026-05-17T23:53:18.377813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:18.377813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O/qkrpMaRB/m8sh4P8a1/YBlOs8ly6LFtAUfzrdbutiHVASgFmwUqi6iQtUu1EDp/d3B7d5fw/3+gktdgifUCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:18.378435Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.6015","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ea85c1b78670cfd9f960021c5a28a1bb70efb66998096a185c5258f04232a09","sha256:394879c7b64a1cf577f382b348bcb341656e956ba157de78f414d470b60ae0ae"],"state_sha256":"98e59ff4f158d9a5d6a1529e88904edfe44c9ebed03cc22a45585af2740d2fa4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rDHJ9hkeyZHGaFyliWIh6D4Wg6P/40/7EcLGWi5pOJQOrkvvURx/Ata1CdI0gA0A2fqHggg5BqDJgx7wXVlADg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T09:56:43.154702Z","bundle_sha256":"8f2dfd688d36f9ceaf9cb858f054efd690892d9048eafc56a4400f1b65da1c65"}}