{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:UU7XABXHU4EZ5NG2LPKQCXPWJ6","short_pith_number":"pith:UU7XABXH","canonical_record":{"source":{"id":"1002.4790","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-02-25T14:09:00Z","cross_cats_sorted":[],"title_canon_sha256":"29813edac6c32d75d264ff65d7686647d71439df90204367765c630d0faf4018","abstract_canon_sha256":"4f03107f1f1207a7db7ecf2dfea45004c29470242fddc90c7ca11b31cbd82398"},"schema_version":"1.0"},"canonical_sha256":"a53f7006e7a7099eb4da5bd5015df64fa4477069ee53cb99cc16f60aeb76693b","source":{"kind":"arxiv","id":"1002.4790","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.4790","created_at":"2026-05-18T04:37:20Z"},{"alias_kind":"arxiv_version","alias_value":"1002.4790v2","created_at":"2026-05-18T04:37:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.4790","created_at":"2026-05-18T04:37:20Z"},{"alias_kind":"pith_short_12","alias_value":"UU7XABXHU4EZ","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"UU7XABXHU4EZ5NG2","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"UU7XABXH","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:UU7XABXHU4EZ5NG2LPKQCXPWJ6","target":"record","payload":{"canonical_record":{"source":{"id":"1002.4790","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-02-25T14:09:00Z","cross_cats_sorted":[],"title_canon_sha256":"29813edac6c32d75d264ff65d7686647d71439df90204367765c630d0faf4018","abstract_canon_sha256":"4f03107f1f1207a7db7ecf2dfea45004c29470242fddc90c7ca11b31cbd82398"},"schema_version":"1.0"},"canonical_sha256":"a53f7006e7a7099eb4da5bd5015df64fa4477069ee53cb99cc16f60aeb76693b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:37:20.758659Z","signature_b64":"lnrwakL/EDUXyr5VN2Hmr98PS+py7grC5oKZAD2u1+/MQwAS6plGqGOFvguZtog2D5CmWmoTW/Ecao6mUsU+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a53f7006e7a7099eb4da5bd5015df64fa4477069ee53cb99cc16f60aeb76693b","last_reissued_at":"2026-05-18T04:37:20.758121Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:37:20.758121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.4790","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:37:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GqZ8XRB3NawvM+zisUA2q/5pjT4sDHlE3FwTvFBYGvJp7xFBJDnGoG2EWAV1bFHIQvV/eKhgLC9RoypYcOk+Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:32:49.949285Z"},"content_sha256":"ce28681b8d99e35f4fa6e0c625d0a27277367793151ebdeabfd162fee1b90f59","schema_version":"1.0","event_id":"sha256:ce28681b8d99e35f4fa6e0c625d0a27277367793151ebdeabfd162fee1b90f59"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:UU7XABXHU4EZ5NG2LPKQCXPWJ6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classification of homomorphisms into simple Z-stable C^*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Hiroki Matui","submitted_at":"2010-02-25T14:09:00Z","abstract_excerpt":"We classify unital monomorphisms into certain simple Z-stable C^*-algebras up to approximate unitary equivalence. The domain algebra C is allowed to be any unital separable commutative C^*-algebra, or any unital simple separable nuclear Z-stable C^*-algebra satisfying the UCT such that C\\otimes B is of tracial rank zero for a UHF algebra B. The target algebra A is allowed to be any unital simple separable Z-stable C^*-algebra such that A\\otimes B has tracial rank zero for a UHF algebra B, or any unital simple separable exact Z-stable C^*-algebra whose projections separate traces and whose extr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.4790","kind":"arxiv","version":2},"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":"2026-05-18T04:37:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IMMdOAQfBHEM8X5o9I/hO2n0Njv1GcflFBh2Cn4xaqIx+qw7ACOm8gCj5BSfaj0gcH4g4lpFEzuM7+Ex36UyAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:32:49.949651Z"},"content_sha256":"a2f1a42441bd9f0bbbed383c3e9d5c967cbab10d82996d85e5c3d9eb96fab1d7","schema_version":"1.0","event_id":"sha256:a2f1a42441bd9f0bbbed383c3e9d5c967cbab10d82996d85e5c3d9eb96fab1d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UU7XABXHU4EZ5NG2LPKQCXPWJ6/bundle.json","state_url":"https://pith.science/pith/UU7XABXHU4EZ5NG2LPKQCXPWJ6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UU7XABXHU4EZ5NG2LPKQCXPWJ6/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":"2026-06-03T01:32:49Z","links":{"resolver":"https://pith.science/pith/UU7XABXHU4EZ5NG2LPKQCXPWJ6","bundle":"https://pith.science/pith/UU7XABXHU4EZ5NG2LPKQCXPWJ6/bundle.json","state":"https://pith.science/pith/UU7XABXHU4EZ5NG2LPKQCXPWJ6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UU7XABXHU4EZ5NG2LPKQCXPWJ6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:UU7XABXHU4EZ5NG2LPKQCXPWJ6","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":"4f03107f1f1207a7db7ecf2dfea45004c29470242fddc90c7ca11b31cbd82398","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-02-25T14:09:00Z","title_canon_sha256":"29813edac6c32d75d264ff65d7686647d71439df90204367765c630d0faf4018"},"schema_version":"1.0","source":{"id":"1002.4790","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.4790","created_at":"2026-05-18T04:37:20Z"},{"alias_kind":"arxiv_version","alias_value":"1002.4790v2","created_at":"2026-05-18T04:37:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.4790","created_at":"2026-05-18T04:37:20Z"},{"alias_kind":"pith_short_12","alias_value":"UU7XABXHU4EZ","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"UU7XABXHU4EZ5NG2","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"UU7XABXH","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:a2f1a42441bd9f0bbbed383c3e9d5c967cbab10d82996d85e5c3d9eb96fab1d7","target":"graph","created_at":"2026-05-18T04:37:20Z","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 classify unital monomorphisms into certain simple Z-stable C^*-algebras up to approximate unitary equivalence. The domain algebra C is allowed to be any unital separable commutative C^*-algebra, or any unital simple separable nuclear Z-stable C^*-algebra satisfying the UCT such that C\\otimes B is of tracial rank zero for a UHF algebra B. The target algebra A is allowed to be any unital simple separable Z-stable C^*-algebra such that A\\otimes B has tracial rank zero for a UHF algebra B, or any unital simple separable exact Z-stable C^*-algebra whose projections separate traces and whose extr","authors_text":"Hiroki Matui","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-02-25T14:09:00Z","title":"Classification of homomorphisms into simple Z-stable C^*-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.4790","kind":"arxiv","version":2},"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:ce28681b8d99e35f4fa6e0c625d0a27277367793151ebdeabfd162fee1b90f59","target":"record","created_at":"2026-05-18T04:37:20Z","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":"4f03107f1f1207a7db7ecf2dfea45004c29470242fddc90c7ca11b31cbd82398","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-02-25T14:09:00Z","title_canon_sha256":"29813edac6c32d75d264ff65d7686647d71439df90204367765c630d0faf4018"},"schema_version":"1.0","source":{"id":"1002.4790","kind":"arxiv","version":2}},"canonical_sha256":"a53f7006e7a7099eb4da5bd5015df64fa4477069ee53cb99cc16f60aeb76693b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a53f7006e7a7099eb4da5bd5015df64fa4477069ee53cb99cc16f60aeb76693b","first_computed_at":"2026-05-18T04:37:20.758121Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:37:20.758121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lnrwakL/EDUXyr5VN2Hmr98PS+py7grC5oKZAD2u1+/MQwAS6plGqGOFvguZtog2D5CmWmoTW/Ecao6mUsU+CA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:37:20.758659Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.4790","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce28681b8d99e35f4fa6e0c625d0a27277367793151ebdeabfd162fee1b90f59","sha256:a2f1a42441bd9f0bbbed383c3e9d5c967cbab10d82996d85e5c3d9eb96fab1d7"],"state_sha256":"262c16358abe8ce1f03650ace640f8facc671a57f1432ae63c308cf34fa5aa56"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HVGYAzP5RsaMkaouswquLXFScM2vqQEOIwQ/RP6NJD3GD4dfW8OyqJcejH2G8zTgsbKDrg/v2m2tXXReYzAeAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T01:32:49.951597Z","bundle_sha256":"3c5314eccc6c86048c82878dc72655f7786e1cd60a2af4d3fd8f4f0d8a42c2a3"}}