{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CLEOJ3GXR4PRZC3HB3CLYI2VCO","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":"8bf6d21ac5f27e3f77819e3d707e068cf3ac06d78b2a885f651f0fdf0aa2b264","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-06-27T04:23:02Z","title_canon_sha256":"b1051ddfe819a2c348c655ab906232e1cb105e0efe078a94c1f3f06006db99c9"},"schema_version":"1.0","source":{"id":"1206.6168","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.6168","created_at":"2026-05-18T03:52:27Z"},{"alias_kind":"arxiv_version","alias_value":"1206.6168v1","created_at":"2026-05-18T03:52:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.6168","created_at":"2026-05-18T03:52:27Z"},{"alias_kind":"pith_short_12","alias_value":"CLEOJ3GXR4PR","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CLEOJ3GXR4PRZC3H","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CLEOJ3GX","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:b6e5fa1b799a25e633c9e133665381259d82cc2e0e255d7564dfe4603d266137","target":"graph","created_at":"2026-05-18T03:52:27Z","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 A be a unital separable simple C*-algebra such that either (1) A has real rank zero, strict comparison and cancellation or (2) A is TAI. We study the kernel of the de la Harpe--Skandalis determinant on GL^0(A), proving that the determinant vanishes exactly on elements which are products of 8 multiplicative commutators. We also have results for the unitary case.","authors_text":"P. W. Ng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-06-27T04:23:02Z","title":"The kernel of the determinant map on certain simple C*-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6168","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:c1085ec643fb5f750c84f2e73c616e932a0e4e632cd8f58ac19b404621beca8f","target":"record","created_at":"2026-05-18T03:52:27Z","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":"8bf6d21ac5f27e3f77819e3d707e068cf3ac06d78b2a885f651f0fdf0aa2b264","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-06-27T04:23:02Z","title_canon_sha256":"b1051ddfe819a2c348c655ab906232e1cb105e0efe078a94c1f3f06006db99c9"},"schema_version":"1.0","source":{"id":"1206.6168","kind":"arxiv","version":1}},"canonical_sha256":"12c8e4ecd78f1f1c8b670ec4bc235513bcc57330196e638974eba81e108eab02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12c8e4ecd78f1f1c8b670ec4bc235513bcc57330196e638974eba81e108eab02","first_computed_at":"2026-05-18T03:52:27.563925Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:27.563925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UN1/DtcuLGuyPkM+b2PQYeMsyOf83QzOqWYbXhmwavMHvV3XjdRJXLUxElsz9CxGmyRz51GbwzY6fCRjUqTFCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:27.564726Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.6168","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1085ec643fb5f750c84f2e73c616e932a0e4e632cd8f58ac19b404621beca8f","sha256:b6e5fa1b799a25e633c9e133665381259d82cc2e0e255d7564dfe4603d266137"],"state_sha256":"d084fbc9d3c40d967c3a69eaa80df1fc307ebf4f42c987edd323c3f8b735355f"}