{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:27YEPKBDR5Z5TXU5MPFMTJRUID","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":"a5dcfb6e2575fcbe113ac4ffe3c6fd8a75f60684dd968fc91045faf65b1c2581","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-04-19T05:03:32Z","title_canon_sha256":"e301d19d4c0ef96ca392d3bcdc9f6518e3a6b16805b78f84337093940144e8e0"},"schema_version":"1.0","source":{"id":"1504.04794","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.04794","created_at":"2026-05-18T01:19:57Z"},{"alias_kind":"arxiv_version","alias_value":"1504.04794v2","created_at":"2026-05-18T01:19:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04794","created_at":"2026-05-18T01:19:57Z"},{"alias_kind":"pith_short_12","alias_value":"27YEPKBDR5Z5","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"27YEPKBDR5Z5TXU5","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"27YEPKBD","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:d58970a1192cab53333bb0253586a5182bb18ceff3a5eafe9474d8cb5179ede6","target":"graph","created_at":"2026-05-18T01:19:57Z","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":"From a suitable groupoid G, we show how to construct an amenable principal groupoid whose C*-algebra is a Kirchberg algebra which is KK-equivalent to C*(G). Using this construction, we show by example that many UCT Kirchberg algebras can be realised as the C*-algebras of amenable principal groupoids.","authors_text":"Adam Sierakowski, Aidan Sims, Jonathan H. Brown, Lisa Orloff Clark","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-04-19T05:03:32Z","title":"Purely infinite simple C*-algebras that are principal groupoid C*-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04794","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":"sha256:4626d4f23f731f154a965f9b527fb4875c586f41c2f69b521978ef932310202b","target":"record","created_at":"2026-05-18T01:19:57Z","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":"a5dcfb6e2575fcbe113ac4ffe3c6fd8a75f60684dd968fc91045faf65b1c2581","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-04-19T05:03:32Z","title_canon_sha256":"e301d19d4c0ef96ca392d3bcdc9f6518e3a6b16805b78f84337093940144e8e0"},"schema_version":"1.0","source":{"id":"1504.04794","kind":"arxiv","version":2}},"canonical_sha256":"d7f047a8238f73d9de9d63cac9a63440c32114cd6ae58d5349375d5da120d7e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7f047a8238f73d9de9d63cac9a63440c32114cd6ae58d5349375d5da120d7e7","first_computed_at":"2026-05-18T01:19:57.475493Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:57.475493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tueuH3cKubDDmNuCzdDMLaoKaGBREGDPHYU/R6q3M7m3xQrJJwFEy2odP+AZeuOEuIChRHGAWRO//fO8tZbqCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:57.476444Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.04794","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4626d4f23f731f154a965f9b527fb4875c586f41c2f69b521978ef932310202b","sha256:d58970a1192cab53333bb0253586a5182bb18ceff3a5eafe9474d8cb5179ede6"],"state_sha256":"e2bf0182fca409400419b0be256e000d797ac981fdd3b056f7cd405d38c052b8"}