{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:JHUM5WAUDPAIYBG6JACTYCYYGM","short_pith_number":"pith:JHUM5WAU","canonical_record":{"source":{"id":"1303.6268","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-03-25T19:47:15Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"dee40b30ebd1d669fd39cbea5ad7c35fd1eb895840fc2f30c7285acf32018116","abstract_canon_sha256":"5058dd11cbd7d897d42c0f5be3fc3040197a26e42fb85f2ddfaac1d8a1f0a0dd"},"schema_version":"1.0"},"canonical_sha256":"49e8ced8141bc08c04de48053c0b1833390d191753b229f49cf2ab5748771ddf","source":{"kind":"arxiv","id":"1303.6268","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.6268","created_at":"2026-05-18T03:27:22Z"},{"alias_kind":"arxiv_version","alias_value":"1303.6268v2","created_at":"2026-05-18T03:27:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6268","created_at":"2026-05-18T03:27:22Z"},{"alias_kind":"pith_short_12","alias_value":"JHUM5WAUDPAI","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JHUM5WAUDPAIYBG6","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JHUM5WAU","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:JHUM5WAUDPAIYBG6JACTYCYYGM","target":"record","payload":{"canonical_record":{"source":{"id":"1303.6268","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-03-25T19:47:15Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"dee40b30ebd1d669fd39cbea5ad7c35fd1eb895840fc2f30c7285acf32018116","abstract_canon_sha256":"5058dd11cbd7d897d42c0f5be3fc3040197a26e42fb85f2ddfaac1d8a1f0a0dd"},"schema_version":"1.0"},"canonical_sha256":"49e8ced8141bc08c04de48053c0b1833390d191753b229f49cf2ab5748771ddf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:22.503768Z","signature_b64":"4+NjShm7B2ByTq9uxl9PCFs2cjN7bl778+CrABdxA9Zyy992WkvXBNBK7i+muVq52cHV8lmDm6Hekr+hqbrxDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49e8ced8141bc08c04de48053c0b1833390d191753b229f49cf2ab5748771ddf","last_reissued_at":"2026-05-18T03:27:22.503058Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:22.503058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.6268","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":"2026-05-18T03:27:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uh4yuytd1EX1ydT6evP2WsDk1GkOzGXslmjpqJGX1z6rSH/yqPmTvBLde6zntlpAUpVqdaKbeMWDeEf6ENnWBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T10:27:57.924981Z"},"content_sha256":"2e2f6c6492f15313220bb5ff8b1d8fa9e8c3cfe6a232c2c4b305a8d9917c070c","schema_version":"1.0","event_id":"sha256:2e2f6c6492f15313220bb5ff8b1d8fa9e8c3cfe6a232c2c4b305a8d9917c070c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:JHUM5WAUDPAIYBG6JACTYCYYGM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Representing Kirchberg algebras as inverse semigroup crossed products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OA","authors_text":"Enrique Pardo, Ruy Exel","submitted_at":"2013-03-25T19:47:15Z","abstract_excerpt":"In this note we show that a combinatorial model of Kirchberg algebras in the UCT, namely the Katsura algebras O_{AB}, can be expressed both as groupoid C*-algebras and as inverse semigroup crossed products. We use this picture to obtain results about simplicity, pure infiniteness and nuclearity of O_{AB} using different methods than those used by Katsura."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6268","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":"2026-05-18T03:27:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tGT8+18r3eFTt7HlUn/CRNm0smWArMlfbYYxhihSzcxJCX2hBqXLk4AEVsb4ax1cit7pKRcMPGwOFHzDsrw7CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T10:27:57.925747Z"},"content_sha256":"48ea219aa5ae6caf077f9a466f82f50dd4e03fc3a3b6163701b63a2766195ee4","schema_version":"1.0","event_id":"sha256:48ea219aa5ae6caf077f9a466f82f50dd4e03fc3a3b6163701b63a2766195ee4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JHUM5WAUDPAIYBG6JACTYCYYGM/bundle.json","state_url":"https://pith.science/pith/JHUM5WAUDPAIYBG6JACTYCYYGM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JHUM5WAUDPAIYBG6JACTYCYYGM/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":"2026-06-10T10:27:57Z","links":{"resolver":"https://pith.science/pith/JHUM5WAUDPAIYBG6JACTYCYYGM","bundle":"https://pith.science/pith/JHUM5WAUDPAIYBG6JACTYCYYGM/bundle.json","state":"https://pith.science/pith/JHUM5WAUDPAIYBG6JACTYCYYGM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JHUM5WAUDPAIYBG6JACTYCYYGM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JHUM5WAUDPAIYBG6JACTYCYYGM","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":"5058dd11cbd7d897d42c0f5be3fc3040197a26e42fb85f2ddfaac1d8a1f0a0dd","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-03-25T19:47:15Z","title_canon_sha256":"dee40b30ebd1d669fd39cbea5ad7c35fd1eb895840fc2f30c7285acf32018116"},"schema_version":"1.0","source":{"id":"1303.6268","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.6268","created_at":"2026-05-18T03:27:22Z"},{"alias_kind":"arxiv_version","alias_value":"1303.6268v2","created_at":"2026-05-18T03:27:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6268","created_at":"2026-05-18T03:27:22Z"},{"alias_kind":"pith_short_12","alias_value":"JHUM5WAUDPAI","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JHUM5WAUDPAIYBG6","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JHUM5WAU","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:48ea219aa5ae6caf077f9a466f82f50dd4e03fc3a3b6163701b63a2766195ee4","target":"graph","created_at":"2026-05-18T03:27:22Z","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":"In this note we show that a combinatorial model of Kirchberg algebras in the UCT, namely the Katsura algebras O_{AB}, can be expressed both as groupoid C*-algebras and as inverse semigroup crossed products. We use this picture to obtain results about simplicity, pure infiniteness and nuclearity of O_{AB} using different methods than those used by Katsura.","authors_text":"Enrique Pardo, Ruy Exel","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-03-25T19:47:15Z","title":"Representing Kirchberg algebras as inverse semigroup crossed products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6268","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":"sha256:2e2f6c6492f15313220bb5ff8b1d8fa9e8c3cfe6a232c2c4b305a8d9917c070c","target":"record","created_at":"2026-05-18T03:27:22Z","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":"5058dd11cbd7d897d42c0f5be3fc3040197a26e42fb85f2ddfaac1d8a1f0a0dd","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-03-25T19:47:15Z","title_canon_sha256":"dee40b30ebd1d669fd39cbea5ad7c35fd1eb895840fc2f30c7285acf32018116"},"schema_version":"1.0","source":{"id":"1303.6268","kind":"arxiv","version":2}},"canonical_sha256":"49e8ced8141bc08c04de48053c0b1833390d191753b229f49cf2ab5748771ddf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49e8ced8141bc08c04de48053c0b1833390d191753b229f49cf2ab5748771ddf","first_computed_at":"2026-05-18T03:27:22.503058Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:22.503058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4+NjShm7B2ByTq9uxl9PCFs2cjN7bl778+CrABdxA9Zyy992WkvXBNBK7i+muVq52cHV8lmDm6Hekr+hqbrxDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:22.503768Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.6268","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e2f6c6492f15313220bb5ff8b1d8fa9e8c3cfe6a232c2c4b305a8d9917c070c","sha256:48ea219aa5ae6caf077f9a466f82f50dd4e03fc3a3b6163701b63a2766195ee4"],"state_sha256":"a3bad75482059d9df7fce30eda5f28c329b37e46ed4711bbe0feabe460ab3904"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QaguTDag2ecYBSJmoRta5YeLg5i4Cc554tN/gbq+USkpGfwUfs+a7Xpy8V4pceZmRaeJ47lUySN9hAcufQmtBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T10:27:57.929685Z","bundle_sha256":"b53e73a32442df0ae0e63482ac6530dcf7543957c9c531e4ee1dd77f4016019e"}}