{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:JPDOTWMGTFX2JTJLL3AFYLWO5V","short_pith_number":"pith:JPDOTWMG","schema_version":"1.0","canonical_sha256":"4bc6e9d986996fa4cd2b5ec05c2eceed756866a5ea9824c6634396957777bbee","source":{"kind":"arxiv","id":"1403.4324","version":1},"attestation_state":"computed","paper":{"title":"Twisted k-graph algebras associated to Bratteli diagrams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Adam Sierakowski, Aidan Sims, David Pask","submitted_at":"2014-03-18T02:47:21Z","abstract_excerpt":"Given a system of coverings of k-graphs, we show that the cohomology of the resulting (k+1)-graph is isomorphic to that of any one of the k-graphs in the system. We then consider Bratteli diagrams of 2-graphs whose twisted C*-algebras are matrix algebras over noncommutative tori. For such systems we calculate the ordered K-theory and the gauge-invariant semifinite traces of the resulting 3-graph C*-algebras. We deduce that every simple C*-algebra of this form is Morita equivalent to the C*-algebra of a rank-2 Bratteli diagram in the sense of Pask-Raeburn-R{\\o}rdam-Sims."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1403.4324","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-03-18T02:47:21Z","cross_cats_sorted":[],"title_canon_sha256":"2ce9b3f927dafe7d44bb4894c8270184bdf8d425a9f87679e98aa687ceb3a985","abstract_canon_sha256":"114419d198f7f84121046ae37a25728e02d5116864baf2d780d6de63b62e1668"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:06.005401Z","signature_b64":"8AWa0iPUctg2VLsFWw+dwxQdbgypRDS8SbvRpnrZr7MVhViP9TXWRghyRplSaQbHyZuHxyb5CZ9TTfU6/eSpCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4bc6e9d986996fa4cd2b5ec05c2eceed756866a5ea9824c6634396957777bbee","last_reissued_at":"2026-05-18T02:56:06.004955Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:06.004955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Twisted k-graph algebras associated to Bratteli diagrams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Adam Sierakowski, Aidan Sims, David Pask","submitted_at":"2014-03-18T02:47:21Z","abstract_excerpt":"Given a system of coverings of k-graphs, we show that the cohomology of the resulting (k+1)-graph is isomorphic to that of any one of the k-graphs in the system. We then consider Bratteli diagrams of 2-graphs whose twisted C*-algebras are matrix algebras over noncommutative tori. For such systems we calculate the ordered K-theory and the gauge-invariant semifinite traces of the resulting 3-graph C*-algebras. We deduce that every simple C*-algebra of this form is Morita equivalent to the C*-algebra of a rank-2 Bratteli diagram in the sense of Pask-Raeburn-R{\\o}rdam-Sims."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4324","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1403.4324","created_at":"2026-05-18T02:56:06.005013+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.4324v1","created_at":"2026-05-18T02:56:06.005013+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.4324","created_at":"2026-05-18T02:56:06.005013+00:00"},{"alias_kind":"pith_short_12","alias_value":"JPDOTWMGTFX2","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"JPDOTWMGTFX2JTJL","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"JPDOTWMG","created_at":"2026-05-18T12:28:35.611951+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JPDOTWMGTFX2JTJLL3AFYLWO5V","json":"https://pith.science/pith/JPDOTWMGTFX2JTJLL3AFYLWO5V.json","graph_json":"https://pith.science/api/pith-number/JPDOTWMGTFX2JTJLL3AFYLWO5V/graph.json","events_json":"https://pith.science/api/pith-number/JPDOTWMGTFX2JTJLL3AFYLWO5V/events.json","paper":"https://pith.science/paper/JPDOTWMG"},"agent_actions":{"view_html":"https://pith.science/pith/JPDOTWMGTFX2JTJLL3AFYLWO5V","download_json":"https://pith.science/pith/JPDOTWMGTFX2JTJLL3AFYLWO5V.json","view_paper":"https://pith.science/paper/JPDOTWMG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.4324&json=true","fetch_graph":"https://pith.science/api/pith-number/JPDOTWMGTFX2JTJLL3AFYLWO5V/graph.json","fetch_events":"https://pith.science/api/pith-number/JPDOTWMGTFX2JTJLL3AFYLWO5V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JPDOTWMGTFX2JTJLL3AFYLWO5V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JPDOTWMGTFX2JTJLL3AFYLWO5V/action/storage_attestation","attest_author":"https://pith.science/pith/JPDOTWMGTFX2JTJLL3AFYLWO5V/action/author_attestation","sign_citation":"https://pith.science/pith/JPDOTWMGTFX2JTJLL3AFYLWO5V/action/citation_signature","submit_replication":"https://pith.science/pith/JPDOTWMGTFX2JTJLL3AFYLWO5V/action/replication_record"}},"created_at":"2026-05-18T02:56:06.005013+00:00","updated_at":"2026-05-18T02:56:06.005013+00:00"}