{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:W76XZYMOM44DREI652ZBUKNPLV","short_pith_number":"pith:W76XZYMO","schema_version":"1.0","canonical_sha256":"b7fd7ce18e673838911eeeb21a29af5d591de6abd8099ea2d294b4aacf23e43f","source":{"kind":"arxiv","id":"1801.00832","version":1},"attestation_state":"computed","paper":{"title":"The Dixmier-Douady Classes of Certain Groupoid $C^*$-Algebras with Continuous Trace","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Aidan Sims, Alex Kumjian, Dana P. Williams, Marius Ionescu","submitted_at":"2018-01-02T20:54:09Z","abstract_excerpt":"Given a locally compact abelian group $G$, we give an explicit formula for the Dixmier--Douady invariant of the $C^*$-algebra of the groupoid extension associated to a \\v{C}ech $2$-cocycle in the sheaf of germs of continuous $G$-valued functions. We then exploit the blow-up construction for groupoids to extend this to some more general central extensions of \\'etale equivalence relations."},"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":"1801.00832","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-01-02T20:54:09Z","cross_cats_sorted":[],"title_canon_sha256":"b280a9d256d33c0b8a4dcaeed8541f3f3071207bb368c1559c8cee92093c2cde","abstract_canon_sha256":"65370ed2796e8c77cad4a5a22caa34e0bbc639f7a18e18837c0d1603230080f0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:48.665669Z","signature_b64":"nh0Vmich7Gx7+K/oi5f4GIvFOjYE121rywrKzp1toS7wvRW+SBnCEa53shVWglY8/0G98RzvHtuTjz7Cf5EGBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7fd7ce18e673838911eeeb21a29af5d591de6abd8099ea2d294b4aacf23e43f","last_reissued_at":"2026-05-18T00:26:48.664938Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:48.664938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Dixmier-Douady Classes of Certain Groupoid $C^*$-Algebras with Continuous Trace","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Aidan Sims, Alex Kumjian, Dana P. Williams, Marius Ionescu","submitted_at":"2018-01-02T20:54:09Z","abstract_excerpt":"Given a locally compact abelian group $G$, we give an explicit formula for the Dixmier--Douady invariant of the $C^*$-algebra of the groupoid extension associated to a \\v{C}ech $2$-cocycle in the sheaf of germs of continuous $G$-valued functions. We then exploit the blow-up construction for groupoids to extend this to some more general central extensions of \\'etale equivalence relations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00832","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":"1801.00832","created_at":"2026-05-18T00:26:48.665052+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.00832v1","created_at":"2026-05-18T00:26:48.665052+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00832","created_at":"2026-05-18T00:26:48.665052+00:00"},{"alias_kind":"pith_short_12","alias_value":"W76XZYMOM44D","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"W76XZYMOM44DREI6","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"W76XZYMO","created_at":"2026-05-18T12:32:59.047623+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/W76XZYMOM44DREI652ZBUKNPLV","json":"https://pith.science/pith/W76XZYMOM44DREI652ZBUKNPLV.json","graph_json":"https://pith.science/api/pith-number/W76XZYMOM44DREI652ZBUKNPLV/graph.json","events_json":"https://pith.science/api/pith-number/W76XZYMOM44DREI652ZBUKNPLV/events.json","paper":"https://pith.science/paper/W76XZYMO"},"agent_actions":{"view_html":"https://pith.science/pith/W76XZYMOM44DREI652ZBUKNPLV","download_json":"https://pith.science/pith/W76XZYMOM44DREI652ZBUKNPLV.json","view_paper":"https://pith.science/paper/W76XZYMO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.00832&json=true","fetch_graph":"https://pith.science/api/pith-number/W76XZYMOM44DREI652ZBUKNPLV/graph.json","fetch_events":"https://pith.science/api/pith-number/W76XZYMOM44DREI652ZBUKNPLV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W76XZYMOM44DREI652ZBUKNPLV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W76XZYMOM44DREI652ZBUKNPLV/action/storage_attestation","attest_author":"https://pith.science/pith/W76XZYMOM44DREI652ZBUKNPLV/action/author_attestation","sign_citation":"https://pith.science/pith/W76XZYMOM44DREI652ZBUKNPLV/action/citation_signature","submit_replication":"https://pith.science/pith/W76XZYMOM44DREI652ZBUKNPLV/action/replication_record"}},"created_at":"2026-05-18T00:26:48.665052+00:00","updated_at":"2026-05-18T00:26:48.665052+00:00"}