{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:S7P344UZ32FD2M63Q6CBRDFOST","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":"01fa93cbafa7165060d2f5b38d3180d227394e041550f5e583eb39313ccd9eb0","cross_cats_sorted":["math.GN","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-05-02T18:52:32Z","title_canon_sha256":"aa54f23e0995152f6f0f3bf3de2092c9b5b5b292d687adcecb6c944404e058cb"},"schema_version":"1.0","source":{"id":"1505.00364","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.00364","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"arxiv_version","alias_value":"1505.00364v3","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00364","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"pith_short_12","alias_value":"S7P344UZ32FD","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"S7P344UZ32FD2M63","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"S7P344UZ","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:b49da77c8dbac5b9413d713fbaf9c0f77f9b7484455bf279da4668991d8cbff6","target":"graph","created_at":"2026-05-18T01:19:53Z","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":"Inspired by recent papers on twisted $K$-theory, we consider in this article the question of when a twist $\\mathcal{R}$ over a locally compact Hausdorff groupoid $\\mathcal{G}$ (with unit space a CW-complex) admits a twisted vector bundle, and we relate this question to the Brauer group of $\\mathcal{G}$.\n  We show that the twists which admit twisted vector bundles give rise to a subgroup of the Brauer group of $\\mathcal{G}$. When $\\mathcal{G}$ is an \\'etale groupoid, we establish conditions (involving the classifying space $B\\mathcal{G}$ of $\\mathcal{G}$) which imply that a torsion twist $\\math","authors_text":"Carla Farsi, Elizabeth Gillaspy","cross_cats":["math.GN","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-05-02T18:52:32Z","title":"Twists over \\'etale groupoids and twisted vector bundles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00364","kind":"arxiv","version":3},"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":"sha256:884d2c5903ed085de61ce8cae08420ae6e55b7ea10e62c77488580824cc13c4f","target":"record","created_at":"2026-05-18T01:19:53Z","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":"01fa93cbafa7165060d2f5b38d3180d227394e041550f5e583eb39313ccd9eb0","cross_cats_sorted":["math.GN","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-05-02T18:52:32Z","title_canon_sha256":"aa54f23e0995152f6f0f3bf3de2092c9b5b5b292d687adcecb6c944404e058cb"},"schema_version":"1.0","source":{"id":"1505.00364","kind":"arxiv","version":3}},"canonical_sha256":"97dfbe7299de8a3d33db8784188cae94c23e898c25f17fd8483225f70ddcc998","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97dfbe7299de8a3d33db8784188cae94c23e898c25f17fd8483225f70ddcc998","first_computed_at":"2026-05-18T01:19:53.896991Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:53.896991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FtkVyGHZjsyg1V8tTMgBbYsuvIgXR0OxOAfgf0xR/ZAJCo5waCNDSPRx/po+te5L2UhahYen9Fx0ln6AVdNPAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:53.897369Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.00364","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:884d2c5903ed085de61ce8cae08420ae6e55b7ea10e62c77488580824cc13c4f","sha256:b49da77c8dbac5b9413d713fbaf9c0f77f9b7484455bf279da4668991d8cbff6"],"state_sha256":"794eb44359746a67277d9a719be9f22b61cec94d27741023bb5cc82ff7842b1b"}