{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:XYVZUKI553RRMGIDH7ZZBI4A3Z","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":"0f64378b9e9aff4c11b0c83b48b298ccd5181f0304bb84c0a6745affc1572785","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-06-07T01:32:38Z","title_canon_sha256":"50d422bde563ef633da1a4bc8a871218946b879ffd874682d4c6c95b4d6c2d0a"},"schema_version":"1.0","source":{"id":"1906.02855","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.02855","created_at":"2026-05-17T23:43:57Z"},{"alias_kind":"arxiv_version","alias_value":"1906.02855v1","created_at":"2026-05-17T23:43:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.02855","created_at":"2026-05-17T23:43:57Z"},{"alias_kind":"pith_short_12","alias_value":"XYVZUKI553RR","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"XYVZUKI553RRMGID","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"XYVZUKI5","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:2571c53139e912593977a9b5d034ce7204960b141e0f98d56cecdfb96a0d0106","target":"graph","created_at":"2026-05-17T23:43:57Z","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":"Suppose $\\mathcal{G}$ is a second-countable locally compact Hausdorff \\'{e}tale groupoid, $G$ is a discrete group containing a unital subsemigroup $P$, and $c:\\mathcal{G}\\rightarrow G$ is a continuous cocycle. We derive conditions on the cocycle such that the reduced groupoid $C^*$-algebra $C_r^*(\\mathcal{G})$ may be realised naturally as the covariance algebra of a product system over $P$ with coefficient algebra $C_r^*(c^{-1}(e))$. When $(G,P)$ is a quasi-lattice ordered group, we also derive conditions that allow $C_r^*(\\mathcal{G})$ to be realised as the Cuntz--Nica--Pimsner algebra of a c","authors_text":"James Fletcher, Lisa Orloff Clark","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-06-07T01:32:38Z","title":"Groupoid algebras as covariance algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.02855","kind":"arxiv","version":1},"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":"sha256:280811342ac678645e48a63f08ba1dc58870305e778a4e22be651a3429f6a933","target":"record","created_at":"2026-05-17T23:43:57Z","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":"0f64378b9e9aff4c11b0c83b48b298ccd5181f0304bb84c0a6745affc1572785","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-06-07T01:32:38Z","title_canon_sha256":"50d422bde563ef633da1a4bc8a871218946b879ffd874682d4c6c95b4d6c2d0a"},"schema_version":"1.0","source":{"id":"1906.02855","kind":"arxiv","version":1}},"canonical_sha256":"be2b9a291deee31619033ff390a380de70911646b8fccff14a55eb2246676b52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be2b9a291deee31619033ff390a380de70911646b8fccff14a55eb2246676b52","first_computed_at":"2026-05-17T23:43:57.282942Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:57.282942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cqd8+mzIFu/rZQbMzfN7SafO2gE1Jo9MkUju0PigrCisytGx7gWs0flwtp7tMia4dYbgHq9ckiNYNNaTQCAaDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:57.283732Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.02855","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:280811342ac678645e48a63f08ba1dc58870305e778a4e22be651a3429f6a933","sha256:2571c53139e912593977a9b5d034ce7204960b141e0f98d56cecdfb96a0d0106"],"state_sha256":"3e7183b84395a8451b60843460de3b93fe4b07c2ff55b7304100402a20ab44ff"}