{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:GIHNMKM6CU7J3AKVZ6WY5SNGNS","short_pith_number":"pith:GIHNMKM6","schema_version":"1.0","canonical_sha256":"320ed6299e153e9d8155cfad8ec9a66cb4e249b56c0307e13d243e0c4bb65488","source":{"kind":"arxiv","id":"1503.03521","version":3},"attestation_state":"computed","paper":{"title":"Cartan subalgebras in C*-algebras of Hausdorff etale groupoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Aidan Sims, Dana P. Williams, Gabriel Nagy, Jonathan H. Brown, Sarah Reznikoff","submitted_at":"2015-03-11T22:12:01Z","abstract_excerpt":"The reduced $C^*$-algebra of the interior of the isotropy in any Hausdorff \\'etale groupoid $G$ embeds as a $C^*$-subalgebra $M$ of the reduced $C^*$-algebra of $G$. We prove that the set of pure states of $M$ with unique extension is dense, and deduce that any representation of the reduced $C^*$-algebra of $G$ that is injective on $M$ is faithful. We prove that there is a conditional expectation from the reduced $C^*$-algebra of $G$ onto $M$ if and only if the interior of the isotropy in $G$ is closed. Using this, we prove that when the interior of the isotropy is abelian and closed, $M$ is a"},"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":"1503.03521","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-03-11T22:12:01Z","cross_cats_sorted":[],"title_canon_sha256":"3704ef9dc7dae8292b01384f58b73f5b726dfe9e2d8be773b749b360ed3cdd67","abstract_canon_sha256":"8ba3326dd5ba7af9cb4b1900df39ab73bac5b30d09c7d0ea653444959f9b202e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:53.067686Z","signature_b64":"q3q3beaztpTglvbC3uJdg46IJHv7dVzSjqFnyZ4dD9Gznvgw4DZYLLPdbRWYKGJGTfqD0E9fWjCwRJoy+ViwCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"320ed6299e153e9d8155cfad8ec9a66cb4e249b56c0307e13d243e0c4bb65488","last_reissued_at":"2026-05-18T01:15:53.067228Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:53.067228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cartan subalgebras in C*-algebras of Hausdorff etale groupoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Aidan Sims, Dana P. Williams, Gabriel Nagy, Jonathan H. Brown, Sarah Reznikoff","submitted_at":"2015-03-11T22:12:01Z","abstract_excerpt":"The reduced $C^*$-algebra of the interior of the isotropy in any Hausdorff \\'etale groupoid $G$ embeds as a $C^*$-subalgebra $M$ of the reduced $C^*$-algebra of $G$. We prove that the set of pure states of $M$ with unique extension is dense, and deduce that any representation of the reduced $C^*$-algebra of $G$ that is injective on $M$ is faithful. We prove that there is a conditional expectation from the reduced $C^*$-algebra of $G$ onto $M$ if and only if the interior of the isotropy in $G$ is closed. Using this, we prove that when the interior of the isotropy is abelian and closed, $M$ is a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03521","kind":"arxiv","version":3},"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":"1503.03521","created_at":"2026-05-18T01:15:53.067287+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.03521v3","created_at":"2026-05-18T01:15:53.067287+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03521","created_at":"2026-05-18T01:15:53.067287+00:00"},{"alias_kind":"pith_short_12","alias_value":"GIHNMKM6CU7J","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"GIHNMKM6CU7J3AKV","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"GIHNMKM6","created_at":"2026-05-18T12:29:22.688609+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/GIHNMKM6CU7J3AKVZ6WY5SNGNS","json":"https://pith.science/pith/GIHNMKM6CU7J3AKVZ6WY5SNGNS.json","graph_json":"https://pith.science/api/pith-number/GIHNMKM6CU7J3AKVZ6WY5SNGNS/graph.json","events_json":"https://pith.science/api/pith-number/GIHNMKM6CU7J3AKVZ6WY5SNGNS/events.json","paper":"https://pith.science/paper/GIHNMKM6"},"agent_actions":{"view_html":"https://pith.science/pith/GIHNMKM6CU7J3AKVZ6WY5SNGNS","download_json":"https://pith.science/pith/GIHNMKM6CU7J3AKVZ6WY5SNGNS.json","view_paper":"https://pith.science/paper/GIHNMKM6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.03521&json=true","fetch_graph":"https://pith.science/api/pith-number/GIHNMKM6CU7J3AKVZ6WY5SNGNS/graph.json","fetch_events":"https://pith.science/api/pith-number/GIHNMKM6CU7J3AKVZ6WY5SNGNS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GIHNMKM6CU7J3AKVZ6WY5SNGNS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GIHNMKM6CU7J3AKVZ6WY5SNGNS/action/storage_attestation","attest_author":"https://pith.science/pith/GIHNMKM6CU7J3AKVZ6WY5SNGNS/action/author_attestation","sign_citation":"https://pith.science/pith/GIHNMKM6CU7J3AKVZ6WY5SNGNS/action/citation_signature","submit_replication":"https://pith.science/pith/GIHNMKM6CU7J3AKVZ6WY5SNGNS/action/replication_record"}},"created_at":"2026-05-18T01:15:53.067287+00:00","updated_at":"2026-05-18T01:15:53.067287+00:00"}