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For simplicity's sake, we first introduce the notion of quotient ultragraph $\\mathcal{G}/(H,B)$ and an associated $C^*$-algebra $C^*(\\mathcal{G}/(H,B))$ such that $C^*(\\mathcal{G}/(H,B))\\cong C^*(\\mathcal{G})/I_{(H,B)}$. We then prove the gauge invariant and the Cuntz-Krieger uniqueness theorems for $C^*(\\mathcal{G}/(H,B))$ 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":"1512.00346","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-11-25T18:29:24Z","cross_cats_sorted":[],"title_canon_sha256":"8f83de18888d1a8e6ce159d3c44af87c33e83d94535c97f352c2de58c730b34c","abstract_canon_sha256":"439d2b104a9d6a3d321f9f7deb8614d07446aa3d9e8cba662ad2c18ab2ab6b9d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:34.830025Z","signature_b64":"I1Ca/xoFvMpA1mTm5VpwUTQhssteWIj1XUZD8YwQ3g7Sj0acMw+4vPMYE4lG2GucX1Ps9wrxSkDDaiew9RgUCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77a8f40652b92ef3d130a355006a8dc262f3830d8fd052a9e2ce657b50f09e0e","last_reissued_at":"2026-05-18T00:53:34.829616Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:34.829616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quotients of Ultragraph C*-Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Hossein Larki","submitted_at":"2015-11-25T18:29:24Z","abstract_excerpt":"Let $\\mathcal{G}$ be an ultragraph and let $C^*(\\mathcal{G})$ be the associated $C^*$-algebra introduced by Mark Tomforde. For any gauge invariant ideal $I_{(H,B)}$ of $C^*(\\mathcal{G})$, we analyze the structure of the quotient $C^*$-algebra $C^*(\\mathcal{G})/I_{(H,B)}$. For simplicity's sake, we first introduce the notion of quotient ultragraph $\\mathcal{G}/(H,B)$ and an associated $C^*$-algebra $C^*(\\mathcal{G}/(H,B))$ such that $C^*(\\mathcal{G}/(H,B))\\cong C^*(\\mathcal{G})/I_{(H,B)}$. We then prove the gauge invariant and the Cuntz-Krieger uniqueness theorems for $C^*(\\mathcal{G}/(H,B))$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00346","kind":"arxiv","version":2},"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":"1512.00346","created_at":"2026-05-18T00:53:34.829679+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.00346v2","created_at":"2026-05-18T00:53:34.829679+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00346","created_at":"2026-05-18T00:53:34.829679+00:00"},{"alias_kind":"pith_short_12","alias_value":"O6UPIBSSXEXP","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"O6UPIBSSXEXPHUJQ","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"O6UPIBSS","created_at":"2026-05-18T12:29:34.919912+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/O6UPIBSSXEXPHUJQUNKQA2UNYJ","json":"https://pith.science/pith/O6UPIBSSXEXPHUJQUNKQA2UNYJ.json","graph_json":"https://pith.science/api/pith-number/O6UPIBSSXEXPHUJQUNKQA2UNYJ/graph.json","events_json":"https://pith.science/api/pith-number/O6UPIBSSXEXPHUJQUNKQA2UNYJ/events.json","paper":"https://pith.science/paper/O6UPIBSS"},"agent_actions":{"view_html":"https://pith.science/pith/O6UPIBSSXEXPHUJQUNKQA2UNYJ","download_json":"https://pith.science/pith/O6UPIBSSXEXPHUJQUNKQA2UNYJ.json","view_paper":"https://pith.science/paper/O6UPIBSS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.00346&json=true","fetch_graph":"https://pith.science/api/pith-number/O6UPIBSSXEXPHUJQUNKQA2UNYJ/graph.json","fetch_events":"https://pith.science/api/pith-number/O6UPIBSSXEXPHUJQUNKQA2UNYJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O6UPIBSSXEXPHUJQUNKQA2UNYJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O6UPIBSSXEXPHUJQUNKQA2UNYJ/action/storage_attestation","attest_author":"https://pith.science/pith/O6UPIBSSXEXPHUJQUNKQA2UNYJ/action/author_attestation","sign_citation":"https://pith.science/pith/O6UPIBSSXEXPHUJQUNKQA2UNYJ/action/citation_signature","submit_replication":"https://pith.science/pith/O6UPIBSSXEXPHUJQUNKQA2UNYJ/action/replication_record"}},"created_at":"2026-05-18T00:53:34.829679+00:00","updated_at":"2026-05-18T00:53:34.829679+00:00"}