{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:O6UPIBSSXEXPHUJQUNKQA2UNYJ","short_pith_number":"pith:O6UPIBSS","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"},"canonical_sha256":"77a8f40652b92ef3d130a355006a8dc262f3830d8fd052a9e2ce657b50f09e0e","source":{"kind":"arxiv","id":"1512.00346","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00346","created_at":"2026-05-18T00:53:34Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00346v2","created_at":"2026-05-18T00:53:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00346","created_at":"2026-05-18T00:53:34Z"},{"alias_kind":"pith_short_12","alias_value":"O6UPIBSSXEXP","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"O6UPIBSSXEXPHUJQ","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"O6UPIBSS","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:O6UPIBSSXEXPHUJQUNKQA2UNYJ","target":"record","payload":{"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"},"canonical_sha256":"77a8f40652b92ef3d130a355006a8dc262f3830d8fd052a9e2ce657b50f09e0e","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"},"source_kind":"arxiv","source_id":"1512.00346","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YBOjPGaKjQngDnkS/+TPGft1aulXaIyL6wWJovsldKDFHK2fnEd/7ddFZLIzr/gEbiSZZCwgN1Uj5v5s8vOWAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:40:48.554241Z"},"content_sha256":"6f7b764d0e5c104a13a9688f9bdde04432766b5b8e93ea990ea4d17703bee2d1","schema_version":"1.0","event_id":"sha256:6f7b764d0e5c104a13a9688f9bdde04432766b5b8e93ea990ea4d17703bee2d1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:O6UPIBSSXEXPHUJQUNKQA2UNYJ","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Li9LUHfhvtQe/5TVl/9KwjFXur8Pmmu8X2dQpPg0qq9Ok3m51OtGV2Kp58Hi0svM83/1wp8BYzZCiaTq0awBDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:40:48.554599Z"},"content_sha256":"9d9144d1382c34d9dd2fb0392e7eb476443c718be1d4e25c424bacebabb3c4e2","schema_version":"1.0","event_id":"sha256:9d9144d1382c34d9dd2fb0392e7eb476443c718be1d4e25c424bacebabb3c4e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O6UPIBSSXEXPHUJQUNKQA2UNYJ/bundle.json","state_url":"https://pith.science/pith/O6UPIBSSXEXPHUJQUNKQA2UNYJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O6UPIBSSXEXPHUJQUNKQA2UNYJ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T15:40:48Z","links":{"resolver":"https://pith.science/pith/O6UPIBSSXEXPHUJQUNKQA2UNYJ","bundle":"https://pith.science/pith/O6UPIBSSXEXPHUJQUNKQA2UNYJ/bundle.json","state":"https://pith.science/pith/O6UPIBSSXEXPHUJQUNKQA2UNYJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O6UPIBSSXEXPHUJQUNKQA2UNYJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:O6UPIBSSXEXPHUJQUNKQA2UNYJ","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":"439d2b104a9d6a3d321f9f7deb8614d07446aa3d9e8cba662ad2c18ab2ab6b9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-11-25T18:29:24Z","title_canon_sha256":"8f83de18888d1a8e6ce159d3c44af87c33e83d94535c97f352c2de58c730b34c"},"schema_version":"1.0","source":{"id":"1512.00346","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00346","created_at":"2026-05-18T00:53:34Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00346v2","created_at":"2026-05-18T00:53:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00346","created_at":"2026-05-18T00:53:34Z"},{"alias_kind":"pith_short_12","alias_value":"O6UPIBSSXEXP","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"O6UPIBSSXEXPHUJQ","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"O6UPIBSS","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:9d9144d1382c34d9dd2fb0392e7eb476443c718be1d4e25c424bacebabb3c4e2","target":"graph","created_at":"2026-05-18T00:53:34Z","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":"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","authors_text":"Hossein Larki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-11-25T18:29:24Z","title":"Quotients of Ultragraph C*-Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00346","kind":"arxiv","version":2},"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":"sha256:6f7b764d0e5c104a13a9688f9bdde04432766b5b8e93ea990ea4d17703bee2d1","target":"record","created_at":"2026-05-18T00:53:34Z","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":"439d2b104a9d6a3d321f9f7deb8614d07446aa3d9e8cba662ad2c18ab2ab6b9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-11-25T18:29:24Z","title_canon_sha256":"8f83de18888d1a8e6ce159d3c44af87c33e83d94535c97f352c2de58c730b34c"},"schema_version":"1.0","source":{"id":"1512.00346","kind":"arxiv","version":2}},"canonical_sha256":"77a8f40652b92ef3d130a355006a8dc262f3830d8fd052a9e2ce657b50f09e0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77a8f40652b92ef3d130a355006a8dc262f3830d8fd052a9e2ce657b50f09e0e","first_computed_at":"2026-05-18T00:53:34.829616Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:34.829616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I1Ca/xoFvMpA1mTm5VpwUTQhssteWIj1XUZD8YwQ3g7Sj0acMw+4vPMYE4lG2GucX1Ps9wrxSkDDaiew9RgUCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:34.830025Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.00346","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f7b764d0e5c104a13a9688f9bdde04432766b5b8e93ea990ea4d17703bee2d1","sha256:9d9144d1382c34d9dd2fb0392e7eb476443c718be1d4e25c424bacebabb3c4e2"],"state_sha256":"96b4f57f679edeafdbaf1fa0e85e70d4432e89997a34dc8476ade1e46ed6fafd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"urNxWAHWmdpaF1tK6uaCIslyimzwM2emLUCjeyyx4tP+iQLPhJXX0wJLmOY5v6YU1acRK1iBNZW4G5iUx89vCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T15:40:48.556557Z","bundle_sha256":"10e8f8b59e35b8802393621cb774bf37c05a5484edeeed9fa324de02708b2cef"}}