{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:GJGREC3VXJC7UEI26MP6BT3P3J","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":"df6f34e05efc1e41158f3bc0812c61a66093cd0e1e180edb1714d0031fd7904a","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2009-04-07T09:10:38Z","title_canon_sha256":"3c795809710f1abdb46348c72a9fb7728cd59d6d44f89b7b653e4df61910fdee"},"schema_version":"1.0","source":{"id":"0904.1085","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.1085","created_at":"2026-07-04T15:40:45Z"},{"alias_kind":"arxiv_version","alias_value":"0904.1085v1","created_at":"2026-07-04T15:40:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.1085","created_at":"2026-07-04T15:40:45Z"},{"alias_kind":"pith_short_12","alias_value":"GJGREC3VXJC7","created_at":"2026-07-04T15:40:45Z"},{"alias_kind":"pith_short_16","alias_value":"GJGREC3VXJC7UEI2","created_at":"2026-07-04T15:40:45Z"},{"alias_kind":"pith_short_8","alias_value":"GJGREC3V","created_at":"2026-07-04T15:40:45Z"}],"graph_snapshots":[{"event_id":"sha256:a2c142ca3fc57c9258188f637b0411b2c59a4467b46d37ef591c27545f97c7a8","target":"graph","created_at":"2026-07-04T15:40:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0904.1085/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Noncommutative tori with real multiplication are the irrational rotation algebras that have special equivalence bimodules. Y. Manin proposed the use of noncommutative tori with real multiplication as a geometric framework for the study of abelian class field theory of real quadratic fields. In this paper, we consider the Cuntz-Pimsner algebras constructed by special equivalence bimodules of irrational rotation algebras. We shall show that associated $C^*$-algebras are simple and purely infinite. We compute the K-groups of associated $C^*$-algebras and show that these algebras are related to th","authors_text":"Norio Nawata","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2009-04-07T09:10:38Z","title":"$C^*$-algebras associated with real multiplication"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.1085","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":"sha256:47f4cb9acfdc2fc6c903989dc7d304eeb11a91176a1c3d1f047d28dbe8cd9c6e","target":"record","created_at":"2026-07-04T15:40:45Z","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":"df6f34e05efc1e41158f3bc0812c61a66093cd0e1e180edb1714d0031fd7904a","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2009-04-07T09:10:38Z","title_canon_sha256":"3c795809710f1abdb46348c72a9fb7728cd59d6d44f89b7b653e4df61910fdee"},"schema_version":"1.0","source":{"id":"0904.1085","kind":"arxiv","version":1}},"canonical_sha256":"324d120b75ba45fa111af31fe0cf6fda507a9f066f1a39806cfa5babfb85f9c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"324d120b75ba45fa111af31fe0cf6fda507a9f066f1a39806cfa5babfb85f9c0","first_computed_at":"2026-07-04T15:40:45.052912Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:40:45.052912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4YyVHdotOsu8ucmp0D+zAfRBszuqSTQ01liKSFgxPoj93libQO6aUoOu3V2c0Vfm9kUE70MD+smTWMCh7KY/Dw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:40:45.053270Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.1085","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47f4cb9acfdc2fc6c903989dc7d304eeb11a91176a1c3d1f047d28dbe8cd9c6e","sha256:a2c142ca3fc57c9258188f637b0411b2c59a4467b46d37ef591c27545f97c7a8"],"state_sha256":"ad5c7d99bee97a1db01d47a0127dc09b066ec7c1379ba5929c8c46f87c230186"}