{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:MI4KGLI4PDZMFPOL4XCCT3APLR","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":"6287d6ef3f35b613b25a898db0bd2a30e85e98d059db819d75a4eb6282aa30ac","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2008-02-20T04:55:50Z","title_canon_sha256":"f4c5925e6856d81c9c8d6ac213cc9957af32b916936f01125ac27329c54af353"},"schema_version":"1.0","source":{"id":"0802.2751","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0802.2751","created_at":"2026-07-04T15:12:55Z"},{"alias_kind":"arxiv_version","alias_value":"0802.2751v2","created_at":"2026-07-04T15:12:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.2751","created_at":"2026-07-04T15:12:55Z"},{"alias_kind":"pith_short_12","alias_value":"MI4KGLI4PDZM","created_at":"2026-07-04T15:12:55Z"},{"alias_kind":"pith_short_16","alias_value":"MI4KGLI4PDZMFPOL","created_at":"2026-07-04T15:12:55Z"},{"alias_kind":"pith_short_8","alias_value":"MI4KGLI4","created_at":"2026-07-04T15:12:55Z"}],"graph_snapshots":[{"event_id":"sha256:8d43a938218bee4b523b95ed9dc923e4ccd5bfe41705f5c4529f0d5adbe648d4","target":"graph","created_at":"2026-07-04T15:12:55Z","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/0802.2751/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we determine the isomorphic classes of Morita equivalent subalgebras of irrational rotation algebras. It is based on the solution of the quadratic Diophantine equations. We determine the irrational rotation algebras that have locally trivial inclusions. We compute the index of the locally trivial inclusions of irrational rotation algebras.","authors_text":"Norio Nawata","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2008-02-20T04:55:50Z","title":"Morita equivalent subalgebras of irrational rotation algebras and real quadratic fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.2751","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:db95274db668dba5c19f0d550664e007e830fed0e12d91028ddfd8cd745b2094","target":"record","created_at":"2026-07-04T15:12:55Z","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":"6287d6ef3f35b613b25a898db0bd2a30e85e98d059db819d75a4eb6282aa30ac","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2008-02-20T04:55:50Z","title_canon_sha256":"f4c5925e6856d81c9c8d6ac213cc9957af32b916936f01125ac27329c54af353"},"schema_version":"1.0","source":{"id":"0802.2751","kind":"arxiv","version":2}},"canonical_sha256":"6238a32d1c78f2c2bdcbe5c429ec0f5c701b8cbfb24c7af8c9131bbab637f74c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6238a32d1c78f2c2bdcbe5c429ec0f5c701b8cbfb24c7af8c9131bbab637f74c","first_computed_at":"2026-07-04T15:12:55.481507Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:12:55.481507Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LuBP3xRKksF1ZkJ9f82feGa59QcUhV9qFY86nCkBijqbLWdyFaJhLtfw0Wk0c4tm5jAaskZt0YqoQGEL7USaAA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:12:55.481886Z","signed_message":"canonical_sha256_bytes"},"source_id":"0802.2751","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db95274db668dba5c19f0d550664e007e830fed0e12d91028ddfd8cd745b2094","sha256:8d43a938218bee4b523b95ed9dc923e4ccd5bfe41705f5c4529f0d5adbe648d4"],"state_sha256":"35530b7ff00f55c3771fcd9c69e2b3c7df52285ae7ea3f6074e17b245eeef928"}