{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:Y7CJ2PZUJB2IVBU4RO3SYMZHSL","short_pith_number":"pith:Y7CJ2PZU","schema_version":"1.0","canonical_sha256":"c7c49d3f3448748a869c8bb72c332792d71499b63150ec55369a1d0eefba9ae2","source":{"kind":"arxiv","id":"1412.6900","version":2},"attestation_state":"computed","paper":{"title":"Irreducible Representations of Bost-Connes systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.OA","authors_text":"Takuya Takeishi","submitted_at":"2014-12-22T08:30:30Z","abstract_excerpt":"The classification problem of Bost-Connes systems was studied by Cornellissen and Marcolli partially, but still remains unsolved. In this paper, we will give a representation-theoretic approach to this problem. We generalize the result of Laca and Raeburn, which concerns with the primitive ideal space on the Bost-Connes system for $\\mathbb{Q}$. As a consequence, the Bost-Connes $C^*$-algebra for a number field $K$ has $h_K^1$-dimensional irreducible representations and does not have finite-dimensional irreducible representations for the other dimensions, where $h_K^1$ is the narrow class numbe"},"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":"1412.6900","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-12-22T08:30:30Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"b0bd008ee65511793b5971b0b00a56e4d9ac64ec5ef96bb85772362c0212c3df","abstract_canon_sha256":"d0a43b5978152110f4416c6f9c150854ab79b4a0ad96b2dfc11d3ef30da06c97"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:46.413070Z","signature_b64":"QXw9xFoCRNul+Xh1k4GeHEQ6Vp98Kw0xZEMuPxizebEVvdL7pA4XBWqxfMuCoTjR2W3XXxz6wmzvn4I5SP1cDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7c49d3f3448748a869c8bb72c332792d71499b63150ec55369a1d0eefba9ae2","last_reissued_at":"2026-05-18T01:27:46.412372Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:46.412372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Irreducible Representations of Bost-Connes systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.OA","authors_text":"Takuya Takeishi","submitted_at":"2014-12-22T08:30:30Z","abstract_excerpt":"The classification problem of Bost-Connes systems was studied by Cornellissen and Marcolli partially, but still remains unsolved. In this paper, we will give a representation-theoretic approach to this problem. We generalize the result of Laca and Raeburn, which concerns with the primitive ideal space on the Bost-Connes system for $\\mathbb{Q}$. As a consequence, the Bost-Connes $C^*$-algebra for a number field $K$ has $h_K^1$-dimensional irreducible representations and does not have finite-dimensional irreducible representations for the other dimensions, where $h_K^1$ is the narrow class numbe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6900","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":"1412.6900","created_at":"2026-05-18T01:27:46.412500+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.6900v2","created_at":"2026-05-18T01:27:46.412500+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.6900","created_at":"2026-05-18T01:27:46.412500+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y7CJ2PZUJB2I","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y7CJ2PZUJB2IVBU4","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y7CJ2PZU","created_at":"2026-05-18T12:28:57.508820+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/Y7CJ2PZUJB2IVBU4RO3SYMZHSL","json":"https://pith.science/pith/Y7CJ2PZUJB2IVBU4RO3SYMZHSL.json","graph_json":"https://pith.science/api/pith-number/Y7CJ2PZUJB2IVBU4RO3SYMZHSL/graph.json","events_json":"https://pith.science/api/pith-number/Y7CJ2PZUJB2IVBU4RO3SYMZHSL/events.json","paper":"https://pith.science/paper/Y7CJ2PZU"},"agent_actions":{"view_html":"https://pith.science/pith/Y7CJ2PZUJB2IVBU4RO3SYMZHSL","download_json":"https://pith.science/pith/Y7CJ2PZUJB2IVBU4RO3SYMZHSL.json","view_paper":"https://pith.science/paper/Y7CJ2PZU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.6900&json=true","fetch_graph":"https://pith.science/api/pith-number/Y7CJ2PZUJB2IVBU4RO3SYMZHSL/graph.json","fetch_events":"https://pith.science/api/pith-number/Y7CJ2PZUJB2IVBU4RO3SYMZHSL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y7CJ2PZUJB2IVBU4RO3SYMZHSL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y7CJ2PZUJB2IVBU4RO3SYMZHSL/action/storage_attestation","attest_author":"https://pith.science/pith/Y7CJ2PZUJB2IVBU4RO3SYMZHSL/action/author_attestation","sign_citation":"https://pith.science/pith/Y7CJ2PZUJB2IVBU4RO3SYMZHSL/action/citation_signature","submit_replication":"https://pith.science/pith/Y7CJ2PZUJB2IVBU4RO3SYMZHSL/action/replication_record"}},"created_at":"2026-05-18T01:27:46.412500+00:00","updated_at":"2026-05-18T01:27:46.412500+00:00"}