{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:6WGLMRHXKVILT4IUT3D4AYBF7V","short_pith_number":"pith:6WGLMRHX","schema_version":"1.0","canonical_sha256":"f58cb644f75550b9f1149ec7c06025fd53400c37dd34598a79ac3e9f40ab8c49","source":{"kind":"arxiv","id":"math/0512030","version":1},"attestation_state":"computed","paper":{"title":"Realization of a simple higher dimensional noncommutative torus as a transformation group C*-algebra","license":"","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Benjam\\'in Itz\\'a-Ortiz, N. Christopher Phillips","submitted_at":"2005-12-01T15:51:57Z","abstract_excerpt":"Let $\\theta$ be a nondegenerate skew symmetric real $d$ by $d$ matrix, and let $A_{\\theta}$ be the corresponding simple higher dimensional noncommutative torus. Suppose that $d$ is odd, or that $d$ is greater or equal to 4 and the entries of $\\theta$ are not contained in a quadratic extension of $\\mathbb{Q}$. Then $A_{\\theta}$ is isomorphic to the transformation group C*-algebra obtained from a minimal homeomorphism of a compact connected one dimensional space locally homeomorphic to the product of the interval and the Cantor set. The proof uses classification theory of C*-algebras."},"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":"math/0512030","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2005-12-01T15:51:57Z","cross_cats_sorted":[],"title_canon_sha256":"5d7b99a2504982d016e5dd3da652f808d84b67c52ee186c93dcc175dcc4ec1b6","abstract_canon_sha256":"5945637c126a675d6b2a0f145eec492a3d2157e9c6b2dc915660da927e931ebf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:50.729124Z","signature_b64":"CFtyMfuJ1WfTh8Y1NlIE54yVF480KMu4eds41edu7k9SGfTmJqj9NvJ32Z+mwO6yb8crQs7L93tYMv6xVaHpCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f58cb644f75550b9f1149ec7c06025fd53400c37dd34598a79ac3e9f40ab8c49","last_reissued_at":"2026-05-18T01:08:50.728455Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:50.728455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Realization of a simple higher dimensional noncommutative torus as a transformation group C*-algebra","license":"","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Benjam\\'in Itz\\'a-Ortiz, N. Christopher Phillips","submitted_at":"2005-12-01T15:51:57Z","abstract_excerpt":"Let $\\theta$ be a nondegenerate skew symmetric real $d$ by $d$ matrix, and let $A_{\\theta}$ be the corresponding simple higher dimensional noncommutative torus. Suppose that $d$ is odd, or that $d$ is greater or equal to 4 and the entries of $\\theta$ are not contained in a quadratic extension of $\\mathbb{Q}$. Then $A_{\\theta}$ is isomorphic to the transformation group C*-algebra obtained from a minimal homeomorphism of a compact connected one dimensional space locally homeomorphic to the product of the interval and the Cantor set. The proof uses classification theory of C*-algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512030","kind":"arxiv","version":1},"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":"math/0512030","created_at":"2026-05-18T01:08:50.728562+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0512030v1","created_at":"2026-05-18T01:08:50.728562+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0512030","created_at":"2026-05-18T01:08:50.728562+00:00"},{"alias_kind":"pith_short_12","alias_value":"6WGLMRHXKVIL","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"6WGLMRHXKVILT4IU","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"6WGLMRHX","created_at":"2026-05-18T12:25:53.335082+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/6WGLMRHXKVILT4IUT3D4AYBF7V","json":"https://pith.science/pith/6WGLMRHXKVILT4IUT3D4AYBF7V.json","graph_json":"https://pith.science/api/pith-number/6WGLMRHXKVILT4IUT3D4AYBF7V/graph.json","events_json":"https://pith.science/api/pith-number/6WGLMRHXKVILT4IUT3D4AYBF7V/events.json","paper":"https://pith.science/paper/6WGLMRHX"},"agent_actions":{"view_html":"https://pith.science/pith/6WGLMRHXKVILT4IUT3D4AYBF7V","download_json":"https://pith.science/pith/6WGLMRHXKVILT4IUT3D4AYBF7V.json","view_paper":"https://pith.science/paper/6WGLMRHX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0512030&json=true","fetch_graph":"https://pith.science/api/pith-number/6WGLMRHXKVILT4IUT3D4AYBF7V/graph.json","fetch_events":"https://pith.science/api/pith-number/6WGLMRHXKVILT4IUT3D4AYBF7V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6WGLMRHXKVILT4IUT3D4AYBF7V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6WGLMRHXKVILT4IUT3D4AYBF7V/action/storage_attestation","attest_author":"https://pith.science/pith/6WGLMRHXKVILT4IUT3D4AYBF7V/action/author_attestation","sign_citation":"https://pith.science/pith/6WGLMRHXKVILT4IUT3D4AYBF7V/action/citation_signature","submit_replication":"https://pith.science/pith/6WGLMRHXKVILT4IUT3D4AYBF7V/action/replication_record"}},"created_at":"2026-05-18T01:08:50.728562+00:00","updated_at":"2026-05-18T01:08:50.728562+00:00"}