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Retract non-rationality of norm one tori for primitive $G\\leq S_{2p}$ where $p$ is a prime number and for the five Mathieu groups $M_n\\leq S_n$ $(n=11,12,22,23,24)$ is also given."},"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":"1811.02145","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-11-06T03:28:33Z","cross_cats_sorted":["math.NT","math.RA"],"title_canon_sha256":"8adf2b54ba9473040ec24d184f0c30d2429af21c6872d47af7d99d31398b242e","abstract_canon_sha256":"d9858a73ca9028d3096f375259b2056fea0452850e1e1fb1e4862b13526c7588"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:58.655579Z","signature_b64":"sobkbklqJ+cNNxUwndpIxQR0Nuhaw5RjSJF2MDTkvLstoxkCxjj4VjD/Be2y6W+IHIS8EuE7sMdQVbkW33bYAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a3aec3d996b32e709e0e2e46a5cb83446634ce6444aa263d86583d1b768b81a","last_reissued_at":"2026-05-17T23:44:58.654910Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:58.654910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rationality problem for norm one tori in small dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT","math.RA"],"primary_cat":"math.AG","authors_text":"Aiichi Yamasaki, Akinari Hoshi, Sumito Hasegawa","submitted_at":"2018-11-06T03:28:33Z","abstract_excerpt":"We classify stably/retract rational norm one tori in dimension $n-1$ for $n=2^e$ $(e\\geq 1)$ is a power of $2$ and $n=12, 14, 15$. 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