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This tame/wild dichotomy is not accounted for by the class group heuristics in the literature. Analogously, when the extensions $F = K(\\sqrt[3]{n})$ of $K = \\mathbb{Q}(\\sqrt{-3})$ are ordered by the norm of $n \\in \\mathcal{O}_K$, we show that the average size of $\\mathrm{Cl}_F[2]$ is $3/2$, as is predicted by th"},"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":"2506.13749","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-06-16T17:55:37Z","cross_cats_sorted":[],"title_canon_sha256":"5b4b2109b3a53228b2ff053b4f98ad6053a59207328f34e52f4f59a8a4f5f12e","abstract_canon_sha256":"55c2b9ddaa9cc5d32eeca76c9df710a5a1f7914a01ba296bbc8579c653281a87"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:48:26.678473Z","signature_b64":"RGu6rHbLAmyiK5ff9FKSg8TBv8igOeEr6GR6wCMHHK8zcjt1oVDRrWS0msLJzqMAUvow8FxCzO+biQ34FxdtCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cdf9fcc9300a8f5743471834ef782352fddb5213d40d7b9e9ec07c2ea9f52c74","last_reissued_at":"2026-07-05T11:48:26.677971Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:48:26.677971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hecke reciprocity and class groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ari Shnidman, Artane Siad","submitted_at":"2025-06-16T17:55:37Z","abstract_excerpt":"We compute the average size of $\\mathrm{Cl}_F[2]$ in the family of cubic fields $F = \\mathbb{Q}(\\sqrt[3]{n})$. 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