{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OXHBC55BMI3GYLPXWR7OPD4DIY","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":"6fc93b1b507061422ac995b8b9f0a4253634edbfa7dbceabd27234f3833e44ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-29T12:46:34Z","title_canon_sha256":"ff9cd94933b415eb5c4cb3a6576e6159d6007e7187a9e64798fdd54f7121a012"},"schema_version":"1.0","source":{"id":"1305.6781","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.6781","created_at":"2026-05-18T00:40:08Z"},{"alias_kind":"arxiv_version","alias_value":"1305.6781v4","created_at":"2026-05-18T00:40:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6781","created_at":"2026-05-18T00:40:08Z"},{"alias_kind":"pith_short_12","alias_value":"OXHBC55BMI3G","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OXHBC55BMI3GYLPX","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OXHBC55B","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:e4467a93e0cff3b8c5bbbeef51ebaf38b5278d67debc3b601c80503c53d80444","target":"graph","created_at":"2026-05-18T00:40:08Z","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"},"paper":{"abstract_excerpt":"Let $U/L$ be a finite abelian extension of number fields. We first construct a universal primitive generator of $U$ over $L$ whose relative trace to any intermediate field $F$ becomes a generator of $F$ over $L$, too. We also develop a similar argument in terms of norm. As its examples we investigate towers of ray class fields over imaginary quadratic fields. And, we further present a new method of finding a normal element for the extension $U/L$.","authors_text":"Dong Hwa Shin, Ja Kyung Koo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-29T12:46:34Z","title":"Generators for abelian extensions of number fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6781","kind":"arxiv","version":4},"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:cac4f7bfe3718f18adbbe151323456903229cccb5a70ce1bf28b844431621a01","target":"record","created_at":"2026-05-18T00:40:08Z","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":"6fc93b1b507061422ac995b8b9f0a4253634edbfa7dbceabd27234f3833e44ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-29T12:46:34Z","title_canon_sha256":"ff9cd94933b415eb5c4cb3a6576e6159d6007e7187a9e64798fdd54f7121a012"},"schema_version":"1.0","source":{"id":"1305.6781","kind":"arxiv","version":4}},"canonical_sha256":"75ce1177a162366c2df7b47ee78f83461e34f8f8ca5acdb5dc3e474b273c3f26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75ce1177a162366c2df7b47ee78f83461e34f8f8ca5acdb5dc3e474b273c3f26","first_computed_at":"2026-05-18T00:40:08.801052Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:08.801052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GuYAZXLrOldVlqRfMJBECC0u3UHbCNyssLOOwESmFSgTkgcA3YBoDeP3DNZNPrlIsjfjgjG60oZJkZDFUzayAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:08.801553Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.6781","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cac4f7bfe3718f18adbbe151323456903229cccb5a70ce1bf28b844431621a01","sha256:e4467a93e0cff3b8c5bbbeef51ebaf38b5278d67debc3b601c80503c53d80444"],"state_sha256":"61d8a5b14a24d3ae1766aa058d6b00d4a543f4b87e23663bd727218b521980a7"}