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For each of the three quadratic extensions $K/k$ inside the absolute genus field $k^{(*)}$ of $k$, we compute the capitulation kernel of $K/k$. Then we deduce that each strongly ambiguous class of $k/Q(i)$ capitulates already in $k^{(*)}$, which is smaller than the relative genus field $\\left(k/Q(i)\\right)^*$."},"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":"1503.01992","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NT","submitted_at":"2015-03-06T15:29:40Z","cross_cats_sorted":[],"title_canon_sha256":"82cab913b5a0943b2a45cf35f75354b573311669da4b6c1830931be12bc708f6","abstract_canon_sha256":"0816179b926cf3744ff2a97d6014b4bbc190e4a2363a4f86cba4d2524a32f2d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:27.098878Z","signature_b64":"oVnQthEp3dxcBpsXeEyB+EcrCqU8/IWRSeK617kkC1OcEQyvj/8/pmONwOV6pSIcLGrSTKHeAOt4pUADunJdBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48e734a74a82bcf60498f38b8bfa37397e0c86261298cc55544b8698348fb957","last_reissued_at":"2026-05-18T02:25:27.098375Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:27.098375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the strongly ambiguous classes of some biquadratic number fields","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Abdelkader Zekhnini, Abdelmalek Azizi, Mohammed Taous","submitted_at":"2015-03-06T15:29:40Z","abstract_excerpt":"We study the capitulation of ideal classes in an infinite family of imaginary bicyclic biquadratic number fields consisting of\n  fields $k =Q(\\sqrt{2pq}, i)$, where $i=\\sqrt{-1}$ and $p\\equiv -q\\equiv1 \\pmod 4$ are different primes. For each of the three quadratic extensions $K/k$ inside the absolute genus field $k^{(*)}$ of $k$, we compute the capitulation kernel of $K/k$. Then we deduce that each strongly ambiguous class of $k/Q(i)$ capitulates already in $k^{(*)}$, which is smaller than the relative genus field $\\left(k/Q(i)\\right)^*$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01992","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":"1503.01992","created_at":"2026-05-18T02:25:27.098451+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.01992v1","created_at":"2026-05-18T02:25:27.098451+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01992","created_at":"2026-05-18T02:25:27.098451+00:00"},{"alias_kind":"pith_short_12","alias_value":"JDTTJJ2KQK6P","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"JDTTJJ2KQK6PMBEY","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"JDTTJJ2K","created_at":"2026-05-18T12:29:27.538025+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/JDTTJJ2KQK6PMBEY6OFYX6RXHF","json":"https://pith.science/pith/JDTTJJ2KQK6PMBEY6OFYX6RXHF.json","graph_json":"https://pith.science/api/pith-number/JDTTJJ2KQK6PMBEY6OFYX6RXHF/graph.json","events_json":"https://pith.science/api/pith-number/JDTTJJ2KQK6PMBEY6OFYX6RXHF/events.json","paper":"https://pith.science/paper/JDTTJJ2K"},"agent_actions":{"view_html":"https://pith.science/pith/JDTTJJ2KQK6PMBEY6OFYX6RXHF","download_json":"https://pith.science/pith/JDTTJJ2KQK6PMBEY6OFYX6RXHF.json","view_paper":"https://pith.science/paper/JDTTJJ2K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.01992&json=true","fetch_graph":"https://pith.science/api/pith-number/JDTTJJ2KQK6PMBEY6OFYX6RXHF/graph.json","fetch_events":"https://pith.science/api/pith-number/JDTTJJ2KQK6PMBEY6OFYX6RXHF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JDTTJJ2KQK6PMBEY6OFYX6RXHF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JDTTJJ2KQK6PMBEY6OFYX6RXHF/action/storage_attestation","attest_author":"https://pith.science/pith/JDTTJJ2KQK6PMBEY6OFYX6RXHF/action/author_attestation","sign_citation":"https://pith.science/pith/JDTTJJ2KQK6PMBEY6OFYX6RXHF/action/citation_signature","submit_replication":"https://pith.science/pith/JDTTJJ2KQK6PMBEY6OFYX6RXHF/action/replication_record"}},"created_at":"2026-05-18T02:25:27.098451+00:00","updated_at":"2026-05-18T02:25:27.098451+00:00"}