{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JDTTJJ2KQK6PMBEY6OFYX6RXHF","short_pith_number":"pith:JDTTJJ2K","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"},"canonical_sha256":"48e734a74a82bcf60498f38b8bfa37397e0c86261298cc55544b8698348fb957","source":{"kind":"arxiv","id":"1503.01992","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01992","created_at":"2026-05-18T02:25:27Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01992v1","created_at":"2026-05-18T02:25:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01992","created_at":"2026-05-18T02:25:27Z"},{"alias_kind":"pith_short_12","alias_value":"JDTTJJ2KQK6P","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JDTTJJ2KQK6PMBEY","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JDTTJJ2K","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JDTTJJ2KQK6PMBEY6OFYX6RXHF","target":"record","payload":{"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"},"canonical_sha256":"48e734a74a82bcf60498f38b8bfa37397e0c86261298cc55544b8698348fb957","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"},"source_kind":"arxiv","source_id":"1503.01992","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:25:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vZfGNwk31r/vqbERiAGYJCcawr4eoExJRYH+8jEkORaJJ/+FiwjquiV7LS3DNB8dGy2VVdwnR5M5uMSByQ/UDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:31:37.484811Z"},"content_sha256":"8a09a60705f0e8a9cca0c8be4ee0beaed9d06b7ad757f7552ef6e7f2c816f786","schema_version":"1.0","event_id":"sha256:8a09a60705f0e8a9cca0c8be4ee0beaed9d06b7ad757f7552ef6e7f2c816f786"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JDTTJJ2KQK6PMBEY6OFYX6RXHF","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:25:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vYdyziHs4S9aG4RAekPcpz78rWT278A3iDKfF1iBIs95NJdfzexkwaD5CZZXDw20nwUEk4dxJHCGs4YDFucYAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:31:37.485162Z"},"content_sha256":"7019516de94e329a4898d8e63ffaf087eb0782f1e8e8ab3a897c0c17636a4376","schema_version":"1.0","event_id":"sha256:7019516de94e329a4898d8e63ffaf087eb0782f1e8e8ab3a897c0c17636a4376"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JDTTJJ2KQK6PMBEY6OFYX6RXHF/bundle.json","state_url":"https://pith.science/pith/JDTTJJ2KQK6PMBEY6OFYX6RXHF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JDTTJJ2KQK6PMBEY6OFYX6RXHF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-21T22:31:37Z","links":{"resolver":"https://pith.science/pith/JDTTJJ2KQK6PMBEY6OFYX6RXHF","bundle":"https://pith.science/pith/JDTTJJ2KQK6PMBEY6OFYX6RXHF/bundle.json","state":"https://pith.science/pith/JDTTJJ2KQK6PMBEY6OFYX6RXHF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JDTTJJ2KQK6PMBEY6OFYX6RXHF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JDTTJJ2KQK6PMBEY6OFYX6RXHF","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":"0816179b926cf3744ff2a97d6014b4bbc190e4a2363a4f86cba4d2524a32f2d5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NT","submitted_at":"2015-03-06T15:29:40Z","title_canon_sha256":"82cab913b5a0943b2a45cf35f75354b573311669da4b6c1830931be12bc708f6"},"schema_version":"1.0","source":{"id":"1503.01992","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01992","created_at":"2026-05-18T02:25:27Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01992v1","created_at":"2026-05-18T02:25:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01992","created_at":"2026-05-18T02:25:27Z"},{"alias_kind":"pith_short_12","alias_value":"JDTTJJ2KQK6P","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JDTTJJ2KQK6PMBEY","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JDTTJJ2K","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:7019516de94e329a4898d8e63ffaf087eb0782f1e8e8ab3a897c0c17636a4376","target":"graph","created_at":"2026-05-18T02:25:27Z","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":"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 $\\left(k/Q(i)\\right)^*$.","authors_text":"Abdelkader Zekhnini, Abdelmalek Azizi, Mohammed Taous","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NT","submitted_at":"2015-03-06T15:29:40Z","title":"On the strongly ambiguous classes of some biquadratic number fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01992","kind":"arxiv","version":1},"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":"sha256:8a09a60705f0e8a9cca0c8be4ee0beaed9d06b7ad757f7552ef6e7f2c816f786","target":"record","created_at":"2026-05-18T02:25:27Z","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":"0816179b926cf3744ff2a97d6014b4bbc190e4a2363a4f86cba4d2524a32f2d5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NT","submitted_at":"2015-03-06T15:29:40Z","title_canon_sha256":"82cab913b5a0943b2a45cf35f75354b573311669da4b6c1830931be12bc708f6"},"schema_version":"1.0","source":{"id":"1503.01992","kind":"arxiv","version":1}},"canonical_sha256":"48e734a74a82bcf60498f38b8bfa37397e0c86261298cc55544b8698348fb957","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48e734a74a82bcf60498f38b8bfa37397e0c86261298cc55544b8698348fb957","first_computed_at":"2026-05-18T02:25:27.098375Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:27.098375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oVnQthEp3dxcBpsXeEyB+EcrCqU8/IWRSeK617kkC1OcEQyvj/8/pmONwOV6pSIcLGrSTKHeAOt4pUADunJdBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:27.098878Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.01992","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a09a60705f0e8a9cca0c8be4ee0beaed9d06b7ad757f7552ef6e7f2c816f786","sha256:7019516de94e329a4898d8e63ffaf087eb0782f1e8e8ab3a897c0c17636a4376"],"state_sha256":"b9cfb2ca24b6a3a006a65553a301544b2ef99e23f5b37bcd4f815b6703ba961c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pJWaRficPEUujAHVZq8ZUs5mIPPQmzkyWqCcblXrtJepo6nVikPdMUi+NYlsFx0Qpv893lCyIAFLZeK8Jz2xAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T22:31:37.487119Z","bundle_sha256":"4a5709615b6c2e3671bea4c47c52402672de2915ef07516cfe6b47828b4b9edb"}}