{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:OHXEFNWHQNHTHDAG2UVEVVQXKX","short_pith_number":"pith:OHXEFNWH","canonical_record":{"source":{"id":"1503.01813","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NT","submitted_at":"2015-03-05T23:00:06Z","cross_cats_sorted":[],"title_canon_sha256":"60982971dad78794d595faf605a17bb754a3624100e1fd0b0e8a250f952d78a9","abstract_canon_sha256":"624b01f73315d10dcaa0bbd32f2ea18f991927d4e9d0fdd25b76d477b6c6a6ac"},"schema_version":"1.0"},"canonical_sha256":"71ee42b6c7834f338c06d52a4ad61755e691ada9491bdd1382cdc6b55e67db89","source":{"kind":"arxiv","id":"1503.01813","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01813","created_at":"2026-05-18T02:25:27Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01813v1","created_at":"2026-05-18T02:25:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01813","created_at":"2026-05-18T02:25:27Z"},{"alias_kind":"pith_short_12","alias_value":"OHXEFNWHQNHT","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OHXEFNWHQNHTHDAG","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OHXEFNWH","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:OHXEFNWHQNHTHDAG2UVEVVQXKX","target":"record","payload":{"canonical_record":{"source":{"id":"1503.01813","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NT","submitted_at":"2015-03-05T23:00:06Z","cross_cats_sorted":[],"title_canon_sha256":"60982971dad78794d595faf605a17bb754a3624100e1fd0b0e8a250f952d78a9","abstract_canon_sha256":"624b01f73315d10dcaa0bbd32f2ea18f991927d4e9d0fdd25b76d477b6c6a6ac"},"schema_version":"1.0"},"canonical_sha256":"71ee42b6c7834f338c06d52a4ad61755e691ada9491bdd1382cdc6b55e67db89","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:27.488097Z","signature_b64":"go/MW34oDZmhntRn3EH4COa/7rhhbwScuw1m1NAHnNrMuTgAJuI5n4GEjUZwrwVH1CfE0MIdV6WZ6FgVStktDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71ee42b6c7834f338c06d52a4ad61755e691ada9491bdd1382cdc6b55e67db89","last_reissued_at":"2026-05-18T02:25:27.487731Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:27.487731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.01813","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":"8fgrd4eBPy0NbC9TpXIRYC65G9H/zw9sx0hIsixNBtJ7ST9aPYIejTQZxlbN/kxTNiUONX8GeU5NdQnDGTk5Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T23:20:58.632052Z"},"content_sha256":"d3a65a7d5170d8d4b5496596875a156637992e28622f6dd4cc1dc08f324bd88d","schema_version":"1.0","event_id":"sha256:d3a65a7d5170d8d4b5496596875a156637992e28622f6dd4cc1dc08f324bd88d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:OHXEFNWHQNHTHDAG2UVEVVQXKX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On some metabelian 2-group whose abelianization is of type (2, 2, 2) and applications","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":"2015-03-05T23:00:06Z","abstract_excerpt":"Let $G$ be some metabelian $2$-group satisfying the condition $G/G'\\simeq \\mathbb{Z}/2\\mathbb{Z}\\times\\mathbb{Z}/2\\mathbb{Z}\\times\\mathbb{Z}/2\\mathbb{Z}$. In this paper, we construct all the subgroups of $G$ of index $2$ or $4$, we give the abelianization types of these subgroups and we compute the kernel of the transfer map. Then we apply these results to study the capitulation problem of the $2$-ideal classes of some fields $\\mathbf{k}$ satisfying the condition $\\mathrm{G}al(\\mathbf{k}_2^{(2)}/\\mathbf{k})\\simeq G$, where $\\mathbf{k}_2^{(2)}$ is the second Hilbert $2$-class field of $\\mathbf{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01813","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":"gTLcZl8ZowKbO9jTO5u90tnFQg3j093BhzwMCRkhtIPP1WcUTFpP89FDvHUGTmGHx5m1MIAu9Cx9ZvMYNJa+Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T23:20:58.632413Z"},"content_sha256":"5ab5c984147cd5c5b2e74024e5cf3a003f938deff4a380ac3ba9dfc274464c9d","schema_version":"1.0","event_id":"sha256:5ab5c984147cd5c5b2e74024e5cf3a003f938deff4a380ac3ba9dfc274464c9d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OHXEFNWHQNHTHDAG2UVEVVQXKX/bundle.json","state_url":"https://pith.science/pith/OHXEFNWHQNHTHDAG2UVEVVQXKX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OHXEFNWHQNHTHDAG2UVEVVQXKX/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":"2026-06-21T23:20:58Z","links":{"resolver":"https://pith.science/pith/OHXEFNWHQNHTHDAG2UVEVVQXKX","bundle":"https://pith.science/pith/OHXEFNWHQNHTHDAG2UVEVVQXKX/bundle.json","state":"https://pith.science/pith/OHXEFNWHQNHTHDAG2UVEVVQXKX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OHXEFNWHQNHTHDAG2UVEVVQXKX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OHXEFNWHQNHTHDAG2UVEVVQXKX","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":"624b01f73315d10dcaa0bbd32f2ea18f991927d4e9d0fdd25b76d477b6c6a6ac","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NT","submitted_at":"2015-03-05T23:00:06Z","title_canon_sha256":"60982971dad78794d595faf605a17bb754a3624100e1fd0b0e8a250f952d78a9"},"schema_version":"1.0","source":{"id":"1503.01813","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01813","created_at":"2026-05-18T02:25:27Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01813v1","created_at":"2026-05-18T02:25:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01813","created_at":"2026-05-18T02:25:27Z"},{"alias_kind":"pith_short_12","alias_value":"OHXEFNWHQNHT","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OHXEFNWHQNHTHDAG","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OHXEFNWH","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:5ab5c984147cd5c5b2e74024e5cf3a003f938deff4a380ac3ba9dfc274464c9d","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":"Let $G$ be some metabelian $2$-group satisfying the condition $G/G'\\simeq \\mathbb{Z}/2\\mathbb{Z}\\times\\mathbb{Z}/2\\mathbb{Z}\\times\\mathbb{Z}/2\\mathbb{Z}$. In this paper, we construct all the subgroups of $G$ of index $2$ or $4$, we give the abelianization types of these subgroups and we compute the kernel of the transfer map. Then we apply these results to study the capitulation problem of the $2$-ideal classes of some fields $\\mathbf{k}$ satisfying the condition $\\mathrm{G}al(\\mathbf{k}_2^{(2)}/\\mathbf{k})\\simeq G$, where $\\mathbf{k}_2^{(2)}$ is the second Hilbert $2$-class field of $\\mathbf{","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":"2015-03-05T23:00:06Z","title":"On some metabelian 2-group whose abelianization is of type (2, 2, 2) and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01813","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:d3a65a7d5170d8d4b5496596875a156637992e28622f6dd4cc1dc08f324bd88d","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":"624b01f73315d10dcaa0bbd32f2ea18f991927d4e9d0fdd25b76d477b6c6a6ac","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NT","submitted_at":"2015-03-05T23:00:06Z","title_canon_sha256":"60982971dad78794d595faf605a17bb754a3624100e1fd0b0e8a250f952d78a9"},"schema_version":"1.0","source":{"id":"1503.01813","kind":"arxiv","version":1}},"canonical_sha256":"71ee42b6c7834f338c06d52a4ad61755e691ada9491bdd1382cdc6b55e67db89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71ee42b6c7834f338c06d52a4ad61755e691ada9491bdd1382cdc6b55e67db89","first_computed_at":"2026-05-18T02:25:27.487731Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:27.487731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"go/MW34oDZmhntRn3EH4COa/7rhhbwScuw1m1NAHnNrMuTgAJuI5n4GEjUZwrwVH1CfE0MIdV6WZ6FgVStktDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:27.488097Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.01813","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d3a65a7d5170d8d4b5496596875a156637992e28622f6dd4cc1dc08f324bd88d","sha256:5ab5c984147cd5c5b2e74024e5cf3a003f938deff4a380ac3ba9dfc274464c9d"],"state_sha256":"9a996a8462e1ef995ba4f66b4b9969fd30274e3d6962c1ec1d1599eaadabdb24"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rsw6Ak9eX5Ja1YgLIjYHj6OhyxSTeTyNw1lXxoevB9vpEdDO6+O3ROW7t+7n4FdwP0jDHvkNc6nP054MaWcVAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T23:20:58.634586Z","bundle_sha256":"1c5d6dceb02362deee67d9cbeaf593047ed0e75a92caa289bd70cf7df38b7298"}}