{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DEM4DS6B44QZVG3LXDAR3GHBIM","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":"248781a8f6787e1af28dcb61d6085bcb2f76853d26a6e15555736b3bd990de8c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-10T20:48:56Z","title_canon_sha256":"fa33a0faf2d021c61834958cbd861037e59dfd7c79afb2c5278177342c33aece"},"schema_version":"1.0","source":{"id":"1609.03087","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03087","created_at":"2026-05-18T01:04:47Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03087v1","created_at":"2026-05-18T01:04:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03087","created_at":"2026-05-18T01:04:47Z"},{"alias_kind":"pith_short_12","alias_value":"DEM4DS6B44QZ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DEM4DS6B44QZVG3L","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DEM4DS6B","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:ececddc7b9d651c373e13a7d0f7dd3d68ea3880d8fb35bd050d3e66cf8fa14d5","target":"graph","created_at":"2026-05-18T01:04:47Z","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 $2$-ideal classes of an infinite family of imaginary biquadratic number fields consisting of fields $k =Q(\\sqrt{pq_1q_2}, i)$, where $i=\\sqrt{-1}$ and $q_1\\equiv q_2\\equiv-p\\equiv-1 \\pmod 4$ 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 $k^{(*)}$.","authors_text":"Abdelkader Zekhnini, Abdelmalek Azizi, Mohammed Taous","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-10T20:48:56Z","title":"Capitulation in the absolutely abelian extensions of some number fields II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03087","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":"sha256:14909d765a2f6c790e752710fcda540c160a5b85a8d0222dbf25abb6555e5a88","target":"record","created_at":"2026-05-18T01:04:47Z","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":"248781a8f6787e1af28dcb61d6085bcb2f76853d26a6e15555736b3bd990de8c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-10T20:48:56Z","title_canon_sha256":"fa33a0faf2d021c61834958cbd861037e59dfd7c79afb2c5278177342c33aece"},"schema_version":"1.0","source":{"id":"1609.03087","kind":"arxiv","version":1}},"canonical_sha256":"1919c1cbc1e7219a9b6bb8c11d98e14301c3e5efb03c1e58a83fda100364cbfd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1919c1cbc1e7219a9b6bb8c11d98e14301c3e5efb03c1e58a83fda100364cbfd","first_computed_at":"2026-05-18T01:04:47.793899Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:47.793899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tbQIYrjmJXo4W19vam9tKlyTRP5RZWAMegBAog1BIkBiztnzRUTMgDuKxAKoHqMwr4vgjVICb+clmPYYDP2+Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:47.794291Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.03087","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14909d765a2f6c790e752710fcda540c160a5b85a8d0222dbf25abb6555e5a88","sha256:ececddc7b9d651c373e13a7d0f7dd3d68ea3880d8fb35bd050d3e66cf8fa14d5"],"state_sha256":"dff899970b3743526fd36ec75309c7e0d6c4cc7dc9054f6addcd7f4c75207b13"}