{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IAK3CLJNDFDP3TGKBL3L2YMPGB","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":"58e4c2cfe136169915a1df2b4fc475ec4517fd85e225603186880036d0e268f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-25T12:33:58Z","title_canon_sha256":"b11fc99c6d6218246f58c4bef1b61721f2b0de5b8986320fd5ea2c0a4846c5ba"},"schema_version":"1.0","source":{"id":"1709.08453","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.08453","created_at":"2026-05-18T00:34:25Z"},{"alias_kind":"arxiv_version","alias_value":"1709.08453v1","created_at":"2026-05-18T00:34:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.08453","created_at":"2026-05-18T00:34:25Z"},{"alias_kind":"pith_short_12","alias_value":"IAK3CLJNDFDP","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IAK3CLJNDFDP3TGK","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IAK3CLJN","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:d0e4022fc962f6c759999b5d100e49cd47b6f92e166b68cc5c5dc67b07ebbdae","target":"graph","created_at":"2026-05-18T00:34:25Z","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 $K$ be a number field and $K_{ur}$ be the maximal extension of $K$ that is unramified at all places. In a previous article, the first author found three real quadratic fields $K$ such that $Gal(K_{ur}/K)$ is finite and nonabelian simple under the assumption of the GRH(Generalized Riemann Hypothesis). In this article, we will identify more quadratic number fields $K$ such that $Gal(K_{ur}/K)$ is a finite nonsolvable group and also explicitly calculate their Galois groups under the assumption of the Generalized Riemann Hypothesis.","authors_text":"Joachim K\\\"onig, Kwang-Seob Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-25T12:33:58Z","title":"Some examples of quadratic fields with finite nonsolvable maximal unramified extensions II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08453","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:ad1bd1b16a662d567a03f741445d3f0c12761d4999fbe38cd9cc15c9aa4e8755","target":"record","created_at":"2026-05-18T00:34:25Z","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":"58e4c2cfe136169915a1df2b4fc475ec4517fd85e225603186880036d0e268f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-25T12:33:58Z","title_canon_sha256":"b11fc99c6d6218246f58c4bef1b61721f2b0de5b8986320fd5ea2c0a4846c5ba"},"schema_version":"1.0","source":{"id":"1709.08453","kind":"arxiv","version":1}},"canonical_sha256":"4015b12d2d1946fdccca0af6bd618f304d49a62efa7499d6fa7cafc88b7c3c49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4015b12d2d1946fdccca0af6bd618f304d49a62efa7499d6fa7cafc88b7c3c49","first_computed_at":"2026-05-18T00:34:25.602105Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:25.602105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ADGqeIcOjg7nAXb0/oq3ZzKvvxn0w25NJsIA+phCGiQoLJITr/i5gqunni9vpLu5vPoNT0Zk9B1PHm3V1O9XCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:25.602626Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.08453","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad1bd1b16a662d567a03f741445d3f0c12761d4999fbe38cd9cc15c9aa4e8755","sha256:d0e4022fc962f6c759999b5d100e49cd47b6f92e166b68cc5c5dc67b07ebbdae"],"state_sha256":"d5364714884f33a0dfba551ebec6cbe2b735ebdc21ce9c1949b569b07972deeb"}