{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:SUVVVMRD7GALR2O4K6DKK45YLP","short_pith_number":"pith:SUVVVMRD","schema_version":"1.0","canonical_sha256":"952b5ab223f980b8e9dc5786a573b85bfc603539a3b50d59db3f16215d7375c2","source":{"kind":"arxiv","id":"1701.01969","version":3},"attestation_state":"computed","paper":{"title":"Galois realizations with inertia groups of order two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Daniel Rabayev, Jack Sonn, Joachim Koenig","submitted_at":"2017-01-08T15:20:30Z","abstract_excerpt":"There are several variants of the inverse Galois problem which involve restrictions on ramification. In this paper we give sufficient conditions that a given finite group $G$ occurs infinitely often as a Galois group over the rationals $\\mathbb Q$ with all nontrivial inertia groups of order $2$. Notably any such realization of $G$ can be translated up to a quadratic field over which the corresponding realization of $G$ is unramified.\n  The sufficient conditions are imposed on a parametric polynomial with Galois group $G$--if such a polynomial is available--and the infinitely many realizations "},"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":"1701.01969","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-08T15:20:30Z","cross_cats_sorted":[],"title_canon_sha256":"9c1d1ce5115f7f762445f649be270591f5e6ff9c7d10c213ffa0cb698de818e0","abstract_canon_sha256":"255721e5727e6bda7daa5a86419786c9c7924bd966621fddd50f78d5e90b54a4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:46.210512Z","signature_b64":"NSrtH21kQJnEpWLxutyKdBbk6enTOHeKGr0Chhdjc+Wr6DuKIpevsAlPHWUlTdFiIgvNLdTWlrlCHvQ53vhhCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"952b5ab223f980b8e9dc5786a573b85bfc603539a3b50d59db3f16215d7375c2","last_reissued_at":"2026-05-18T00:30:46.209907Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:46.209907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Galois realizations with inertia groups of order two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Daniel Rabayev, Jack Sonn, Joachim Koenig","submitted_at":"2017-01-08T15:20:30Z","abstract_excerpt":"There are several variants of the inverse Galois problem which involve restrictions on ramification. In this paper we give sufficient conditions that a given finite group $G$ occurs infinitely often as a Galois group over the rationals $\\mathbb Q$ with all nontrivial inertia groups of order $2$. Notably any such realization of $G$ can be translated up to a quadratic field over which the corresponding realization of $G$ is unramified.\n  The sufficient conditions are imposed on a parametric polynomial with Galois group $G$--if such a polynomial is available--and the infinitely many realizations "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01969","kind":"arxiv","version":3},"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":"1701.01969","created_at":"2026-05-18T00:30:46.210008+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.01969v3","created_at":"2026-05-18T00:30:46.210008+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01969","created_at":"2026-05-18T00:30:46.210008+00:00"},{"alias_kind":"pith_short_12","alias_value":"SUVVVMRD7GAL","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"SUVVVMRD7GALR2O4","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"SUVVVMRD","created_at":"2026-05-18T12:31:43.269735+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/SUVVVMRD7GALR2O4K6DKK45YLP","json":"https://pith.science/pith/SUVVVMRD7GALR2O4K6DKK45YLP.json","graph_json":"https://pith.science/api/pith-number/SUVVVMRD7GALR2O4K6DKK45YLP/graph.json","events_json":"https://pith.science/api/pith-number/SUVVVMRD7GALR2O4K6DKK45YLP/events.json","paper":"https://pith.science/paper/SUVVVMRD"},"agent_actions":{"view_html":"https://pith.science/pith/SUVVVMRD7GALR2O4K6DKK45YLP","download_json":"https://pith.science/pith/SUVVVMRD7GALR2O4K6DKK45YLP.json","view_paper":"https://pith.science/paper/SUVVVMRD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.01969&json=true","fetch_graph":"https://pith.science/api/pith-number/SUVVVMRD7GALR2O4K6DKK45YLP/graph.json","fetch_events":"https://pith.science/api/pith-number/SUVVVMRD7GALR2O4K6DKK45YLP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SUVVVMRD7GALR2O4K6DKK45YLP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SUVVVMRD7GALR2O4K6DKK45YLP/action/storage_attestation","attest_author":"https://pith.science/pith/SUVVVMRD7GALR2O4K6DKK45YLP/action/author_attestation","sign_citation":"https://pith.science/pith/SUVVVMRD7GALR2O4K6DKK45YLP/action/citation_signature","submit_replication":"https://pith.science/pith/SUVVVMRD7GALR2O4K6DKK45YLP/action/replication_record"}},"created_at":"2026-05-18T00:30:46.210008+00:00","updated_at":"2026-05-18T00:30:46.210008+00:00"}