{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SUVVVMRD7GALR2O4K6DKK45YLP","short_pith_number":"pith:SUVVVMRD","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"},"canonical_sha256":"952b5ab223f980b8e9dc5786a573b85bfc603539a3b50d59db3f16215d7375c2","source":{"kind":"arxiv","id":"1701.01969","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01969","created_at":"2026-05-18T00:30:46Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01969v3","created_at":"2026-05-18T00:30:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01969","created_at":"2026-05-18T00:30:46Z"},{"alias_kind":"pith_short_12","alias_value":"SUVVVMRD7GAL","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SUVVVMRD7GALR2O4","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SUVVVMRD","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SUVVVMRD7GALR2O4K6DKK45YLP","target":"record","payload":{"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"},"canonical_sha256":"952b5ab223f980b8e9dc5786a573b85bfc603539a3b50d59db3f16215d7375c2","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"},"source_kind":"arxiv","source_id":"1701.01969","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:30:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nRdObaZk0FGLL3Rf3Ub4SCEkbmbO06EzNfeCuW6vgNvmm1dOZgsYzOkiTFBlufd17Q8PlDwiLVZMghmD8GLJCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:35:09.134730Z"},"content_sha256":"1c3ea81648c0f838d1f53ad85519ff3c60d30ccd14a97883adad73cf4cc8d985","schema_version":"1.0","event_id":"sha256:1c3ea81648c0f838d1f53ad85519ff3c60d30ccd14a97883adad73cf4cc8d985"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SUVVVMRD7GALR2O4K6DKK45YLP","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:30:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ObWxdbGGYS1EeDd5MxSHx2GTWKvfV9SmVBFfF8IhOpBkrJcn7hpdTVStGz0O9c2/IaldVICbvrOmGQ+6hyIZBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:35:09.135151Z"},"content_sha256":"be04f7ecc3e7c68bf18f2dfd1191d24d148ec982c030537fbe7e08feb842417e","schema_version":"1.0","event_id":"sha256:be04f7ecc3e7c68bf18f2dfd1191d24d148ec982c030537fbe7e08feb842417e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SUVVVMRD7GALR2O4K6DKK45YLP/bundle.json","state_url":"https://pith.science/pith/SUVVVMRD7GALR2O4K6DKK45YLP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SUVVVMRD7GALR2O4K6DKK45YLP/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":"2026-05-27T10:35:09Z","links":{"resolver":"https://pith.science/pith/SUVVVMRD7GALR2O4K6DKK45YLP","bundle":"https://pith.science/pith/SUVVVMRD7GALR2O4K6DKK45YLP/bundle.json","state":"https://pith.science/pith/SUVVVMRD7GALR2O4K6DKK45YLP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SUVVVMRD7GALR2O4K6DKK45YLP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SUVVVMRD7GALR2O4K6DKK45YLP","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":"255721e5727e6bda7daa5a86419786c9c7924bd966621fddd50f78d5e90b54a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-08T15:20:30Z","title_canon_sha256":"9c1d1ce5115f7f762445f649be270591f5e6ff9c7d10c213ffa0cb698de818e0"},"schema_version":"1.0","source":{"id":"1701.01969","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01969","created_at":"2026-05-18T00:30:46Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01969v3","created_at":"2026-05-18T00:30:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01969","created_at":"2026-05-18T00:30:46Z"},{"alias_kind":"pith_short_12","alias_value":"SUVVVMRD7GAL","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SUVVVMRD7GALR2O4","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SUVVVMRD","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:be04f7ecc3e7c68bf18f2dfd1191d24d148ec982c030537fbe7e08feb842417e","target":"graph","created_at":"2026-05-18T00:30:46Z","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":"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 ","authors_text":"Daniel Rabayev, Jack Sonn, Joachim Koenig","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-08T15:20:30Z","title":"Galois realizations with inertia groups of order two"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01969","kind":"arxiv","version":3},"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":"sha256:1c3ea81648c0f838d1f53ad85519ff3c60d30ccd14a97883adad73cf4cc8d985","target":"record","created_at":"2026-05-18T00:30:46Z","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":"255721e5727e6bda7daa5a86419786c9c7924bd966621fddd50f78d5e90b54a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-08T15:20:30Z","title_canon_sha256":"9c1d1ce5115f7f762445f649be270591f5e6ff9c7d10c213ffa0cb698de818e0"},"schema_version":"1.0","source":{"id":"1701.01969","kind":"arxiv","version":3}},"canonical_sha256":"952b5ab223f980b8e9dc5786a573b85bfc603539a3b50d59db3f16215d7375c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"952b5ab223f980b8e9dc5786a573b85bfc603539a3b50d59db3f16215d7375c2","first_computed_at":"2026-05-18T00:30:46.209907Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:46.209907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NSrtH21kQJnEpWLxutyKdBbk6enTOHeKGr0Chhdjc+Wr6DuKIpevsAlPHWUlTdFiIgvNLdTWlrlCHvQ53vhhCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:46.210512Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.01969","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c3ea81648c0f838d1f53ad85519ff3c60d30ccd14a97883adad73cf4cc8d985","sha256:be04f7ecc3e7c68bf18f2dfd1191d24d148ec982c030537fbe7e08feb842417e"],"state_sha256":"25396b9402595995ae735912a6fde2fa9492dee370b9cd406ceed4d93b99a286"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qDLmPG5OsgI9KfCB1e/TrwfU2W8VtJExBl0H0jS2HqRZcsV4Og3mRhbqP5UpNBpCKHwObVmTnuOTBbZHL9eWBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T10:35:09.137500Z","bundle_sha256":"934a9cd4d6fef3d24b4aa8196e7d156d2c1320dd1ba7f5ed1f7407a13cd380cf"}}