{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UL5KGWZKKSJDEPVJTBPKJ455QY","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":"0623645d1878cfda2403cc0afe158ec6fa6fc677547a083e2a3f4cc66bd83433","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-02-19T11:31:39Z","title_canon_sha256":"60dfbda814dab43220c8937df6d4ecb579b76c647c474d39489d8e68cd4e5d20"},"schema_version":"1.0","source":{"id":"1102.3984","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3984","created_at":"2026-05-18T04:28:19Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3984v1","created_at":"2026-05-18T04:28:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3984","created_at":"2026-05-18T04:28:19Z"},{"alias_kind":"pith_short_12","alias_value":"UL5KGWZKKSJD","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UL5KGWZKKSJDEPVJ","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UL5KGWZK","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:d858c9a8600a4b4a52b467a78cf85a3582101a92b44780278615309fdde20692","target":"graph","created_at":"2026-05-18T04:28:19Z","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 field of characteristic $p>0$, which has infinitely many discrete valuations. We show that every finite embedding problem for $\\Gal(k)$ with finitely many prescribed local conditions, whose kernel is a $p$-group, is properly solvable. We then apply this result in studying the admissibility of finite groups over global fields of positive characteristic. We also give another proof for a result of Sonn.","authors_text":"Nguyen Duy Tan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-02-19T11:31:39Z","title":"Embedding problems with local conditions and the admissibility of finite groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3984","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":"sha256:7174b048ed49a2cc26fd253d9a5b6103243a3606b6fbad07c58c78081c8af13d","target":"record","created_at":"2026-05-18T04:28:19Z","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":"0623645d1878cfda2403cc0afe158ec6fa6fc677547a083e2a3f4cc66bd83433","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-02-19T11:31:39Z","title_canon_sha256":"60dfbda814dab43220c8937df6d4ecb579b76c647c474d39489d8e68cd4e5d20"},"schema_version":"1.0","source":{"id":"1102.3984","kind":"arxiv","version":1}},"canonical_sha256":"a2faa35b2a5492323ea9985ea4f3bd8611d57cc4b5d7ff5cc99e6bd00452d564","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2faa35b2a5492323ea9985ea4f3bd8611d57cc4b5d7ff5cc99e6bd00452d564","first_computed_at":"2026-05-18T04:28:19.319301Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:19.319301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"427hnnxVGlwOFA4hdu7ejzPL6q9hH5rk5FurMRXEjbIa+S2znmX9dW6f8TvDJvhbEEpzsThrBVOtt47zY+QUAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:19.319811Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.3984","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7174b048ed49a2cc26fd253d9a5b6103243a3606b6fbad07c58c78081c8af13d","sha256:d858c9a8600a4b4a52b467a78cf85a3582101a92b44780278615309fdde20692"],"state_sha256":"5fba3ab7eaaca36d5ad61686200f8d08f6c452d9984c15ff6db6ad0cc567f1f7"}