{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:C7BQO3NXLP2Y5MBGI645MQYFUT","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":"4e649ad4f1401e2d6fef37e05334e3b9a1efe2517fa6b65484202cadc5511f24","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-12T17:41:22Z","title_canon_sha256":"0ec3a92fe68ffc387fde40ae07ca1bc878c4d51948ce17b3447e318971aaf953"},"schema_version":"1.0","source":{"id":"1706.03751","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.03751","created_at":"2026-05-18T00:41:47Z"},{"alias_kind":"arxiv_version","alias_value":"1706.03751v3","created_at":"2026-05-18T00:41:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.03751","created_at":"2026-05-18T00:41:47Z"},{"alias_kind":"pith_short_12","alias_value":"C7BQO3NXLP2Y","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"C7BQO3NXLP2Y5MBG","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"C7BQO3NX","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:c45aa425ae4738ef97c5e1df29e5b1d3b335a9182234fe3dae49aef0fbd3b08f","target":"graph","created_at":"2026-05-18T00:41:47Z","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":"For a prime $p$, a cyclic-by-$p$ group $G$ and a $G$-extension $L|K$ of complete discrete valuation fields of characteristic $p$ with algebraically closed residue field, the local lifting problem asks whether the extension $L|K$ lifts to characteristic zero. In this paper, we characterize $D_4$-extensions of fields of characteristic two, determine the ramification breaks of (suitable) $D_4$-extensions of complete discrete valuation fields of characteristic two, and solve the local lifting problem in the affirmative for every $D_4$-extension of complete discrete valuation fields of characterist","authors_text":"Bradley Weaver","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-12T17:41:22Z","title":"The Local Lifting Problem for $D_4$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03751","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":"sha256:18a55989d0236f6414943de5b7edaa9bb04c193534a2f4695db3705c9a8323f6","target":"record","created_at":"2026-05-18T00:41:47Z","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":"4e649ad4f1401e2d6fef37e05334e3b9a1efe2517fa6b65484202cadc5511f24","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-12T17:41:22Z","title_canon_sha256":"0ec3a92fe68ffc387fde40ae07ca1bc878c4d51948ce17b3447e318971aaf953"},"schema_version":"1.0","source":{"id":"1706.03751","kind":"arxiv","version":3}},"canonical_sha256":"17c3076db75bf58eb02647b9d64305a4da562ce6c937d028bcb47cbf3fe161ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17c3076db75bf58eb02647b9d64305a4da562ce6c937d028bcb47cbf3fe161ae","first_computed_at":"2026-05-18T00:41:47.541203Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:47.541203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A4LwqLvrpu3Qvoi3HpTpFYG1OoaxMlCewpxe+TDkyw0xg+y1NYrjzE3E+MzzfDUVBcSaWhR95BIJdWP4KTWYDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:47.542011Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.03751","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18a55989d0236f6414943de5b7edaa9bb04c193534a2f4695db3705c9a8323f6","sha256:c45aa425ae4738ef97c5e1df29e5b1d3b335a9182234fe3dae49aef0fbd3b08f"],"state_sha256":"5f04c436cac5b5ac9c60e2ff51ddb14440d485131bf6aba90b7d0cd18a00301c"}