{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:C7BQO3NXLP2Y5MBGI645MQYFUT","short_pith_number":"pith:C7BQO3NX","schema_version":"1.0","canonical_sha256":"17c3076db75bf58eb02647b9d64305a4da562ce6c937d028bcb47cbf3fe161ae","source":{"kind":"arxiv","id":"1706.03751","version":3},"attestation_state":"computed","paper":{"title":"The Local Lifting Problem for $D_4$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Bradley Weaver","submitted_at":"2017-06-12T17:41:22Z","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"},"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":"1706.03751","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-12T17:41:22Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"0ec3a92fe68ffc387fde40ae07ca1bc878c4d51948ce17b3447e318971aaf953","abstract_canon_sha256":"4e649ad4f1401e2d6fef37e05334e3b9a1efe2517fa6b65484202cadc5511f24"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:47.542011Z","signature_b64":"A4LwqLvrpu3Qvoi3HpTpFYG1OoaxMlCewpxe+TDkyw0xg+y1NYrjzE3E+MzzfDUVBcSaWhR95BIJdWP4KTWYDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17c3076db75bf58eb02647b9d64305a4da562ce6c937d028bcb47cbf3fe161ae","last_reissued_at":"2026-05-18T00:41:47.541203Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:47.541203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Local Lifting Problem for $D_4$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Bradley Weaver","submitted_at":"2017-06-12T17:41:22Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03751","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":"1706.03751","created_at":"2026-05-18T00:41:47.541329+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.03751v3","created_at":"2026-05-18T00:41:47.541329+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.03751","created_at":"2026-05-18T00:41:47.541329+00:00"},{"alias_kind":"pith_short_12","alias_value":"C7BQO3NXLP2Y","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"C7BQO3NXLP2Y5MBG","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"C7BQO3NX","created_at":"2026-05-18T12:31:08.081275+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/C7BQO3NXLP2Y5MBGI645MQYFUT","json":"https://pith.science/pith/C7BQO3NXLP2Y5MBGI645MQYFUT.json","graph_json":"https://pith.science/api/pith-number/C7BQO3NXLP2Y5MBGI645MQYFUT/graph.json","events_json":"https://pith.science/api/pith-number/C7BQO3NXLP2Y5MBGI645MQYFUT/events.json","paper":"https://pith.science/paper/C7BQO3NX"},"agent_actions":{"view_html":"https://pith.science/pith/C7BQO3NXLP2Y5MBGI645MQYFUT","download_json":"https://pith.science/pith/C7BQO3NXLP2Y5MBGI645MQYFUT.json","view_paper":"https://pith.science/paper/C7BQO3NX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.03751&json=true","fetch_graph":"https://pith.science/api/pith-number/C7BQO3NXLP2Y5MBGI645MQYFUT/graph.json","fetch_events":"https://pith.science/api/pith-number/C7BQO3NXLP2Y5MBGI645MQYFUT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C7BQO3NXLP2Y5MBGI645MQYFUT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C7BQO3NXLP2Y5MBGI645MQYFUT/action/storage_attestation","attest_author":"https://pith.science/pith/C7BQO3NXLP2Y5MBGI645MQYFUT/action/author_attestation","sign_citation":"https://pith.science/pith/C7BQO3NXLP2Y5MBGI645MQYFUT/action/citation_signature","submit_replication":"https://pith.science/pith/C7BQO3NXLP2Y5MBGI645MQYFUT/action/replication_record"}},"created_at":"2026-05-18T00:41:47.541329+00:00","updated_at":"2026-05-18T00:41:47.541329+00:00"}