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In non-effective form IFT first appeared in \\cite{Imp}.\n From algebraic geometry view-point IFT can be described as lifting solutions of equations into generic points of algebraic varieties.\n  Moreover, we show that the con"},"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":"math/0407110","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2004-07-07T16:47:56Z","cross_cats_sorted":[],"title_canon_sha256":"6293b79f1e8824e4f9c5a05fd26cc65808b6314c1aa5c3c65b4b4a90b000f13e","abstract_canon_sha256":"7382d8f87882f4bfc4b21d85929486329c5afcc6fcd7c4c954dc334b76a29f5e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:26.231116Z","signature_b64":"sJ4rxi92iygMM9ZKIVg0X4IwNqgtSi25ec6O1TGTcMo1+Q2JkSeQhWfiQgs0S4ZGIgYceBsAuMYn3Qai7Aa8Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e33fb597195c6a5a60130c0fb47656a692ee858e03baa306b56189532a1b5d40","last_reissued_at":"2026-05-18T01:05:26.230563Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:26.230563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algebraic Geometry over Free Groups: Lifting Solutions into Generic Points","license":"","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexei Myasnikov, Olga Kharlampovich","submitted_at":"2004-07-07T16:47:56Z","abstract_excerpt":"In this paper we prove Implicit Function Theorems (IFT) for algebraic varieties defined by regular quadratic equations and, more generally, regular NTQ systems over free groups. 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