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Assume that we have a biholomorphism $Q:= Q_X\\to Q_Y$ and an open cover $\\{U_i\\}$ of $Q$ and $G$-biholomorphisms $\\Phi_i\\colon p_X^{-1}(U_i)\\to p_Y^{-1}(U_i)$ inducing the identity on $U_i$. There is a sheaf of groups $\\mathcal A$ on $Q$ such that the isomorphism classes of all possible $Y$ is the cohomology set $H^1(Q,\\mathcal A)$. The main question we address is to what extent $H^1(Q,\\mathcal A)$ contains only topological "},"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":"1608.05156","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-08-18T02:13:12Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"e5962eebcef6a61c1c7777ae742c54226b85cb08d34526c2e393b758fc18d520","abstract_canon_sha256":"658b22512436902fc578a9887d9b541e3a19bd5f7c2904da68b767f94d2b09c2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:07.708294Z","signature_b64":"TUcW/a2eoFthGHelxlQYPhELPcn+SmVBIXvKzxPFQl51TwwF5dwyaS10AP2rCc8LCjc00DhfEeTt5RObZfigBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a15eaed4949fa09e4b63d397243cedf6875f2e7a2a73662c10899189b67e9d9","last_reissued_at":"2026-05-18T00:53:07.707935Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:07.707935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Oka principle for Stein G-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CV","authors_text":"Gerald W. 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