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We construct a continuous family of $J_b$-conformal minimal immersions $u_b:X\\to \\mathbb{R}^3$, $b\\in B$, properly projecting to $\\mathbb{R}^2$ and having an arbitrary given family of flux homomorphisms ${\\rm Flux}_{u_b}:H_1(X,\\mathbb{Z})\\to\\mathbb{R}^3$. In particular, there are continuous families of proper $J_b$-holomorphic nul"},"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":"2605.19883","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-05-19T14:14:48Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"0f0d76df024990f232b18de39cf78a96e9fb31e37f6bb8816cbd82864dc0d45f","abstract_canon_sha256":"43d0939f19d7c461bc1ecb7f4cb466ca284d749665e9294c89fe09b5181fe408"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T01:06:19.072650Z","signature_b64":"YJCVA5l1jIWE8p73dYngNnTxcGvIddpaW055aWHQmarEF4oVMLrojn7GM8LTIP9TYTrZoRgXGxLMC5apm99iDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb9c2c474d3a445df633b6b978bdad15bb82b777e447b0cc696d6227b712019d","last_reissued_at":"2026-05-20T01:06:19.071870Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T01:06:19.071870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Families of proper minimal surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Antonio Alarcon, Franc Forstneric","submitted_at":"2026-05-19T14:14:48Z","abstract_excerpt":"Assume that $X$ is a connected, open, oriented smooth surface, $B$ is a compact Euclidean neighbourhood retract, and $\\mathscr{J}=\\{J_b\\}_{b\\in B}$ is a continuous family of complex structures on $X$ of local H\\\"older class $\\mathscr{C}^\\alpha$ for some $0<\\alpha<1$. We construct a continuous family of $J_b$-conformal minimal immersions $u_b:X\\to \\mathbb{R}^3$, $b\\in B$, properly projecting to $\\mathbb{R}^2$ and having an arbitrary given family of flux homomorphisms ${\\rm Flux}_{u_b}:H_1(X,\\mathbb{Z})\\to\\mathbb{R}^3$. 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