Deformations of spherical CR uniformizations of the magic 3‐manifold

In Ma and Xie [Comm. Anal. Geom. 32 (2024), no. 9, 2381–2465], Ma and the second author constructed a spherical Cauchy‐Riemann (CR) uniformization of the magic 3‐manifold whose peripheral holonomies are all unipotent. In this paper, we deform this uniformization to obtain a 1‐parameter family of holonomy representations. In these deformations, exactly one of the three cusps acquires screw‐parabolic peripheral holonomy, while the other two remain unipotent. We prove that for sufficiently small deformation parameters, these representations are discrete and faithful, and that they yield a 1‐parameter family of pairwise non‐conjugate spherical CR uniformizations of the magic 3‐manifold.