Ball characterization conjecture for Stein spaces with standard contact boundary

Let $W$ be a Stein space of dimension $n\geq 3$ with at most finitely many isolated normal singularities. Assume that $W$ has a compact strongly pseudoconvex smooth boundary $\partial W$ whose CR structure is contactomorphic to $(S^{2n-1},\xi_{std})$. Ball characterization conjecture. Then $W$ is a smooth Stein manifold and is diffeomorphic to the complex unit ball ${\mathbb B}^n$. This conjecture asks whether a standard contact-sphere boundary rules out the allowed isolated singularities and forces the global Stein space to be the ball; the surrounding discussion points to known local obstructions in dimension two and to higher-dimensional examples where a sphere link alone is insufficient.