Conjecture on minimal algebraic Bergman-kernel degree in higher dimensions

Let $G\subset \mathbb{C}^n$ with $n\geq 2$ be a smoothly bounded pseudoconvex domain, and let $K$ be the Bergman kernel of $G$. The minimal-degree conjecture. If $K$ is algebraic, then the total degree of $K$ equals $2n+3$ if and only if $G$ is the unit ball up to a complex affine transformation in $\mathbb{C}^n$. This conjecture proposes the sharp higher-dimensional analogue of the paper's two-dimensional degree characterization, where the lowest possible algebraic degree should characterize the ball. Its status is not resolved in the supplied text.