Principal conjecture on fixed points of generic automorphisms

Let $G$ be an infinite simple group of finite Morley rank, and let $\alpha$ be a generic automorphism of $G$. The fixed-point subgroup of $\alpha$ is $C_G(\alpha)$. Principal conjecture. The fixed-point subgroup $C_G(\alpha)$ is pseudofinite. This conjecture concerns the proposed pseudofiniteness of fixed-point subgroups arising from generic automorphisms in infinite simple groups of finite Morley rank. The supplied text attributes its formulation to work motivated by Hrushovski's results, but does not state that it has been resolved.