Sargsyan's regular Suslin unreachability conjecture

Assume $AD^+$. Let $\kappa$ be a regular Suslin cardinal. Sargsyan's conjecture. The successor cardinal $\kappa^+$ is $S(\kappa)$-unreachable. The abstract presents this as the analogue of the projective unreachability results for arbitrary regular Suslin pointclasses. The paper proves the conjecture when the pointclass $S(\kappa)$ is inductive-like, but the general statement remains open.