  Cuspidal systems parameterize KLR algebra representations via root partitions
$\pi$, where simple modules $L(\pi)$ arise as heads of proper standard modules.
Working in affine type A with an arbitrary convex preorder, we construct
explicit skew diagrams $\zeta(\pi)$ such that the skew Specht module
$S^{\zeta(\pi)}$ has simple head $L(\pi)$ and a filtration by proper standard
modules. This result arises from an in-depth study of the combinatorial
interplay between cuspidal systems and RoCK cyclotomic KLR algebras.
