  We show that the hyperplane arrangement of a coconvex set in a finite root
system is free if and only if it is free in corank 4. As a consequence, we show
that the inversion arrangement of a Weyl group element w is free if and only if
w avoids a finite list of root system patterns. As a key part of the proof, we
use a recent theorem of Abe and Yoshinaga to show that if the root system does
not contain any factors of type C or F, then Peterson translation of coconvex
sets preserves freeness. This also allows us to give a
Kostant-Shapiro-Steinberg rule for the coexponents of a free inversion
arrangement in any type.
