Good-characteristic parity conjecture for standard sheaves

Let ${\mathbf G}$ be the group in the geometric Satake setting, let $p$ be a prime, and let the standard sheaves on the affine Grassmannian have coefficients in a field of characteristic $p$. A sheaf is $*$-parity when its nonzero stalks are concentrated in one parity.

Good-characteristic parity conjecture. If $p$ is a good prime for ${\mathbf G}$, then the standard sheaves with coefficients in a field of characteristic $p$ are $*$-parity.

This is presented as a reformulation of the modified Mirković–Vilonen conjecture after excluding bad primes. The source gives no further resolution beyond this good-characteristic formulation.