Vanishing conjecture for local shtuka cohomology

Let $b\in B(G)$ be basic, let $\mu_\bullet$ be a finite collection of cocharacters, and let $\rho$ be an irreducible admissible representation of $G_b(\bbQ_p)$ whose parameter $\phi=\phi_\rho$ is elliptic. Let $R\Gamma(G,b,\mu_\bullet)[\rho]$ denote the shifted intersection cohomology complex of the local shtuka space in the $\rho$-isotypic part. Vanishing conjecture. The cohomology is concentrated in the middle degree:

$$H^n(R\Gamma(G,b,\mu_\bullet)[\rho])=0\qquad\text{for }n\ne0.$$

This predicts that the local shtuka cohomology has no contribution outside the normalized middle degree; the source states the prediction but supplies no resolution.