The vanishing conjecture for fixed log étale cohomology

Let $s=\operatorname{Spec}(k)$ be the standard log point, let $X$ be a projective vertical log smooth fs log scheme over $s$, let $\ell$ be invertible in $k$, and write

$$H^m(X)_{\ell}=H^m_{\operatorname{\log\acute{e}t}}(X_{\overline{s}(\log)},\mathbb{Q}_{\ell}),\qquad G=\pi_1^{\log}(s).$$

The fixed-part vanishing conjecture.

$$H^m(X)_{\ell}(r)^G=0$$

unless $m\geq 2r$. This extends the usual vanishing outside the Tate range to log étale cohomology; the source says it is well known in the semistable-reduction case but gives no resolution.