Bloch's pole-order conjecture in logarithmic K-theory

Let $V$ be a variety with strictly semistable reduction $X$ over a local field with residue field $k$, assume that $k$ is finite, and define

$$L(H^m(V),s)=\det(1-\varphi\,\sharp(k)^{-s};H^m(V_{\overline{K}},\mathbb{Q}_{\ell})^{N=0})^{-1},$$

where $\varphi$ is geometric Frobenius. Let $K(X,m,r)$ be the group defined in the finer logarithmic Tate conjecture. The modified Bloch pole-order conjecture. The order of the pole of $L(H^m(V),s)$ at $s=r\in\mathbb{Z}$ equals

$$\dim_{\mathbb{Q}}K(X,m,r).$$

The source describes this as a modification of a conjecture of S. Bloch and notes that the finer log Tate conjecture implies it under semisimplicity of Frobenius; it is not resolved here.