The non-abelian zeta-distribution main conjecture for Artin motives

Let $M$ be an Artin motive, let $k>1$, let $S$ and $G_\infty$ be as before with $G_\infty$ pro-$p$ and without $p$-torsion, and assume that ${\Bbb Q}[G_n]\otimes M(k)$ is critical for all $n$. Let $\Lambda={\Bbb Z}_p[[G_\infty]]$ and let $D$ be the total ring of fractions used in the paper. The zeta distribution is

$$\mathcal{L}_S(G_\infty,M^\lor,1-k)=\varprojlim L_S(G_n,M^\lor,1-k)\in\varprojlim Z({\Bbb Q}_p[G_n])^*.$$

Zeta-distribution main conjecture. There exist $f,g\in\Lambda$ such that $(\operatorname{rn}(f_ng_n^{-1}))_n$ is the zeta distribution $\mathcal{L}_S(G_\infty,M^\lor,1-k)$ and the characteristic ideal

$$[R\Gamma({\Bbb Z}[1/S],\Lambda\otimes T_p(k))[1]]\in K_0(\mathcal{T})$$

coincides with the image of $fg^{-1}\in(D^*)^{\mathrm{ab}}$.

This is the torsion, critical Artin-motive specialization of the non-abelian Iwasawa Main Conjecture, relating zeta distributions to characteristic ideals. The source gives no resolution evidence.