Ritter–Weiss non-smoothed equivariant main conjecture with uniqueness

Let $L/K$ be a finite Galois CM extension, let $L^+_\infty$ be the cyclotomic $\mathbb Z_p$-extension of its maximal totally real subextension, and let $\mathcal G=\operatorname{Gal}(L^+_\infty/K)$. Let $S$ contain all places ramifying in $L^+_\infty/K$ and all infinite places. Let $C_S^\bullet(L^+_\infty/K)$ be the perfect torsion complex whose class lies in $K_0(\Lambda(\mathcal G),\mathcal Q(\mathcal G))$, and let $\Phi_S(L^+_\infty/K)$ be the equivariant $p$-adic Artin $L$-function.

Non-smoothed equivariant main conjecture with uniqueness. There exists a unique element $\zeta_S(L^+_\infty/K)\in K_1(\mathcal Q(\mathcal G))$ such that

$$\operatorname{nr}(\zeta_S(L^+_\infty/K))=\Phi_S(L^+_\infty/K)$$

and

$$\partial(\zeta_S(L^+_\infty/K))=-[C_S^\bullet(L^+_\infty/K)].$$

This is the unsmoothed equivariant Iwasawa main conjecture together with uniqueness. The source presents it as a conjecture and gives no resolution in the stated generality.