Gersten's acyclicity conjecture for regular local rings

Let $X = \operatorname{Spec} A$, where $(A,\mathfrak{m}_A,L)$ is a regular local ring. For each $n \geq 0$, let $\mathcal{G}_n(X)$ be the Gersten complex associated with the codimensional filtration, whose terms are built from the groups $K_{n-p}(k(x))$ at points of codimension $p$. Gersten's Conjecture. The complex $\mathcal{G}_n(X)$ resolves $K_n(X)$, meaning

$$H^p(\mathcal{G}_n(X)) = \begin{cases} K_n(X) & p = 0 \\ 0 & p > 0. \end{cases}$$

This is the acyclicity conjecture for the Gersten complex of a regular local ring and is a central problem in algebraic $K$-theory. The source does not specify a resolution status for the general statement.