Base change conjecture for motivic cohomology of a regular model

Let $\mathcal{O}_K$ be an excellent henselian discrete valuation ring with quotient field $K$ and residue field $k=\mathcal{O}_K/\pi\mathcal{O}_K$, assume that $1/n\in k$, and let $X$ be a regular scheme, flat and projective over $\operatorname{Spec}\mathcal{O}_K$ with fibre dimension $d$. Let $X_0$ be the reduced special fibre. Write $A_2(X,-1)$ and $A_1(X_0,0)$ for the cycle-complex homology groups used in the source. Base change injectivity conjecture. The map

$$res:A_2(X,-1)\rightarrow A_1(X_0,0)$$

is injective. This is presented as a conjecture concerning injectivity of the restriction map; the paper proves injectivity in the case $d=2$ under its stated hypotheses, but the general assertion is not resolved in the supplied text.