Goettsche's conjecture on effective Chow motives

Let $k$ be a field, and let $Mot^{eff}_k$ be the category of effective Chow motives over $k$ with rational coefficients. For objects $M,N$ of $Mot^{eff}_k$, write $[M]$ and $[N]$ for their classes in the Grothendieck ring $K_0(Mot^{eff}_k)$. Goettsche's conjecture. If $M$ and $N$ are objects of $Mot^{eff}_k$, then

$$[M]=[N] \text{ in } K_0(Mot^{eff}_k) \quad\Longleftrightarrow\quad M\text{ and }N\text{ are isomorphic}.$$

If true, this would imply that the natural map from the Grothendieck ring of effective Chow motives to that of Chow motives is injective, equivalently that the Lefschetz motive is not a zero divisor in $K_0(Mot^{eff}_k)$. The source does not give evidence of a resolution, so the conjecture remains open.