D-equivalence implies L-equivalence for simply connected varieties

Let $X$ and $Y$ be smooth projective simply connected varieties. Write $\mathbb{D}(X)$ for the bounded derived category of coherent sheaves on $X$, and let $\mathbb L=[\mathbb A^1]$ be the class of the affine line in the Grothendieck ring $K_0(\operatorname{Var}/\Bbbk)$. The varieties $X$ and $Y$ are L-equivalent when $([X]-[Y])\mathbb L^r=0$ for some integer $r\geq 0$. D–L equivalence conjecture. If

$$\mathbb{D}(X)\cong\mathbb{D}(Y),$$

then there is a nonnegative integer $r\geq 0$ such that

$$([X]-[Y])\mathbb L^r=0.$$

In other words, D-equivalence of varieties implies their L-equivalence.

The conjecture is motivated by examples of derived-equivalent Calabi–Yau threefolds whose classes become equal after multiplication by a power of $\mathbb L$. Simple connectedness is essential: the source notes that derived-equivalent abelian varieties need not be L-equivalent. The conjecture's resolution status is not specified in the source.