Soltan's homothetic covering conjecture

Let $K\in\mathcal{K}^d$ be a convex body, and let $\lambda_1,\ldots,\lambda_n\in(0,1)$. The homothets $\lambda_iK$ are translated by vectors so as to cover $K$.

Soltan's homothetic covering conjecture. Assume that $K \in \mathcal{K}^d$ and that $\lambda_1 K, \ldots, \lambda_n K$ permit a translative covering of $K$ with $\lambda_i \in (0,1)$ for every $i$. Then

$$\sum_{i=1}^n \lambda_i \geq d.$$

This conjecture concerns the total homothety ratio required for a translative covering. The supplied text identifies it as a related conjecture due to Soltan and gives no resolution.