The matrix paving conjecture

Let $A_1,\ldots,A_m$ be Hermitian, positive semi-definite matrices of the same size satisfying

$$\sum_{i=1}^m A_i = I$$

and $\operatorname{tr} A_i \leq \delta$ for all $i$. The matrix paving conjecture. There exists $y \in \{-1,+1\}^m$ such that

$$\left\|\sum_{i=1}^m y_i A_i\right\| \leq O(\sqrt{\delta}).$$

This conjecture is presented as a common generalization of the matrix discrepancy statement of Marcus, Spielman, and Srivastava and the diagonal-matrix case of the paper’s theorem. The source does not state that it has been resolved.