Drew–Johnson–Loewy conjecture on the CP-rank of completely positive matrices

Let $A$ be a real completely positive matrix of order $n$, meaning that $A=BB^{T}$ for some nonnegative real matrix $B$. The CP-rank of $A$, denoted by $\operatorname{CP\text{-}rank}(A)$, is the least number of columns of such a matrix $B$. Drew–Johnson–Loewy conjecture. If $n\geq 4$, then

$$\operatorname{CP\text{-}rank}(A)\leq \left[n^{2}/4\right].$$

The conjecture gives the expected sharp general upper bound for the number of rank-one nonnegative Gram summands needed to represent a completely positive matrix. It was listed as an open problem by Xingzhi Zhan in Open Problems in Matrix Theory; the supplied source does not report a resolution.