Fixed-rank NP-hardness conjecture for nonnegative rank

For a nonnegative matrix $M$, its nonnegative rank $\operatorname{rank}_+(M)$ is the least inner dimension of a factorization of $M$ into two nonnegative matrices. The ordinary rank $\operatorname{rank}(M)$ is the usual matrix rank. Fixed-rank NP-hardness conjecture. Computing $\operatorname{rank}_+(M)$ and a corresponding nonnegative factorization is NP-hard when $\operatorname{rank}(M)$ is fixed and at least $4$, and possibly even when it is fixed at $3$. The conjecture concerns the computational complexity of nonnegative rank at fixed ordinary rank; the source does not state that this problem has been resolved.