Limiting distribution conjecture for the optimal objective value

Let $m$, $n$, and $A(n)$ be as in Theorem~, and for each $n$ let $c=c(n)$ be a uniformly random unit cost vector independent of $A(n)$. Write $z^*$ for the optimal objective value. Limiting distribution conjecture. The sequence of normalized random variables

$$\frac{z^*-{\mathbb E}\,z^*}{\sqrt{{\rm Var}\,z^*}}$$

converges in distribution to the standard Gaussian. Numerical experiments for Gaussian and Rademacher coefficient matrices support the conjecture, but no proof or resolution is given here.