Univalence or typical reality of the multiplier function

Let $N$ and $T$ be positive integers, and let $\Phi(z)$ be the function constructed from the stabilization polynomials and the parameter $\gamma$.

Univalence conjecture. For any $N$ and $T$ there is a choice of $\gamma$ such that the function $\Phi(z)$ is univalent or typically real in $\mathbb D$. The largest value of $\gamma$ is a point of interest, since it produces the widest region for the multipliers.

If $\Phi$ is univalent or typically real, then its boundary image has only the two intersections with the real axis at $\Phi(1)=1$ and $\Phi(-1)$. This would yield estimates for the optimization problem and enlarge the region of multipliers for which the closed-loop system has a stable $T$-cycle. The source gives no resolution of the conjecture.