Roune–Woods conjecture on the parametric Frobenius number

Let $n\geq 2$, and let $P_1,\ldots,P_n\in\mathbb{R}[u]$ be polynomials that map $\mathbb{Z}$ to $\mathbb{Z}$ and have positive leading coefficient. For every $t$ such that $P_i(t)>0$ for all $i$, define

$$D(t)=F(P_1(t),\ldots,P_n(t)).$$

Here $F(a_1,\ldots,a_n)$ denotes the Frobenius number of the positive integers $a_1,\ldots,a_n$.

Roune–Woods conjecture. The function $D$ is an eventual quasi-polynomial (EQP).

This conjecture concerns the eventual quasi-polynomial behavior of the Frobenius number when its arguments vary polynomially with a parameter. The source attributes it to Roune and Woods; the supplied text does not state whether it has been resolved.