Unbounded-critical-point conjecture for non-planar Potts-model zeros

Consider a family of non-planar connected graphs $G_{n,L}$ with $n$ identical layers of width $L$ and periodic boundary conditions in the $n$-direction, together with a curve $v=f(Q)$ in the $(Q,v)$-plane. Unbounded-critical-point conjecture. There exists such a graph family and curve for which the limiting zero set of the Potts-model partition function $Z_G(Q,v)$ satisfies the stated chromatic accumulation pattern, but with

$$\lim_{L\to\infty}Q_c(L)=\infty.$$

This is proposed as the non-planar analogue of the planar sharp-bound construction and is not established in the source.