The punctured-disk zero-free conjecture for series-parallel graphs

Let $B_{5/27}(1)$ denote the disk of radius $5/27$ centered at $1$, and let $Z(G;q)$ be the chromatic polynomial of a series-parallel graph $G$. The punctured-disk zero-free conjecture. For every

$$q\in B_{5/27}(1)\setminus\{1\}$$

and every series-parallel graph $G$, one has

$$Z(G;q)\neq 0.$$

The conjecture is motivated by the paper's computational picture and the preceding zero-free criterion. No proof or disproof is supplied in the source.