Conjecture on the Mayer-series radius after removing collapsing even coefficients

Let $b_{2j}$, $j=1,\ldots,n$, be the leading even coefficients of the Mayer series, and let $\beta_{2n}$ and $\beta_{2(n+1)}$ denote the corresponding inverse-temperature thresholds. Mayer-series convergence conjecture. If the leading $n$ even coefficients $b_{2j}$ are removed from the Mayer series, then the radius of convergence of the resulting series remains positive for every

$$\beta \in [\beta_{2n},\beta_{2(n+1)}).$$

Consequently, it remains positive for every $\beta<\beta_{2(n+1)}$. This conjecture concerns avoiding the collapse of neutral clusters in the two-dimensional Yukawa gas; it is stated as an open problem in the cited work.