The left-skewed Gumbel conjecture for persistent homology

Let $\mathcal{L}^*$ be the limiting distribution of the persistent $\ell$-values, and let $\mathrm{LGumbel}$ denote the left-skewed Gumbel distribution with cumulative distribution function

$$F(x)=1-e^{-e^x}.$$

Left-skewed Gumbel conjecture. The universal limiting distribution is

$$\mathcal{L}^*=\mathrm{LGumbel}.$$

The conjecture is motivated by the close agreement between the empirical distributions and the left-skewed Gumbel distribution in the paper's experiments; no proof or resolution is supplied.