The Kontsevich–Zorich hyperelliptic Lyapunov exponent conjecture

For each genus $g$, consider the hyperelliptic components $\overline{\mathcal{H}}^{\mathrm{hyp}}_g(2g-2)$ and $\overline{\mathcal{H}}^{\mathrm{hyp}}_g(g-1,g-1)$, and let $\lambda_2$ be the second Lyapunov exponent. Kontsevich–Zorich conjecture. For these hyperelliptic components,

$$\lim_{g\rightarrow\infty}\lambda_2=1.$$

This is presented as a corollary of the paper’s main polygon conjecture together with the stated continuity assumption. The claimed limit follows from the lower bound approaching $1$ and the general upper bound $\lambda_2\leq 1$.