The zero-curvature JT area-tail conjecture with conformal matter

Let $\rho^0_{\beta_{\mathrm q}}(A)$ be the area distribution of zero-curvature JT gravity coupled to conformal matter with $c\leq0$, and let $\nu$ be the critical exponent specified by the paper. Zero-curvature area-tail conjecture. There are a strictly positive constant $\kappa_\nu$ and a strictly increasing exponent $\chi_\nu$ such that

$$\ln\rho^0_{\beta_{\mathrm q}}(A)\sim-\kappa_\nu\left(A/\beta_{\mathrm q}^{2\nu}\right)^{\chi_\nu}\qquad(A\to+\infty),$$

with

$$\lim_{\nu\to1/2^+}\chi_\nu=1,\qquad\lim_{\nu\to1^-}\chi_\nu=+\infty.$$

The exponent greater than one for $\nu>1/2$ is intended to ensure existence for all cosmological constants; the claimed tail is motivated by limiting cases and saddle-point analysis.