The low-genus Kodaira-dimension conjecture for $\overline{\mathcal{M}}_g$

Let $\overline{\mathcal{M}}_g$ be the moduli space of stable curves of genus $g$, and let $\kappa(\overline{\mathcal{M}}_g)$ denote its Kodaira dimension. Low-genus Kodaira-dimension conjecture.

$$\kappa(\overline{\mathcal{M}}_g)=-\infty\quad\text{for all }g<23.$$

This statement is presented as an immediate consequence of the slope conjecture. The general-type threshold is known to begin at $g\geq 24$, but the asserted negative Kodaira dimension for every $g<23$ remains the conjectural part in the source.