Asymptotic sharp-slope conjecture for effective divisors on moduli spaces of curves

For an effective divisor $D=a\lambda-b\delta$ on $\overline{\mathcal M}_g$ with $a,b>0$, define its slope by

$$s(D)=\frac{a}{b}.$$

Here $g$ tends to infinity. Asymptotic sharp-slope conjecture. There exist effective divisors on $\overline{\mathcal M}_g$ with slopes arbitrarily close to

$$\frac{576}{5g}$$

as $g$ goes to infinity. If true, this would make the currently known order $O(1/g)$ the sharp asymptotic lower bound for slopes of effective divisors; the source contrasts it with the absence of any known effective divisor of slope at most $6$ and gives no resolution status.