The slope inequality for genus-$g$ Lefschetz fibrations over $S^2$

Let $f:X\rightarrow S^2$ be a relatively minimal genus-$g$ Lefschetz fibration, and let $\lambda_f$ denote its slope.

Slope inequality conjecture. For every genus-$g$ Lefschetz fibration $f:X\rightarrow S^2$, the slope inequality

$$\lambda_f\geq 4-4/g$$

holds.

This is motivated by the slope inequality for holomorphic fibrations and is known for hyperelliptic Lefschetz fibrations, in particular for genus-$2$ Lefschetz fibrations. At the time of the source, the inequality was not known for all Lefschetz fibrations over $S^2$; the source notes that all known examples satisfy it.