The slope conjecture for relative irregularity of fibred surfaces

Let $f\colon S \longrightarrow B$ be a fibration of genus $g$, and let $q_f$ denote its relative irregularity, with $q_f<g-1$. The slope $s(f)$ is the ratio of the relevant relative invariants of the fibration. Slope conjecture. The slope satisfies

$$s(f) \geq 4\frac{g-1}{g-q_f}.$$

This conjecture proposes a lower bound for the slope that increases with the relative irregularity. It refines the classical slope inequality and is motivated by known stronger bounds in cases such as positive relative irregularity, but its general status is not established in the supplied source.