Bounded positive Dehn-twist length conjecture

Let $\Gamma_g^r$ be the mapping class group of a genus-$g$ surface with $r>0$ boundary components. A right-handed Dehn twist is a Dehn twist with the positive orientation convention. Bounded-length conjecture. For $h\in\Gamma_g^r$ with $r>0$, there exists a constant $C_h$ such that whenever

$$h=t_1\cdots t_n$$

with each $t_i$ a right-handed Dehn twist, one has $n\leq C_h$.

This is a weakening of the finiteness conjecture for Euler characteristics of Stein fillings: positive Dehn-twist factorizations give Stein fillings, and bounding their lengths would bound the corresponding Euler characteristics. The paper does not provide a resolution.