Uniform boundedness conjecture for semistable holomorphic chains

Let $X$ be the compact Riemann surface under consideration, let $n$ be a nonnegative integer, and let $t=(r_j,j=0,...,n;d_j,j=0,...,n)$ be a type of holomorphic chain. Assume that $0$ is the only parameter for which there exist $\boldsymbol{\alpha}$-semistable linear chains of type $(r_j,j=0,...,n)$ over $\mathbb{C}(X)$. Here $R(t)\subset\mathbb{R}^n$ denotes a region of parameters.

Uniform boundedness conjecture. For every type $t$, there is a bounded region

$$R(t)\subset\mathbb{R}^n$$

such that the existence of an $\boldsymbol{\alpha}$-semistable holomorphic chain of type $t$ implies $\boldsymbol{\alpha}\in R(t)$.

This asserts that the parameters admitting semistable holomorphic chains of a fixed type are uniformly bounded under the stated generic-fibre hypothesis. The supplied text does not indicate whether the conjecture has been resolved.