Gersten's recursive upper bound for Dehn functions of linear groups

Let $f\colon\mathbb{N}\to\mathbb{N}$ be a recursive function, for example $f(n)=2^n$, and consider finite presentations of linear groups. The Dehn function, denoted by $\operatorname{Area}(n)$, measures the maximal minimal filling area of null-homotopic words of length at most $n$.

Gersten's conjecture. There is a recursive function $f\colon\mathbb{N}\to\mathbb{N}$, such that every finite presentation of a linear group has

$$\operatorname{Area}(n)\preceq f(n).$$

The question is motivated by the problem of extending linear filling-length bounds from nilpotent groups to polycyclic or, more generally, linear groups. The source presents this as a conjectural consequence supported by progress toward those filling-length bounds, and no resolution is supplied.