Dolgachev–Weisfeiler conjecture for partial residual coordinates

Let $R$ be a ring and let $f_1,\ldots,f_m\in R^{[n]}$. A partial system of residual coordinates is a tuple for which the inclusion

$$R[f_1,\ldots,f_m]\hookrightarrow R^{[n]}$$

is an affine fibration. A partial system of coordinates is a tuple that can be completed to an element of ${\rm GA}_n(R)$. Partial residual-coordinate conjecture. Every partial system of residual coordinates is a partial system of coordinates. This is the partial-system formulation of the Dolgachev–Weisfeiler problem; the source presents it as a conjectural extension of the single-coordinate question.