Stable coordinate conjecture over rings of characteristic zero

Let $A$ be a ring of characteristic zero, and let $f \in A^{[n]}$. Stable coordinate conjecture. If there is some $m>0$ such that $f$ is a coordinate in $A^{[n+m]}$, then $f$ is a coordinate in $A^{[n]}$. This is a stable-coordinate or cancellation problem for polynomial automorphisms; the source places it among longstanding criteria for recognizing coordinates and indicates that related examples remain open.