Finiteness conjecture for d-representation-finite dimensions

Let $A$ be a finite-dimensional $k$-algebra. The property of being $d$-representation-finite means that $A$ has this representation-theoretic finiteness property for a positive integer $d$.

Finiteness conjecture. For a given finite-dimensional $k$-algebra $A$, there are only finitely many integers $d$ such that $A$ is $d$-representation-finite.

This conjecture concerns the possible higher representation-finite dimensions of a fixed finite-dimensional algebra. The surrounding discussion notes that, for fixed $n$, one expects at most finitely many positive integers $d$ for which the associated condition holds, while the stated conjecture asserts finiteness as $d$ varies.