The W-goodness finite-dimensional quotient conjecture

Let $W$ be a real reflection group with reflection representation $V$. A positive integer $r$ is $W$-good if, for every parameter $c$ with $|c|=r$, the Cherednik algebra $H_c(W)$ admits a finite-dimensional module of the form $S(V)/S(V)V_r$, where $V_r\subset S^r(V)$ is an irreducible $W$-submodule of dimension $\dim V$. Let $V^{(r;c)}$ be the distinguished copy of the defining module in the degree-$r$ quasiharmonics at parameter $c$. W-goodness quotient conjecture. If $r$ is $W$-good, then

$$S(V)/S(V)V^{(r;c)}$$

is finite-dimensional. The conjecture connects the universal quasiharmonic submodule $V^{(r;c)}$ with the finite-dimensional representations guaranteed by $W$-goodness. The source provides examples of $W$-good integers for types $A$, $B$, $D$, and $I_2(m)$, but does not establish the conjecture in general.