The Euler-number specialization conjecture for Gordon's ring

Let $W$ be the finite Coxeter group considered in the paper, let $R_W$ be Gordon's ring, and let $\varDelta$ be its bigraded character as a character of $W$. Let $S_W$ denote the Springer number of $W$.

Euler-number specialization conjecture.

$$\left.\varDelta(1_W)\right\vert_{t=-q=1}=S_W.$$

The identity is motivated by the reflection case of the $\Lambda\Sigma=\Delta$ conjecture and specializes to the Euler number when $W=\mathfrak{S}_n$. The supplied status evidence says that the preceding conjecture has been confirmed in dihedral types by direct examination, including this specialization.