Local functional equation conjecture for dualizing modules of singularities

Assume $(*)$. Let $R$ be the local ring under consideration, let $d\geq 0$, and let $\Omega$ be its dualizing module. Set

$$E:=\Omega^{\oplus d}.$$

Local functional equation conjecture. As rational functions in $t$,

$$\mathit{NZ}_E(t)=(\mathbb{L}^{d^2}t^{2d})^{\delta}\mathit{NZ}_E(\mathbb{L}^{-d}t^{-1})\in K_0(\operatorname{Var}_k)(t).$$

The conjecture gives a local formulation of the functional equation beyond the planar case; the source notes that the Gorenstein condition suffices for the broader setting. Its status is not resolved there.