Positivity conjecture for even plane curve singularities

For $m\geq 1$ and $d\geq 0$, let $R=R^{(2,2m)}$. Let $\mathit{NZ}_{R^d}(t)$ be the motivic numerator and $\widehat{\mathit{NZ}}_R(t)$ its completed version. Positivity conjecture.

$$\mathit{NZ}_{R^d}(-t)\in\mathbb{N}[\mathbb{L},t],\qquad \widehat{\mathit{NZ}}_R(-t)\in\mathbb{N}[[\mathbb{L}^{-1},t]].$$

The conjecture is motivated by the contrast between the understood odd case and the mysterious even case, and by numerical data. No proof or disproof is given in the source.