Local Motivic Monodromy Conjecture for formal schemes

Assume that $k$ has characteristic zero and that $R$ is complete. Let $\mathfrak{X}$ be a regular $stft$ formal $R$-scheme, with special fiber $\mathfrak{X}_s$, motivic Weil generating series $S(\mathfrak{X};T)$, nearby-cycle functor $\psi_{\mathfrak{X}}$, monodromy operator $\sigma$, and cyclotomic polynomial $\Phi_n(t)$. Let $\tau(a/b)$ denote the order of the root of unity ${\mathcal{E}\mathrm{xp}}(2\pi i a/b)$.

Local Motivic Monodromy Conjecture. There exists a finite subset $\mathcal{S}\subset\mathbb{Z}\times\mathbb{Z}_{>0}$ such that

$$S(\mathfrak{X};T)\in \mathcal{M}_{\mathfrak{X}_s}\left[T,\frac{1}{1-\mathbb{L}^aT^b}\right]_{(a,b)\in\mathcal{S}}$$

and, for each $(a,b)\in\mathcal{S}$, the cyclotomic polynomial $\Phi_{\tau(a/b)}(t)$ divides the characteristic polynomial of $\sigma$ on $R^i\psi_{\mathfrak{X}}(\mathbb{Q}_\ell)_x$ for some $i\in\mathbb{Z}_{\geq0}$ and some geometric closed point $x$ of $\mathfrak{X}_s$.

The conjecture predicts that every denominator contributing to the motivic Weil generating series is detected by monodromy on nearby-cycle cohomology. The supplied text does not state a resolution.