Denef–Sargos nonvanishing conjecture for stable Newton faces

Let $f$ be non-degenerate with respect to its Newton polyhedron, and let $\tau_{0}$ be a codimension-one simplex whose only lattice points in its intersection with the support of $f$ are its vertices. Assume $s_{0}\notin\mathbb{Z}$, and write the quantities $\varepsilon_{j}$, $\gamma_{j}$ and $a_{j}$ as in the associated formula for the coefficient $\mu(\varphi)$. A face $\tau_{0}$ is stable when it satisfies the stability condition of Denef and Sargos. Denef–Sargos nonvanishing conjecture. With this notation and these hypotheses, if $\tau_{0}$ is stable, then

$$\sum_{\beta\in\{-1,1\}^{n}} \prod_{j=1}^{n}e^{\operatorname{sign}(\varepsilon_j\beta^{a_j})\frac{\pi i}{2}\gamma_j}\neq 0.$$

This is a combinatorial assertion intended to ensure that the leading coefficient does not vanish for a stable face; its resolution is not indicated in the supplied text.