Triangulation-dependent conjecture for the Łojasiewicz exponent

Let $f\in\mathbb{C}\{z_0,z_1,\ldots,z_n\}$ be Newton nondegenerate and define an isolated singularity, and let $\mathcal{T}$ be a triangulation of its Newton diagram $\Gamma(f)$. Let $\mathcal{F}_{\mathrm{ne}}^{\mathcal{T}}$ denote the subset of coordinate facets selected by the triangulation-dependent nonexceptionality condition, and let $\mathcal{M}(F)$ be the maximal axial number of a coordinate facet $F$.

Triangulation-dependent Łojasiewicz conjecture. Then

$$\mathop{\mathcal{L}}(f,0)=\max_{F\in\mathcal{F}_{\mathrm{ne}}^{\mathcal{T}}}\mathcal{M}(F)-1,$$

with the possible exception of a Morse point in an even number of variables.

This conjecture is proposed as a replacement for the refuted Brzostowski–Krasiński–Oleksik conjecture and is motivated by local $h$-polynomials and a formula for the Newton number. The source does not provide evidence resolving it.