Almirón's $3/2$ conjecture for surface hypersurface singularities

Let $f\in\mathbb{C}[[x,y,z]]$ be an isolated hypersurface singularity, with Milnor number $\mu$ and Tjurina number $\tau$. Almirón's conjecture.

$$\frac{\mu}{\tau}<\frac{3}{2}.$$

This is described as a weak version of Durfee's conjecture and remains open in the supplied context.