Sasakian Hodge number bound for Calabi-Yau links

Let $f$ be a ${\bf w}$-homogeneous polynomial defining a Calabi-Yau $3$-fold, and let the associated link have Sasakian Hodge number $h_S^{2,1}$, while the Calabi-Yau $3$-fold has Hodge number $h_{CY}^{2,1}$. Sasakian Hodge number bound. The Sasakian Hodge number is bounded above by the Calabi-Yau Hodge number:

$$h_S^{2,1}\leq h_{CY}^{2,1}.$$

The claim is suggested by the strong empirical correlation observed in the computed examples and remains open in the source.