Quark masses and mixing from Modular $S'_4$ with Canonical K\"ahler Effects

We propose a quark flavor model based on modular $S'_4$ with a general CP symmetry. CP violation in the quark sector is entirely realized by the modulus $\langle \tau \rangle$. We show that the canonical normalization induced by the K\"ahler metric plays a crucial role in reproducing the observed hierarchies, while maintaining coupling constants of order $\mathcal{O}(1)$. The minimal model achieves a great fit to the quark sector data, which we take as the PDG 2024 data extrapolated to the GUT scale.