Geometric Origin of the CKM Matrix in the ODD Framework

We extend the Operator-Derived Dimension (ODD) framework to the quark sector. We propose that the Cabibbo–Kobayashi–Maskawa (CKM) matrix, which governs the mixing of quark generations, is not a set of arbitrary parameters but arises from the geometric overlap of five-dimensional quark wavefunctions in the bulk. This provides a geometrically constrained mechanism for generating the observed hierarchical structure and CP-violating phase of the CKM matrix, unifying it with the leptonic (PMNS) sector under a single operator-based geometric principle.