Characterizations of Transversal Lightlike Submanifolds in Indefinite Golden Statistical Geometry

We investigate transversal and radical transversal lightlike submanifolds (TLSs) of indefinite golden statistical manifolds (IGSMs). Using the dual affine connections associated with statistical structures, we obtain decomposition formulas and derive necessary and sufficient conditions for the integrability of the radical, screen, and lightlike transversal distributions. Criteria for totally geodesic foliations and local product structures are established. Explicit examples are provided to illustrate the theory. These results extend lightlike submanifold geometry to the golden statistical setting.