Abstract
Self-testing constitutes one of the most powerful forms of device certification, enabling a complete and device-independent characterization of a quantum apparatus solely from the observed correlations. In recent work by the authors [23], a general framework was introduced for constructing Bell inequalities that self-test entire families of Clifford generators. In this manuscript, we develop an alternative and complementary self-testing criterion based on symmetric spanning sets. This formulation provides an explicit and constructive route to designing self-testing Bell inequalities in arbitrary dimensions.