Fig. 1: An example illustrating the construction of a gadget with prescribed maximum overlap between the distinguished vectors \(\vert {v}_{1}^{(2)}\rangle ,\vert {v}_{8}^{(2)}\rangle\) of \(\frac{1}{2}\) for any real orthogonal representation.
From: Optimal measurement structures for contextuality applications

The example illustrates the utility of gadgets in deriving contextuality tests that allow for optimal randomness certification for d = 4.