 Since it is semi-classical, \(\mathcal{A}^{\sim}\) admits a classical interpretation, as per Lemma 7.1. Let’s examine this. An element of \(S(\mathcal{A}^{\sim}\)) amounts to a mapping \(f : \mathcal{A}^{\sim} \rightarrow X\), assigning to each test \(E \in \mathcal{A}\), an outcome \(f(E) \in E\). This is a (rather brutal) example of what is meant by a contextual (dispersion-free) hidden variable. The construction above tells us that such contextual hidden variables will be available for statistical models quite generally. For other results to the same effect, see Kochen and Specker [1967], Gudder [1970], Holevo [1982], and, in a different direction, Pitowsky  [1989].[19]