  We discuss representations and colorings of orthogonality hypergraphs in
terms of their two-valued states interpretable as classical truth assignments.
Such hypergraphs, if they allow for a faithful orthogonal representation, have
quantum mechanical realizations in terms of intertwined contexts or maximal
observables that are widely discussed as empirically testable criteria for
contextuality. Reconstruction is possible for the class of perfectly separable
hypergraphs. Colorings can be constructed from a minimal set of two-valued
states. Some examples from exempt categories are presented that either cannot
be reconstructed by two-valued states or whose two-valued states cannot yield a
chromatic number that is equal to the maximal clique number.
