We discuss chromatic constructions on orthogonality hypergraphs which are classical set representable or have a faithful orthogonal representation. The latter ones have a quantum mechanical realization in terms of intertwined contexts or maximal observables. Structure reconstruction of these hypergraphs from their table of two-valued states is possible for a class of hypergraphs, namely perfectly separable hypergraphs. Some examples from exempt categories that either cannot be reconstructed by two-valued states or whose set of two-valued states does not yield a coloring are presented.
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