  We introduce a contextual quantum system comprising mutually complementary
observables organized into two or more collections of pseudocontexts with the
same probability sums of outcomes. These pseudocontexts constitute
non-orthogonal bases within the Hilbert space, featuring a state-independent
sum of probabilities. In other words, regardless of the initial state
preparation, the total probability remains constant but may be distinct from
unity. The measurement contextuality in this setup arises from the quantum
realizations of the hypergraph, which adhere to a specific bound on the linear
combination of probabilities. In contrast, classical realizations can surpass
this bound. The violation of quantum bounds stems from the inability of
classical ontological models, specifically the set-theoretic representation of
the hypergraph corresponding to the quantum observables' collections, to adhere
to and explain the observed statistics.
