Monotonicity conjecture for contextual fraction under n-contextuality

Let a contextuality model be evaluated in the hierarchy of $n$-contextuality, where increasing $n$ permits inclusion of larger simplices in the underlying simplicial complex, and let its contextual fraction quantify the contextual part of the model. Monotonicity conjecture. The contextual fraction cannot decrease with the increase of the hierarchy of $n$-contextuality. This is an open question about whether contextuality, as measured by the contextual fraction, always increases when larger simplices are included.