Exact Measurement-Dependence Cost of Faithful GHZ–Mermin Correlations

We determine the exact measurement-setting dependence required by faithful local deterministic models of multipartite GHZ–Mermin correlations. For every integer n ≥ 3, with R = 2^{⌊(n−1)/2⌋}, the minimum surrendered fraction is F_n = R/[2(R+1)] when the model must reproduce both all n-body GHZ–Mermin correlators and all vanishing proper-subset correlators. Quadratic Walsh spectra provide normalized constructions for odd and even n, while a nondegenerate R²-setting subsystem and a matching uniform-pair dual establish optimality. The result yields a parity-paired staircase approaching one half from below and provides a sharp, scalable benchmark for how strongly faithful multipartite local simulations must relax measurement independence.