Classical two-channel detector model reproducing quantum correlations in Bell experiments

An explicit local hidden-variable model with a stochastic two-channel detector is constructed that reproduces the quantum correlation E(a,b) = −cos(a−b) for the singlet state. The model uses only: (i) a shared classical phase λ ∈ [0,2π), uniformly distributed; (ii) Malus-law detection probabilities; (iii) two independent binary channels per detector. The standard Bell ±1 encoding is shown to be a lossy compression of the two-channel output, and the CHSH parameter |S| = 2√2 emerges from this encoding without any non-local mechanism. The raw (unnormalised) correlation satisfies CHSH (|S| = √2 ≤ 2); the normalised (Pearson) correlation violates it (|S| = 2√2 > 2), without any change in the underlying physical model. The CHSH test, as currently implemented, cannot distinguish between an entangled quantum source and the classical model presented here.