Construct a physically motivated strongly local contextual Bell model violating BCHSH

Construct a physically motivated strongly local contextual Bell model based on local physical dynamics that violates the BCHSH inequality for suitable detector settings, extending the purely mathematical Popescu–Rohrlich-based example.

Background

The paper constructs a discrete contextual Bell model that is strongly local according to the paper’s definition yet achieves the maximal algebraic violation of the BCHSH inequality. However, that construction is introduced as a mathematical proof of concept and does not explain how the setting-dependent probabilities arise physically.

The unresolved task is to derive such a model from physical dynamics—preferably classical or quantum relativistic dynamics—while retaining strong locality and producing a BCHSH violation for appropriate settings. The conclusion identifies a classical special-relativistic model, potentially involving electromagnetism and stochastically dependent initial particle data, as a possible route.