Horvat proves Probabilistic Locality plus "Irrelevance of History" jointly imply Bell's Local Causality — so Bell-violations may falsify history-irrelevance, not locality

physicsphysics.hist-phquant-phquantum-foundationsbell-theoremlocalitydeterminismarxiv

Sebastian Horvat defines "Irrelevance of History" as the assumption that the probability distribution governing what happens after some collection of events is the same regardless of what preceded those events — physical dynamics being Markovian all the way down. His Proposition 3 shows this Markovian assumption, together with Probabilistic Locality, entails Bell's Local Causality (and hence Bell's inequalities). Since quantum experiments empirically violate Bell's inequalities, and the paper argues there is no independent reason to doubt Probabilistic Locality or the "statistical independence" assumption also used in Bell's derivation, Horvat concludes that the Irrelevance-of-History assumption is the one that must be false — recasting Bell-violating correlations as evidence against history-irrelevance rather than against locality, relativity, or realism.