Temporal Bell Inequalities and Global Consistency in Modal Triplet Theory

Temporal Bell inequalities, such as the Leggett–Garg inequalities, test whether a singlesystem can be described by a time-local realist model. Quantum mechanics violates theseinequalities while preserving operational causality. In this work we give a proof-forwardaccount of temporal Bell inequalities within Modal Triplet Theory (MTT). We show that any temporally factorized realist model satisfies the Leggett–Garg bound.We then demonstrate that MTT generically violates temporal factorization because physicallyadmissible histories are selected by global coherence and fixed-point constraints, ratherthan by independent time-local hidden variables. Despite this failure of temporalfactorization, MTT preserves no-retro-signaling: later measurement choices do not alterearlier observable marginals. As a result, MTT reproduces standard quantum Leggett–Garg violations without invokingretrocausal dynamics or abandoning realism of the underlying modal configuration.Temporal Bell violations and spatial Bell nonlocality are identified as two projections ofthe same global-consistency mechanism. The framework is fully compatible with currentexperiments and standard quantum predictions.