A No-Go Theorem on the Emergence of Temporal Duality in Effective Geometries Mediated by Scalar Fields

We establish a no-go theorem that provides the mathematical foundation for dual-foliationspacetime models, particularly the MINT (Model of Intertwined Narratives in Time) frame-work. For convex interpolation of Lorentzian metrics mediated by a single scalar field—interpreted physically as a coherence parameter between temporal foliations—we prove undernatural assumptions of regularity, discrete symmetry, absence of fine-tuning, and geometricstability that such interpolation cannot involve more than two effective geometric classes,regardless of the total number of initial metrics. This result demonstrates that the bimetricform geff = χg(1) + (1 − χ)g(2), central to MINT and related dual-foliation approaches, is notmerely an ad hoc choice but a structural necessity under scalar mediation. The proof followsfrom a purely geometric analysis of the weight simplex and symmetry group action, withoutdynamical circularity. Consequently, this theorem establishes a rigorous mathematical basisfor the emergence of temporal duality in effective geometric theories, validating the coreassumption of the MINT research program. Version 2. This revision corrects minor formal issues, clarifies the role of stability assumptions, strengthens the proof of the main no-go theorem, and expands the discussion of physical interpretation and generalizations.