When Does Global Rationality Exist? A Representation Theory for Evaluative Systems

Architecture-dependent systems pose a local-to-global problem in which locally admissible and locally evaluated changes need not admit a globally coherent scalar representation. We develop a systems-theoretic framework combining system state and architecture, admissible directions of change, local evaluation, and induced dynamics within a differential-geometric structure. We establish that, under connectedness and bracket generation, a global scalar representation exists if and only if the horizontal evaluation form has zero circulation along every closed horizontal curve, with an equivalent result if horizontal evaluation is path-independent. When it exists, the representation is unique up to an additive constant and reproduces the primitive canonical rational correspondence. Along canonical rational trajectories, its rate of change equals the maximal local evaluative rate; with additional regularity, feasible inaction, and precompactness, this yields strict ascent outside rational equilibrium, excludes non-equilibrium recurrence, and confines limiting behaviour to rational equilibria. An endogenous-opportunity application shows when locally rational economic adjustments admit a global utility or welfare representation. Representability is equivalent to the cross-channel compatibility condition ($r\in Im\left(C^{\mathsf{T}}\right)$), while distance from this subspace quantifies failure of global welfare coherence. The framework therefore distinguishes local optimisation from the stronger systems property of global evaluative coherence.