Emergence of Internal Reliability in Dynamical Networks from the Universal Ψ Lagrangian

This paper demonstrates that the internal reliability and anti–reliability phenomenaobserved in dynamical networks (Matteuzzi et al., 2025) emerge directly from thecoherence constraints of the Universal Lagrangian. The stability of each unit, classicallydescribed by the sign of its transversal Lyapunov exponent, arises as the naturalbalance between temporal and informational gradients within the self–referential variationalfield. Without invoking coupling constants, noise terms, or external drives,the framework reproduces numerically the same reliability transition patterns reportedin Kuramoto and recurrent neural networks, including the spatial localizationof anti–reliable nodes and the global synchronization thresholds.