Critical Assessment of the Proper-Time FRG

This work provides a critical evaluation of the recent manuscript “Proper-time functional renormalization in O(N) scalar models coupled to gravity” (Bonanno, Glaviano, Vacca, arXiv:2508.00807), showing that its conclusions lack fundamental physical meaning due to intrinsic regulator dependence, absence of variational closure, and reliance on externally inserted couplings. All fixed points, critical exponents, and stability properties vary significantly with the proper-time cutoff, demonstrating that the framework is not universal and cannot serve as a fundamental theory. In contrast, we show how the Universal Ψ Equation constitutes a fully closed, regulator-free variational structure where scalar, vector, and gravitational sectors arise coherently from a single functional identity, without arbitrary flow parameters or external inputs. The comparison highlights the conceptual and structural superiority of a closed variational principle over proper-time FRG approaches, which remain inherently phenomenological.