Proportional Stationarity and Structural Stability in Perturbative Field Theories

We formulate a structural stability criterion for dimensionless physical constants within standard perturbative field frameworks. The analysis introduces a response-ratio functional Γ=κ/τ, defined from second-order sensitivity and first-order deformation measures associated with admissible variations in a field configuration. Stability is characterized by proportional stationarity of Γ, expressed as a first-order operator condition along transformation flows. The framework characterizes, within a declared variational model, when invariance of fixed constants can be represented as a stationarity condition. Under compactness and convexity assumptions typical of variational systems, stationary response ratios arise as isolated solutions of the associated operator equation; more general settings permit continuous spectra. Explicit functional definitions are provided within a conventional analytic setting, and the criterion is illustrated in representative classical field models. The results position proportional stationarity as a model-relative structural consistency condition for perturbative stability; isolation is conditional on compactness and non-degeneracy hypotheses, and continuous families may occur outside that regime. Limitations and possible extensions, including discretized spacetime formulations, are discussed.