Power-law scaling appears ubiquitously in complex systems, including network growth, self-organizing processes, and critical phenomena. Most generative models produce scaling behavior with fixed exponents determined by topology rules or attachment kernels. Mechanisms capable of generating smoothly tunable scaling exponents without modifying underlying topology remain limited. We investigate constraint-weighted admissible growth, a stochastic extension process in which candidate structural increments are selected via an exponential compatibility kernel penalizing dispersion. Varying a single constraint parameter produces a monotone dependence of the time-scaling exponent while preserving topology rules. Beyond first-order scaling behavior, we derive a coarse-grained transport-like coefficient directly from the same kernel as the expected squared increment per discrete growth step. A stylized analytic treatment shows that exponential tail truncation introduces a cutoff scale yielding conditional superlinear gradient sensitivity in the weakly constrained regime and sharp suppression once Numerical experiments confirm monotonic exponent suppression, robustness under control tests, and nonlinear collapse of gradient elasticity. The results isolate exponential compatibility weighting as a minimal structural mechanism linking scaling modulation and nonlinear transport suppression. Supporting code archive: Zenodo DOI 10.5281/zenodo.18845699.Actively maintained code repository: GitHub repository listed in the manuscript
Georgios K. Kouvidis (Wed,) studied this question.