Standard Generalized Uncertainty Principle (GUP) models with a universal deformation parameter (1) are under increasing tension from precision Gamma-Ray Burst (GRB) and LHAASO observations. We propose a phenomenological ansatz where the deformation parameter scales with the square of the interaction coupling: ᵢ ᵢ². We demonstrate that this hierarchy (_ _ ₇₀₃ₑ₎₍) naturally satisfies all current multi-messenger constraints, including the tight bounds from GRB 221009A and the Crab Nebula PeVatron, without invoking arbitrary scales. Crucially, the framework breaks the degeneracy of universal models by predicting a species-dependent time delay hierarchy (t_ > t_) with a fixed ratio determined by Standard Model couplings: t_ / t_ (W / ₄₌) ² 21. 5. This mechanism resurrects the parameter space for Linear (n=1) quantum gravity models, predicting macroscopic (10 s) delays for PeV neutrinos that are falsifiable with current generation detectors.
Stephen Cotton (Fri,) studied this question.