We investigate the physical implications of a nonlinear hyperbolic compression constant I ≈ 0.37159, emerging from a distributional fixed-point operator. Interpreting this constant as a universal information-compression parameter, we explore its role in three domains: (i) quantum gravity corrections to black hole entropy, (ii) perturbative modifications to black hole quasi-normal mode spectra, and (iii) corrections to the dark energy equation of state. We show that I can be consistently embedded as a prefactor in logarithmic entropy corrections, induces controlled deformations of effective potentials governing perturbations, and yields observationally viable cosmological deviations when appropriately coupled. This establishes a unifyinginterpretation of I as a cross-domain information-geometric parameter.
SİNAN İBAGÜNER (Tue,) studied this question.