We establish universal scaling laws and quantify aging in three-dimensional uniformly heated hard sphere granular gases through large-scale event-driven molecular dynamics ( \(N=500{,}000\) ). We report three primary quantitative results: (i) The characteristic energy decay time exhibits a universal inverse scaling \(\tau _0 \propto \epsilon ^{-1.03 \pm 0.02}\) with the dissipation parameter \(\epsilon = 1 - e^2\) . (ii) The steady-state temperature follows a precise power-law \(T_{\textrm{steady}} \propto \epsilon ^{-1.51 \pm 0.03}\) , reflecting the non-linear balance between thermostat heating and collisional dissipation. (iii) The velocity autocorrelation function \(\bar{A}(\tau _w, \tau )\) demonstrates pronounced aging, with decay rates \(\lambda \) following a power-law slowing down \(\lambda (\tau _w) \propto \tau _w^{-0.82 \pm 0.05}\) . (iv) A characteristic cluster size \(\xi (\tau _w)\) extracted from g(r) grows as \(\xi \propto \tau _w^{0.38\pm 0.04}\) , and the VACF decay rate follows \(\lambda \propto \xi ^{-2.16\pm 0.20}\) , providing the first quantitative structural-dynamical link between spatial coarsening and velocity decorrelation in a 3D driven granular gas. The aging exponent \(\lambda (\tau _w) \propto \tau _w^{-0.82\pm 0.05}\) , verified over 1.6 decades of \(\tau _w\) and robust across two noise intensities and two densities, provides the first quantitative evidence for aging dynamics in the driven steady-state regime, distinct from previously studied freely cooling cases.
