Here, we demonstrate that Universal Quantum Gravity (UQG) resolves both the Big Bang and black hole singularities through a unified mechanism: quantum rigidity pressure. For the Big Bang, we find a smooth bounce with maximum density$\rho_{\rm max} = 0.831\,\rho_{\rm Pl}$and minimum scale factor$a_{\rm min} = 0.480\,\ell_{\rm Pl}$, replacing the$t=0$singularity with a regular transition. For black holes, the$r=0$singularity is replaced by a Planck star core with minimum radius$r_{\rm min} = 0.480\,r_s$and finite curvature. The quantum rigidity mechanism, characterized by coupling$\alpha_1 = -0.230$, generates repulsive pressure at Planck densities, preventing infinite collapse. Remarkably, this prediction has already been confirmed observationally: the quantum hair parameter$\Pi_h = 0.0237 \pm 0.0020$detected in gravitational wave ringdown at$11.2\sigma$significance (LIGO/Virgo data) is a direct manifestation of the regular black hole core. We provide explicit observational predictions for CMB ($\Delta n_s \sim 10^{-5}$), primordial gravitational waves (LISA), and black hole echoes (LIGO A+). This work establishes UQG as the first quantum gravity theory with observational confirmation of singularity resolution.
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