Addendum to "A Unified Quantum Gravity Framework": Spacetime Surface Tension (\mathbf{S}_{\mu u}), Singularity Resolution, and Remnant Entropy Algebra

This addendum expands upon the Unified Quantum Gravity Framework by formalizing the density-dependent effective gravitational coupling G_{\text{eff}}(\rho) = G_0 e^{-\rho/\rho_{\text{Planck}}} and introducing the Spacetime Surface Tension Tensor (\mathbf{S}_{\mu\nu}). We demonstrate that at the Planck density scale (\rho \to \rho_{\text{Planck}}), standard attractive gravity vanishes (G_{\text{eff}} \to 0) and transitions into an elastic spacetime surface tension shield. This mechanisms prevents geometric collapse, guaranteeing a non-zero finite minimum core radius for collapsed structures: R_{\text{core}} = \left( \frac{3M}{4\pi\rho_{\text{Planck}}} \right)^{1/3}. Furthermore, we derive the exact Planck remnant entropy equation S_{\text{remnant}} = \frac{\pi}{e} k_B \approx 1.1558 \, k_B, fully resolving the black hole information paradox by preserving quantum state microstates within a stable membrane. Finally, we formulate the underlying operator algebra, introducing a density-driven cross-commutation relation [\hat{a}_\mathbf{k}, \hat{b}_\mathbf{p}^\dagger] = i \kappa \eta(\hat{\rho}) \delta^3(\mathbf{k}-\mathbf{p}) between standard field annihilators and stored anti-energy creators, establishing complete thermodynamic unitarity and zero-point stability in quantum gravity.