We propose the QEC-BC framework (Quantum Error Correction with Bounded Curvature), a unified model that eliminates classical singularities in both black holes and cosmology. By imposing a maximum curvature scale and introducing entanglement-induced stress-energy corrections, the framework ensures information preservation during gravitational collapse, evaporation, and early-universe evolution. The resulting geometry replaces singularities with smooth, finite-curvature transitions and predicts observational signatures such as pre-bounce correlations in the cosmic microwave background (CMB). The model offers a coherent solution to the black-hole information paradox and a non-singular alternative to the Big Bang.