The Yang–Mills existence and mass gap problem (solved) as a Millennium Prize challenge. We demonstrate that quantum Yang–Mills theory emerges as an effective description of three geometric scalar-field corrections in the Modified Einstein Spherical (MES) Universe. Critically, the mass gap arises entirely from the overall spacetime curvature via the Mass Generation Equation, imposing a universal minimum mass scale. Quantum-geometric forests serve as natural laboratories for quantum gravity, and the Yang–Mills mass gap is the geometric shadow of forest canopies. This work establishes MES cosmology as a complete unified field theory.