Yang-Mills Mass Gap Solution

I present a rigorous analytical solution to the Yang-Mills mass gap problem on R³ x S¹ by employing compactification, heat kernel techniques, and Ward identities. The existence of a mass gap Δ 0 is proved, the confinement mechanism is explained, and a mass gap formula Δ = Ce^ (-A/g²) relating Δ to the gauge coupling g is derived. Furthermore, I provide a self-contained proof of the existence of a non-zero mass gap on the full four-dimensional Euclidean spacetime R⁴ (sec. O), without relying on compactification or dimensional reduction. Key theoretical and computational aspects are clarified and phenomenological implications explored.