Solution to the Yang-Mills Mass Gap Problem on R4

I present a rigorous analytical solution to the Yang-Mills mass gapproblem on R4 by employing non-perturbative techniques, heat kernelmethods, and Ward identities. The existence of a mass gap ∆ > 0 isproved, and a mass gap formula ∆ = Ce−A/g2 relating ∆ to the gaugecoupling g is derived. The solution adheres to the criteria set by the ClayMathematics Institute and addresses the points raised by Michael Peskin.