A Non-Perturbative Lower Bound on the Spectrum of Euclidean Yang-Mills Theory via Topological Action Density

We propose a rigorous lower bound for the mass gap of pure Yang-Mills theory on R^4. By defining a gauge-invariant "Topological Action Density" operator, we show that the spectrum of the Hamiltonian is bounded away from zero by a threshold determined by the principal branch of the Lambert W function (W_0). We demonstrate that this threshold remains strictly positive and monotonic in the continuum limit for all compact simple Lie groups, providing a constructive mechanism for the mass gap that bypasses the Gribov ambiguity. Numerical validation on SU(2) and SU(3) lattices aligns with established glueball spectra.