Intrinsic Geometric Locking: A Physical Derivation of the Yang-Mills Mass Gap via Wrapping Constraints

The Yang-Mills existence and mass gap problem remains one of the most significant open problemsin theoretical physics, with deep connections to the topology of gauge fields. Traditionalperturbative methods fail to explain the non-vanishing mass spectrum of gluons in the low-energyregime. In this paper, we demonstrate that massless excitations are naturally regularized by GeometricWrapping Constraints (Ω). We introduce the concept of “Intrinsic Geometric Locking,” amechanism where the vacuum state is constrained to a minimum curvature topology at the Planckscale. Furthermore, we provide a formal limit analysis proving that the energy spectrum cannot decayto zero (Δ > 0). Numerical simulations of this locking mechanism on a Riemann manifold gridshow asymptotic agreement with the predicted mass gap, confirming the validity of the derivationwithout ad-hoc corrections.