Resolution of the Yang–Mills Mass Gap Problem Using RigbySpace

The Yang--Mills mass gap problem—the assertion that non-Abelian gauge theories exhibit a positive lower bound on excitations above the vacuum—is a central challenge in quantum field theory. In this paper, we present a stand–alone approach based on the RigbySpace (RS) framework, which eliminates $\pi$ via discrete Algebraic Trigonometry (AT) and Trigonometric Algebra (TA) transformations. By replacing continuous integrals with finite sums, the RS framework naturally regularizes ultraviolet divergences. We introduce an RS–modified Yang–Mills Lagrangian and coupling, derive a corresponding Hamiltonian, and show that its discrete spectrum exhibits a nonzero mass gap. Detailed theoretical derivations and numerical calibration methods are provided, along with a discussion on the implications for confinement and future research directions.