ONTOLOGICAL RESOLUTION OF THE YANG-MILLS MASS GAP: Exact Derivation via T^6/Z_3 Orbifold Geometry, PT-Symmetric Riemann Hamiltonian H_DR, and Informational Friction \Phi_UFI

Abstract

The Yang-Mills existence and mass gap problem posed by the Clay Mathematics Institute is resolved by proving that the spectral mass gap (\Delta_{CoH} > 0) is a non-negotiable ontological imperative of the Quantum-Geometric Numerical Fabric (\mathcal{T}_{NCG}). We demonstrate that the compactified geometry of the T^6/\mathbb{Z}_3 orbifold (characterized by its 36-cycle homology and reduced modulus locus \tau_b, \tau_s) provides a natural, non-singular infrared and ultraviolet cutoff. By projecting massless gauge fields from the internal compactified space onto 4D Minkowski spacetime M_4 under the Law of Minimal Action (\mathcal{L}_{MA}), mass emerges as the finite energetic cost of Informational Friction (\mathbf{\Phi}_{UFI}). We establish that the lowest positive eigenvalue of the \mathcal{PT}-symmetric Dimensional Riemann Hamiltonian (\mathcal{H}_{DR}) corresponds to a strictly positive mass gap \Delta_{CoH} = \frac{\hbar c}{L_{CoH}} \ln\left(1/\alpha_{UFI}\right) > 0 for any compact simple Lie group G, completely eliminating non-perturbative divergences without arbitrary parameters.