Topological Resolution of the Yang-Mills Mass Gap Problem: Quantum-Geometric Mass Generation via 5D Information-Metric Manifolds

This disclosure addresses the Yang-Mills existence and mass gap problem on R4. Wedemonstrate that non-abelian gauge theory exhibits a strictly positive mass gap Δ > 0 as adirect topological consequence of embedding gauge fields into the five-dimensional informationmetricvacuum manifold M5 of the Cosmic Awareness Theory of Liquid Spacetime (CATLS)framework. We prove that vacuum fluctuations are constrained by the quantum-geometricsaturation suture constant Ceff, preventing zero-mass massless excitations and generating adiscrete lower bound for the energy spectrum.