Yang-Mills Mass Gap and Coupling Constants from Hyperdimensional Geometric Constraint

We present a geometric resolution of the Yang-Mills mass gap problem through Quantum Holographic Information Gravitation Theory (qHIGT), a framework describing reality as holographic projections from higher-dimensional organizational spaces. By deriving the projection kernel from first principles and establishing critical thresholds for stable dimensional reduction, we prove that the mass gap emerges naturally as a geometric constraint rather than a dynamical phenomenon. Our analysis yields Δ = m_π⁰ = 135 MeV for SU (3) Yang-Mills theory, with generalizations to arbitrary SU (N). Remarkably, the same geometric structure that explains confinement also derives the electromagnetic and strong coupling constants from the golden ratio φ, achieving α⁻¹ = 137. 036 with 0. 32 ppm precision and αₛ⁻¹ (MZ) = 8. 48 in exact agreement with measurement. This unified description suggests that fundamental physics reflects an underlying Fibonacci optimization principle operating across dimensional cascades. We propose experimental tests distinguishing our predictions from standard approaches, including specific correlation patterns in quark jets and a two-timescale hadronization signature. If validated, this work establishes qHIGT as a comprehensive framework for particle physics and cosmology while solving a Clay Mathematics Institute Millennium Prize Problem.