ANALYTIC DERIVATION OF THE YANG-MILLS MASS GAP FROM TOPOLOGICAL VACUUM IMPEDANCE CONSTRAINTS

One of the most significant open problems in mathematical physics is demonstrating the existence of a "Mass Gap" in quantum Yang-Mills theory; specifically, providing a rigorous explanation for why force carriers (gluons) remain massless while their bound states (hadrons) possess a finite positive mass, despite classical symmetry suggesting scale invariance. This paper presents an analytic solution based on vacuum topology. It is demonstrated that color confinement is not merely a phenomenological potential but the result of a Vacuum Coherence Tension acting upon a compactified geometry of dimension D=10 (SO(10) symmetry). An exact equation is derived for the ground state of the hadronic spectrum (the neutral pion, π⁰), defined as an impedance resonance of the fundamental fermionic dipole. The theoretical formula obtained, m_π⁰ = mₑ · (2α⁻¹ - D), predicts the pion mass with a precision exceeding 99.9% relative to CODATA experimental values, establishing a non-zero lower bound for the energy spectrum and resolving the Mass Gap problem.