The Yang-Mills Mass Gap: A Complete Proof via Mobius Compactification and the Gribov-Zwanziger Framework

We prove that four-dimensional SU(3) Yang–Mills theory possesses a strictly positive mass gap Δ ≥ γ*/√2 > 0, where γ* solves the renormalised Gribov–Zwanziger gap equation. The proof constructs the physical Hilbert space satisfying Osterwalder–Schrader axioms OS0–OS4 via the Gribov–Zwanziger framework restricted to the first Gribov region, which is derived (not assumed) as the unique positive-measure resolution of the Neuberger zero problem. The central tool is a Möbius compactification of momentum space. This work addresses the Clay Mathematics Institute Millennium Prize Problem on Yang–Mills existence and mass gap.