Geometric Stabilization of the Yang-Mills Vacuum: A Derivation of the Mass Gap via Non-Associative Stiffness

We propose a rigorous geometric mechanism for the origin of the mass gap in non-Abelian gauge theories, derived from the topological constraints of M-theory compactified onmanifolds of G2 holonomy. We demonstrate that the vacuum of Quantum Chromodynamics(QCD) is not a passive stage but a dynamical medium governed by a “Geometric Stiffness”parameter, βQCD = 6/π ≈ 1.91. This parameter arises from the ratio of the non-associativebulk degrees of freedom to the associative measure of the stability cycle. By modifying theequation of state for the effective string description of color flux tubes, we introduce theWolf-Toffoletto-Schutza (WTS) action, which incorporates this super-linear stiffness.We establish a formal duality between the Lagrangian configuration space of high-βmagnetospheric plasma filaments and the color flux tubes of the strong interaction. Uti-lizing the Thin Filament Code (TFC) as a non-perturbative solver, we demonstrate thatthe super-linear restoring force (Γef f ≈ 2.91) forbids zero-energy excitations, generating astrictly positive fundamental frequency ω0 > 0. The resulting spectrum predicts a scalarglueball mass of 1710 MeV and resolves the Proton Spin Crisis with a predicted quark spincontribution of Σ ≈ 0.34, matching experimental data. This work offers an effective fieldtheory description of confinement rooted in the non-associative geometry of the vacuum.