I present closed-form, parameter-free values for nine glueball masses, the confining string tension, and the mass gap of pure SU (3) Yang-Mills theory in 3+1 dimensions. The derivation has two parts. The first is a theorem: in any asymptotically free gauge theory with a single dynamical scale, dimensionless ratios of physical observables at the same angular weight are rational numbers whose prime factors come from the gauge group and the heat kernel of the kinetic operator. For pure SU (3), this forces all such ratios to be ratios of powers of 2 and 3. The second part is empirical: comparison with lattice data determines which specific rationals appear. Each dimensionless quantity, expressed in units of the Sommer parameter r0, takes the form (2π) ʷ × h with h a 3-smooth rational and w = 0, 1, 2, or 3. The string tension value is r0√σ = (3/8) π. All ten quantities agree with continuum-limit lattice QCD data to within one standard deviation, with a combined χ² = 2. 30 for nine masses and zero free parameters. The mass gap is Δ = m (0++) = (32/9) √σ, a pure 3-smooth rational times √σ. The ratio m (0⁻⁺) /m (0⁺⁺) = 3/2 matches the measured value to the center of the error bar. The three heaviest states carry no factors of π and take pure rational values, two of which coincide numerically with the one-loop and two-loop QCD beta function coefficients: r0 m (3++) = 9 = β₀ and r0 m (1+-) = 64/9 = β₁/β₀ for SU (3) with nf = 3 active flavors. Since the glueball spectrum is computed in pure gauge theory (nf = 0), where β₀ = 11 carries the prime 11, this numerical coincidence requires explanation.
Eric Yaw (Wed,) studied this question.