Ricci Curvature of the Orbit Space of Lattice Gauge Theory and Single-Scale Log-Sobolev Inequalities

We establish that the orbit space B = A/G of SU(N_c) lattice gauge theory satisfies the Riemannian curvature-dimension condition RCD*(N_c/4, dim A); in particular, it satisfies CD(N_c/4, infinity) in the sense of Lott-Villani-Sturm. The proof shows that the configuration space A = SU(N_c)^{|B_1(Lambda)|}, with the bi-invariant product metric = -2 tr(XY), is an Einstein manifold with Ric_A = (N_c/4) g_A (Proposition 2.2), and applies the stability of the RCD* condition under quotients by compact groups of measure-preserving isometries (Galaz-Garcia-Kell-Mondino-Sosa). This bypasses O'Neill computations and handles the singular stratum (reducible connections) automatically. As a consequence we derive a conditional log-Sobolev inequality for measures d mu = e^{-Phi} d nu / Z with constant alpha = (N_c/4) e^{-osc(Phi)}. All constants are computed explicitly for SU(2) and SU(3). This provides the geometric input in a program aiming at a volume-uniform log-Sobolev inequality for SU(N_c) lattice Yang-Mills theory at weak coupling; the complementary analytic input is developed in the companion papers cited in Section 6.1. Note added (v3). Version 3 accompanies the paper with a numerical verification suite (full Einstein tensor for SU(2/3/4); the convention triangle N_c/4 <-> N_c/2 <-> 1/2 closing the series' Ricci bookkeeping; the horizontal characterization at machine precision; the Bakry-Emery convention on the Gaussian via the exact Gross optimizers; Holley-Stroock in LSI form; and the exact energy/entropy correspondence for a Z_2 quotient toy). It corrects a sign in Section 5.1 ([T^a,T^b] = +eps^{abc} T^c requires T^a = -(i/2) sigma^a), repairs the attributions in Section 1.4 (the O'Neill-sketch Ricci statement lives in ai.viXra:2602.0036, whose v2 sharpened the -tr-convention value to N_c/2, consistent with N_c/4 here), adds the measured sectional-curvature range of SU(3) to Section 5.2, and fills in the companion identifiers in Section 6.1 with their honest status. No statement of v2 is refuted.