Uniform Poincare Inequality for Lattice Yang-Mills Theory Via Multiscale Martingale Decomposition

We prove that the lattice Yang-Mills measure with gauge group SU(N_c) in d = 4 dimensions at sufficiently large beta = 2N_c/g^2 satisfies a Poincare inequality with constant alpha* > 0 uniform in the lattice size L, conditionally on Balaban's constructive RG and an RG-normalized disintegration hypothesis. The proof uses: (i) the Ricci curvature bound of the gauge orbit space -- sharpened in v2 to Ric_B >= N_c/2, following the correction at its source in ai.viXra:2602.0036 (v2) -- giving a uniform spectral gap for conditional fast modes at each RG scale; (ii) Balaban's polymer derivative bounds, controlling residual cross-scale coupling; and (iii) a multiscale martingale variance decomposition avoiding recursive composition losses, with commutator coefficients D_k <= C e^{-2 kappa} 2^{-3k} made summable by the geometric scaling of transversal block averaging. Version 2 corrects the coupling-flow direction in the statement of Balaban's theorem (which improves the fallback bound of Remark 2.7: beta_k <= beta is bounded, rather than O(k)), records that the summability is robust to the block-averaging convention (new Remark 2.8: the Balaban-style convention gives 2^{-(d-2)k}, still summable), clarifies that the commutator coefficient involves the centered gradient of the conditional potential (which is the mechanism by which G_k-measurable parts drop out, as Assumption 2.6 asserts), and updates the companion references. Unlike other v2's of this series, no statement of v1 is refuted: the entire martingale machinery (commutator identity, telescoping, absorption, the assembled constant alpha*) is validated end-to-end in a companion numerical suite, exactly in a two-scale Gaussian model and against the true spectral gap in a compact four-rotor model, where the recipe's alpha* is confirmed as a valid lower bound.