Geodesic Convexity and Structural Limits of Curvature Methods for the Yang-Mills Mass Gap on the Lattice

This replacement withdraws the global orbit-space Ricci lower bound and the spectral-gap corollaries derived from it. The printed proof of Theorem 3.1 traces O'Neill's horizontal sectional-curvature identity as though the total-space Ricci tensor contained only horizontal directions. The correct trace also subtracts the mixed horizontal-vertical sectional curvatures. For the bi-invariant product metric these terms are nonnegative before subtraction, so the omitted contribution has the unfavorable sign; the manuscript does not prove that the positive O'Neill term dominates it. Accordingly Theorem 3.1 is not established, rather than asserted false, and Corollaries 3.2-3.3 are withdrawn. The correction also separates a finite-dimensional orbit-space statement from later RCD results formulated for a different measure and operator, and records the broken dependency on a version of ai.viXra:2602.0035 that was not present in its public record. The local geodesic-convexity results and the independently stated structural obstruction are retained only within their stated scope.