Consistency check for asymptotic convergence of classical Yang-Mills fields in the Lorentz gauge

We derive the class of restricted local gauge transformations of Yang-Mills fields that leave the four-divergence of these fields invariant. They form a symmetry of the Yang-Mills equations combined with the Lorentz condition and lead, in Euclidean space-time, to the Gribov ambiguity. We make use of this symmetry in order to check possible inconsistencies arising from the supposition of asymptotic convergence of classical Yang-Mills fields, obeying the Lorentz condition, to free fields. Inconsistencies would support the common conjecture of color confinement. We show that residual gauge transformations of the interpolating fields induce Abelian gauge transformations and global $\mathrm{S}{\mathrm{U}}_n$ rotations on the hypothetical asymptotic fields thereby revealing no inconsistency of the hypothetical asymptotic convergence.