Previous results show a strong sensitivity of the values of \(\log\langle R_{\kappa}\rangle\) to the variation of the parameter \(\gamma\) in the foreground contaminating Ly-\(\alpha\) forest (see section 4 in this document). Using the correlation between \(\Delta\gamma(foreground)\) and \(\Delta\log\langle R_{\kappa}\rangle\) we can attempt a prediction for the expected log(R) evolution in different scenarios of possible \(\gamma\) evolution with redshift. We show how considerable departure from a little evolution in \(\gamma\) would manifest itself as a detectable footprint in the evolution of \(\log\langle R_{\kappa}\rangle\) with redshift, inconsistent with our observations.