  The light-front holographic mapping of classical gravity in AdS space,
modified by a positive-sign dilaton background, leads to a nonperturbative
effective coupling $\alpha_s^{AdS}(Q^2)$. It agrees with hadron physics data
extracted from different observables, such as the effective charge defined by
the Bjorken sum rule, as well as with the predictions of models with built-in
confinement and lattice simulations. It also displays a transition from
perturbative to nonperturbative conformal regimes at a momentum scale $ \sim 1$
GeV. The resulting $\beta$ function appears to capture the essential
characteristics of the full $\beta$ function of QCD, thus giving further
support to the application of the gauge/gravity duality to the confining
dynamics of strongly coupled QCD. Commensurate scale relations relate
observables to each other without scheme or scale ambiguity. In this paper we
extrapolate these relations to the nonperturbative domain, thus extending the
range of predictions based on $\alpha_s^{AdS}(Q^2)$.
