-2.25 -2 -1.75 -1.5 -1.25 -1 -0.75 -0.5 -0.25 0 10 -1 1 10 Q (GeV) (Q) From  $_{g1}$ (pQCD) From GDH sum rule constraint on  g1 Lattice QCD (2004) Lattice QCD (2007) From  g1 Hall A/CLAS From  $_{g1}$ CLAS From  F3 AdS Modified AdS FIG. 2. Holographic model prediction for the β function compared to JLab and CCFR data, lattice simulations and results from the Bjorken sum rule. twist scaling behavior z τ at short distances, z → 0. [15] A similar scale for parton-hadron transition region has been observed in inclusive reactions. [42] Also shown on Fig. 2 are the β functions obtained from phenomenology and lattice calculations. For clarity, we present on Fig. 2 only the LF holographic predictions, the lattice results from, [38] and the experimental data supplemented by the relevant sum rules. The width of the continuous band is computed from the uncertainty of α$_{g}$$_{1}$ in the perturbative regime. The dot-dashed curve corresponds to the extrapolated approximation given by Eq. (11). Only the point-to-point uncorrelated uncertainties of the JLab data are used to estimate the uncertainties, since a systematic shift cancels in the derivative in (12). The data have been recombined in fewer points to improve the statistical uncertainty; nevertheless, the uncertainties are still large. Upcoming JLab Hall A and Hall B data [43] should reduce further this uncertainty. The β function extracted from LF holography, as well as the forms obtained from the works of Cornwall, Bloch, Fisher et al. , [44] Burkert and Ioffe [45] and Furui and Nakajima, [38] are seen to have a similar shape and magnitude. 13