order Q $^{∗∗∗}$. All these contributions are again added in quadrature. The various truncation uncertainties are estimated by taking the value of the last known term of the series. The very good agreement of the results [69] allows us to check the consistency and the applicability of CSR, even into the IR-UV transition region, albeit with large uncertainties. Throughout the paper, we limit the order of our calculation to α 3 s so that no IR terms appear. A similar test of CSR is also shown on the bottom panel of Fig. 7. It shows α$_{g}$$_{1}$ computed using four different methods. 1) The continuous band corresponds to the results using the Bjorken sum rule and α$_{MS}$ . 2) cross-hatched band [70]: using the CSR to obtain α$_{g}$$_{1}$ as a function of α$_{MS}$ . 3) Dashed line: using the CSR to obtain α$_{g}$$_{1}$ as a function of α$_{V}$ . This latter is computed from the two-loop computation of Ref. [61]. 4) Continuous line: using α$_{V}$ from pQCD [61] as an input to the appropriate CSR to form α$_{MS}$ . This later is used as input in another CSR to form α$_{g}$$_{1}$ . There is again excellent agreement. In addition, that the dashed and continuous lines are on top of each other verifies the transitivity property of the CSR. These agreements are nontrivial consistency checks of QCD since the CSR are central predictions of pQCD. [1] See for example: D. Binosi and J. Papavassiliou, “Pinch Technique: Theory and Applications,” Phys. Rept. 479 , 1 (2009) [ arXiv:0909.2536 [hep-ph]], and references therein. [2] J. M. Maldacena, “The large N limit of superconformal field theories and supergrav- ity,” Adv. Theor. Math. Phys. 2 , 231 (1998) [Int. J. Theor. Phys. 38 , 1113 (1999)] [ arXiv:hep-th/9711200 ]. [3] S. S. Gubser, I. R. Klebanov and A. M. Polyakov, “Gauge theory correlators from non- critical string theory,” Phys. Lett. B 428 , 105 (1998) [ arXiv:hep-th/9802109 ]; E. Wit- ten, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys. 2 , 253 (1998) [ arXiv:hep-th/9802150 ]. [4] G. F. de Teramond and S. J. Brodsky, “Light-Front Holography: A First Approximation to QCD,” Phys. Rev. Lett. 102 , 081601 (2009) [ arXiv:0809.4899 [hep-ph]]. [5] S. J. Brodsky and G. F. de Teramond, “Hadronic spectra and light-front wavefunctions in holographic QCD,” Phys. Rev. Lett. 96 , 201601 (2006) [ arXiv:hep-ph/0602252 ]; “Light- Front Dynamics and AdS/QCD Correspondence: The Pion Form Factor in the Space- and 25