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This paper presents the complete QED contribution to the electron g-2 up tothe tenth order. With the help of the automatic code generator, we haveevaluated all 12672 diagrams of the tenth-order diagrams and obtained 9.16(58)(\alpha/\pi)^5. We have also improved the eighth-order contributionobtaining -1.9097(20)(\alpha/\pi)^4, which includes the mass-dependentcontributions. These results lead to a_e(theory)=1 159 652 181.78 (77) \times10^{-12}. The improved value of the fine-structure constant \alpha^{-1} =137.035 999 174 (35) [0.25 ppb] is also derived from the theory and measurementof a_e.

Tenth-Order QED Contribution to the Electron g-2 and an Improved Value of the Fine Structure Constant