Positronium contribution to the electron g-2

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The contribution of positronium to the electron g-2 (aₑ) has been computed in Ref. [1] and found to be of the same order of α as that of five-loop perturbative QED. We confirm this result and correct a few errors in its first derivation. As recently calculated in Ref. [2], a continuum nonperturbative contribution to aₑ cancels one-half of the positronium one. We show by explicit calculation that the remaining half is already included in the five-loop perturbative result. We also show that it arises from the class I(i) of five-loop diagrams containing only one closed electron loop.