QED confronts the proton's radius

Recent results on muonic hydrogen [1] and the ones compiled by CODATA on ordinary hydrogen and $ep$-scattering [2] are $5\sigma$ away from each other. Three reasons justify a further look at this subject: 1) There is an apparent error in [1] in solving a cubic equation. This error is equivalent to a shift of the proton's radius by 3.4 of the standard deviations of [1], in the "right" direction of data-reconciliation. 2) One of the approximations used in [1] is not valid for muonic hydrogen. This amounts to an extra $\sim 3\sigma$ in the same direction. In field-theory terms, the error is a mismatch of renormalization scales. Once corrected, the proton radius "runs", much as the QCD coupling "constant" does. 3) The result of [1] requires a choice of the "third Zemach moment". Its published independent determination is based on an analysis with a $p$-value --the probability of obtaining data with equal or lesser agreement with the adopted (fit form-factor) hypothesis-- of $3.92\times 10^{-12}$. In this sense, this quantity is not empirically known. Its value would regulate the level of "tension" between muonic- and ordinary-hydrogen results, currently {\it at most} $\sim 3.5\sigma$. There is no tension between the results of [1] and the proton radius determined with help of the analyticity of its form factors.