Statistically, there is a relatively simple way to validate (or demonstrate falsification) the overall distribution. It is commonly used by census bureaus and statistical agencies. One takes a random and small subset from a studied distribution (statistics) and repeat survey (voting) under full control. If the re-estimated statistics is quite different from the previously obtained result one may express a doubt in the accuracy of the original survey (voting). The size of the re-estimated set should be defined by the originally observed statistics and specifically from the polling stations with most suspicious results.
Therefore, one does not need to repeat the full election process everywhere. We need only a relatively small number of polling stations which can be determined by lottery from the set with distributions of votes in favour of United Russia far from the expected Gaussian distribution. United Russia would be happy to prove that these results are not falsified to calm down the protests and indignation.