You back up reported results with documents (registrations, physical ballots) then verify the documents
It's SOP in a real investigation
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The object of the investigation is to catch those who practiced fraud. It is NOT to make Thune the winner.
I will be satisfied if it is pursued through the DOJ. If you do a recount, you will accomplish nothing except ill will.
Example: It is not necessary to do a recount to ascertain that there was a huge increase in registration of certain counties. It is not necessary to see that these new registrants had an exceptionally high turnout. What the DOJ will do is see if these are REAL people, if they indeed voted, and if they were eligible. Should 500 of them be found to be fraudulent, you cannot simply take 500 votes away from Johnson. How are you going to prove how these 500 fraudulent voters voted? We can assume that they were Johnson votes, but you can't PROVE it.
A recount does nothing to help the investigation. I realize you are frustrated, but we are in a long war here, and your state unfortunately was a defeat AT THIS TIME. But if there is widespread fraud uncovered and prosecuted, then Thune's sacrifice and that of the Republicians WHO VOTED FOR HIM in South Dakota will be part of a larger victory.