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Lila15 SCOTUS can accept cases on a few different grounds. For instance, in this election, constitutional grounds may be argued in two ways:
1. Some votes were cast unconstitutionally because the voting procedures were changed by either a lower court, attorney general or election official. Article One of the constitution states that only a state's legislature may determine how the election is conducted. For example, the Pennsylvania Supreme Court ruled that absentee ballots that were received after election day could be counted. It's a clear argument to make that the Pennsylvania Supreme Court overstepped it's authority by allowing these ballots to be counted, when only the state legislature may make that determination.
2. The Equal Protection Clause of the constitution requires equal treatment for all citizens. Evidence of fraud, such has having more votes cast than the number of registered voters in a county, demonstrates that citizens were not treated equally by the introduction of ballots that are fraudulent.
Those are two simple examples, but there are many others. But the bottom line is that in all the states, Article One and the Equal Protection Clause are the arguments that will be used.