What is proof of citizenship, anyway?

Scalia And Sotomayor Clash In Proof-Of-Citizenship Voting Case

Even a birth certificate only proves somebody of a certain name was born at a certain place to certain parents, etc.

What counts as proof you are him?

Anyway, National Voter Registration Act?

How did congress acquire the authority to prescribe registration rules to the states?

Not that it’s not a good idea.

But where exactly did that power come from?

Justices Narrowly Divided In Voter Registration Case

There is only limited federal authority to meddle with actual elections, though there are numerous constraints in the constitution on state regulation of the franchise.

Mostly, they tell states the franchise cannot be denied because of X, Y, or Z.

Or that the qualifications for voting for the federal legislature shall be the same in any state as they are for voting for the most numerous branch of that state's legislature - whatever those may be.

Other than that, congress can overrule the states in making provision for the times, places, and "manner" of electing federal legislators, though it cannot alter the states' determination of the "places of choosing senators."

And that's all.

So I don't really see any authority over the process of voter registration and not really very much even over who gets the franchise.