At least, TX is the only state I know of now that satisfies all of these requirements;
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I don’t doubt that for an instant. However, any state can pass a law requiring candidates to provide specific proof that they are eligible to hold the office they are running for to be put on the ballot.
I want states to pass such a law.
But why bother? The election official in each state - in most states, this is the SoS - already has the authority to promulgate the rules to carry out his or her job. Why not just add the verification process to the rules? After all, just because a candidate cannot get his or her name on the ballot does not mean the Electors cannot still elect that person to be President. (Presumably, however, they wouldn’t dare!)