Fifty states, fifty ways of doing it. But the devil is in the details.
In the Maine Secretary of State ruling, she states in the opening part;
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She goes on to hinge her argument on Mr. Trump's disqualification due to the standard commentary about his actions in relation to insurrection. However, while she does not specifically go on to identify why Trump's "declaration on his candidate consent form is false", she does very much identify the form, her role in the "administrative procedures" and the need for fairness. On reading that excerpt, my question was, 'what does the form say' and (okay, maybe a second question) 'what does Maine law say about eligibility'. Well, on the SofS site they do link to the form in question.
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If, as the Secretary ruled, that Mr. Trump is ineligible for the primary because he made a false declaration on his consent form, perhaps she could explain which of those qualifications he does not meet. I have yet to find anything else in Maine's code that gives the Secretary of State authority to pass judgement on anything other than "administrative" irregularities. Much like some of the other states.