The Constitution doesn't say anything about "running for President", in fact, it doesn't even recognize the existence of Presidential elections.
There is no restriction at the Federal level against anyone "running for President", ballot access is up to the State Legislatures and there's no reason in principle an ineligible person couldn't be listed on a ballot, but ineligible to receive electoral votes.
“The Constitution doesn’t say anything about “running for President”, in fact, it doesn’t even recognize the existence of Presidential elections.”
That statement is a bald faced lie. The election of the President of the United States of America is mandated in the Constitution Article II Section 1. . . . He shall hold his Office during the Term of four Years, and, together with the Vice President, chosen for the same Term, be elected, as follows. . . .
“There is no restriction at the Federal level against anyone “running for President”, ballot access is up to the State Legislatures and there’s no reason in principle an ineligible person couldn’t be listed on a ballot, but ineligible to receive electoral votes.”
Yes, it is responsibility of each State to decide how the State’s Electors are to be appointed by the State. No, each State is not at liberty to appoint delegates for the purpose of violating a Constitutional article prohibiting the eligibility of a candidate for President, due to the supremacy of Federal Law.