"The legislatures of the states did not ratify the Constitution. Conventions elected by the people living in each state specifically for that purpose did so and then sent the ratification directly to Congress."
True, but this is not the major point of the question, the independent state, not individual persons, not a union of states, were to either accept the Constitution or reject the Constitution. States did not even have to participate in the process and secede from the current government. This is a natural right of a state being exercised. The act or creating, judging, and giving birth to the Constitution was done completely outside any legislative law or government. The authority of the political body of the independent state was the creator and judge of the Constitution. These were supreme acts above and beyond the power of the Constitution, completely within the realm of the natural rights of states.
"that this assent and ratification is to be given by the people, not as individuals composing one entire nation, but as composing the distinct and independent States to which they respectively belong. It is to be the assent and ratification of the several States, derived from the supreme authority in each State" Madison.
Many people make the mistake and say the 1860/61 state governments cannot secede from the Constitution since they did not creat the Constitution. Remember the state governments did not vote on secession, the representives at convention or in some cases a popular vote, determined to reject the Constitution, very simular to the ratification process. A natural and supreme act of the people of a state.
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David Upton