The delegates sign, "the States present".
If that were all, "the States" could mean either the people of the states or their governments,
but as the Constitution is one whole document the affirmation must be read with reference to the Preamble,
which makes it clear that the delegates represent the united people of the United States.
If the Preamble had no force of law the state governments, rather than the people,
could be the entities conferring on the United States government its rights, privileges, powers, duties and restrictions:
it, and the Constitution, could be established solely by noncitizen state governments. This fantasy would have two results:
both the people and a subordinate federal government serving a federation of state governments,
with no recognized right or power to create or abolish any kind of government.
We really ought to rescue our trusty Preamble from the revolutionaries.