The Nuclear Non-Proliferation Treaty (mysteriously abbreviated NPT instead of NNPT, or NNT) which the U.S. (and the five UN recognized nuclear weapons states) have all signed and ratified has this clause:
Article VI
Each of the Parties to the Treaty undertakes to pursue negotiations in good faith on effective measures relating to cessation of the nuclear arms race at an early date and to nuclear disarmament, and on a treaty on general and complete disarmament under strict and effective international control.
It is clear that the U.S., and all the other nuclear weapons states, are blatantly ignoring their duty under this article. None have shown any interest or inclination in ‘pursuing negotiations in good faith on a treaty on general and complete disarmament’ (like the one discussed by this piece).