Hyperproliferation

Sanctions will not work because Russia and China are helping North Korea’s nuclear missile program, accelerating capabilities to threaten the United States, a process that might be termed “hyperproliferation”: […] Some of the implications of hyperproliferation are that Russia and China are part of the problem, not part of the solution; that hyperproliferation by these actors is a weapon in the New Cold War; and that we should reassess the nuclear missile threat from other nations of concern — including Pakistan and Iran.

Source: wiktionary

And regional hyperproliferation becomes inevitable as Egypt, Turkey, Saudi Arabia and others seek shelter in going nuclear themselves.

Source: wiktionary

There is no greater spur to hyperproliferation than the furling of the American nuclear umbrella.

Source: wiktionary