Proliferation.
Here’s the definition, I think you have the word confused with something else.
It means the rapid increase and that’s what the song was about the rapid growth of the nuclear arsenal’s of major players in the world at that time
1 : to grow by rapid production of new parts, cells, buds, or offspring. 2 : to increase in number as if by proliferating : multiply. transitive verb. 1 : to cause to grow by proliferating.
In 1955 there were 3 nuclear powers - US and UK, 1945, and USSR 1949.
That was it and there was no substantial discussion of proliferation, even after France joined in 1960. When China exploded a bomb in 1965 and Israel stole the US plutonium in 1967, the issue of proliferation became an issue.