unless im stupid (which is a high probability), this meownimum cycles. 

(nerd emoji) According to my calculations you could also get this same exact cycle count by using the glyph of proliferation on gold instead of silver. This gives you a better rate because you don't have to use 1/4th of the proliferation outputs to feed back into proliferation, but at the cost of longer startup.

The ominous glyph of purification that I never used has me worried that I missed something incredibly obvious, but if I didn't, I'm guessing a lot of people will get 38 because of how easy this felt to calculate and actually build.

End of notes.

Fun fact about this solution: Meow!