It is common in mathematics to assume some unknown hypothesis or conjecture to be true or false, and then prove results dependent on said assumption. This can lead to many interesting developments from studying ramifications.
I've seen lots of posts like this for things such as the Riemann Hypothesis or one of the answers to this question about the Collatz Conjecture, but when looking at implications of $P=NP$ or $P\neq NP$ I find lots of posts that give very "real world" examples of algorithmic implications such as here.
I was wondering if you knew of any theoretical results dependent on the results of $P$ vs. $NP$ in a similar vein to that shown in Riemann Hypothesis posts?
