# Consequences of Ramsey-numbers of hypergraphs

We know that the (2-color) Ramsey-numbers for $$3$$-uniform hypergraphs are between roughly $$2^{n^2}$$ and $$2^{2^n}$$, and the situation is similar to $$k$$-uniform hypergraphs for every $$k\ge 3$$. (A recent paper.)

Are there any consequences of these Ramsey-number being close to either the above upper or the lower bound?

Here I don't mean the obvious consequence that we get about the Ramsey-numbers that come from the stepping-up lemma, but some possible solutions to conjectures/complexity results etc.