Which $SIZE$-$DEPTH(s, d)$ classes with $log(s(n))^{d(n) - 1} = o(n)$ can we not separate by known methods?
Lets say that we have $s, d$ where $log(s(n))^{d(n) - 1} = o(n)$. Let $d'(n)$ be arbitrary and $s'(n) = 2^{\sqrt[d'(n) - 1]{log(s(n))^{d(n) - 1}}}$. Then we have that $log(s(n))^{d(n) - 1} = log(s'(n))^{d'(n) - 1}$. Thus, we have a question, for various interesting ranges of $s, d, s'$, which is not seemingly answered by Boppana:

$SIZE$-$DEPTH(s, d) =_? SIZE$-$DEPTH(2^{\sqrt[d'(n) - 1]{log(s(n))^{d(n) - 1}}}, d'(n))$

Thinking about the limit was overcomplicating this clearly and this is easy to see. It shows the size-depth tradeoff I expected, as well, where the new size goes up as the depth goes down, making the circuit "harder to beat" in both directions. I think, speaking of this, that you will be able to show that these classes are incomparable. Does anybody else have any thoughts on the relationship between the two classes and can you prove something about it?