Slog(x^^^2)

[Catullus]

How fast does  grow, with a base of slog greater than eta?

[JmsNxn]

Hmmmm

I was going to say this is another dumb thread, but Tommy could probably back me in saying.... polynomially? At most it grows exponentially...

I honestly don't know. We don't know everything Catullus. But just by deduction:

\[
\begin{align}
\text{slog}(x \uparrow \uparrow 2) \le \text{slog}(x) + C + 1\\
\text{slog}(x\uparrow \uparrow x) \le \text{slog}(x) + x + C + 1\\
\end{align}
\]

I'd bet you can bound it by at least \(O(x^2)\). But other than that, I don't know. Don't think any one knows. If you could prove it you could probably prove something worthy of the Field's medal, lmao.