User blog comment:Wythagoras/Conway's game of life/@comment-27014275-20151012075717/@comment-1605058-20151013111117

I can say that. For a given N, there are 2^N^4 possible initial configurations fitting in an N^2 x N^2 box. Some of them will eventually stabilize, some won't, but we only care about the former. If we look at the stabilizing times of these, we will get at most 2^N^4 numbers, and the largest of these is by definition SS(n).

Of course you are right that glider-into-block isn't the most effective method. Slow construction salvos aren't the best ones either, because they require very large bounding boxes.

A good idea for proving SS(n) is fast growing is the following: it is possible to build a Turing machine in GoL. If you are careful about your construction, you can arrange it so that when the simulated machine halts, all the moving elements are destroyed in a controlled way so that the pattern stabilizes. This will give us SS(f(n)) > BB(n) for some computable function f, which is enough to establish SS eventually dominates all recursive functions.