User blog comment:Wythagoras/Conway's game of life/@comment-27014275-20151012075717/@comment-1605058-20151013075152

Note that at the end of informal definitions section it's said "The starting patterns must fit in an N^2 by N^2 square", so SS(9) will not be infinite. Also, this makes SS(500) to be at least around a million - just take a glider flying along a 250000 x 250000 square heading a block.