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There are a lot of pictures though, hopefully that helps.
Wow, this is a really long post! Probably will take me quite some time to digest...
Yes, the upper bound is 587, the lower bound is 13, although establishing the lower bound involved a lot of manual looking at pictures, it would be better to automate that to make sure I did not miss anything.
This is really nice; does this mean that we now have definite lower and upper bounds on the rule complexity of the laws of physics?