[seanhunter]

> The reason why it is true is because there exists some finite unavoidable and reducible set of configurations.

OK but respectfully that's just restating the problem in an alternative form. We don't get any insight from it. Why does there exist this limit? What is it about this problem that makes this particular structure happen?

[lacker]

Perhaps the key insight is that there is no concise explanation that underlies this particular structure. Many mathematical statements are true for no concise reason. If you want to discover if these things are true or not, perhaps you need a computer-assisted search, and that's the intellectual lesson to be drawn here.