[david_for_you]

Hm, I'm not sure I would say that knowing an upper bound would be any help in solving these open problems, unless the way to prove that upper bound would involve a collatz type problem. We already know from the lower bound of BB(6) that we cannot iterate that far in this universe.

[_alternator_]

An upper bound U for BB(6) implies that any program that runs longer than U never terminates. Thus the specific Collatz-type problems that can be encoded in 6 instructions can be run U+1 steps and if they don’t halt, they won’t halt.

The proof that BB(6) is relevant is that you can encode it in a 6 instruction program, which is what the link does.

[david_for_you]

I understand that, what I am saying is, that the upper bound can never be useful because the lower bound is already so high that we cannot run U+1 steps, ever.