User:Wythagoras/Rado's sigma function/BB(7)

\(\Sigma(7) > 10^{10^{10^{10^{18705353}}}}\) 0 _ 1 l 4 1 _ 1 r 2 1 1 1 r 5 2 _ 1 l 3 2 1 _ r 1 3 _ 1 r 4 3 1 _ l 2 4 _ 1 l 6 4 1 _ r 3 5 _ 1 r halt 5 1 1 r 2 6 _ 1 r 1 6 1 1 l 4

Explanation
I found here some interesting notes on the record holder for \(\Sigma(6)\). This machine is based on the champion for \(\Sigma(6)\). (note: 6=old state A and 1=old state B, 2=old state C, 3=old state D, etc)

After the first step: _1, head on the blank, state 4

After the second step: _11, head on the blank, state 6.

The site says, that when _11 is entered and the head is on the blank and the machine is in state A, it will run for over \(10^{10^{10^{10^{10^7}}}}\) steps. (here is a proof by Cloudy176).

Thanks
Many thanks to Cloudy176 for the proof,

And of course to Pavel Kropitz for the \(\Sigma(6)\) machine and to Pascal Michel for the idea.