Busy beaver shift function $BB(7)$

The maximum number of steps made by a $7$-state, 2-symbol Turing machine that halts when started on a blank tape.

Lower bound: $2\uparrow^{11} 2\uparrow^{11} 3$
Upper bound: Unknown

Updates from the literature

Lower bound: $10^{2\times10^{10^{10^{18705353}}}}$
Reference unknown
[via The Busy Beaver Frontier, Scott Aaronson, 2020-09-29]
2025-05 Lower bound: $2\uparrow^{11} 2\uparrow^{11} 3$
Pavel Kropitz in May 2025
[via The Busy Beaver Competition: a historical survey, Pascal Michel]