Concerning the busy beaver with $6$ states , there recently occured a major breakthrough : Pavel Kropitz has proven $bb(6)>10\uparrow \uparrow 15$.
The old record was just in an "astronomical" level and a machine with $7$ states was derived proving $bb(7)\gg10\uparrow\uparrow 5$.
What is the best lower bound that can be derived from the new record of $bb(6)$ in a similar way ? Is this bound the best known lower bound for $bb(7)$ ?