2023/10/19/greens-machines about sligocki.github.io HOT 3 OPEN

I can confirm independently that Green-9 halts in ~10↑↑30 steps.

I can't verify the Green-10 result, although I can confirm that if it does halt, it does so in a spectacular number of steps. My simulator can run exponential rules, but not an exponential number of times. If that occurs, there is a line that raises an emergency stop. Green-10 is the first program I've encountered that actually triggered that stop. So as a result of this post, my test coverage is improved!

To clarify, Green-10 is spectacular only with respect to existing BB results. With respect to the "true" BB values, Green's machines are absolutely pitiful, as will be any constructed solution. It is entirely possible that BB(6, 2) already exceeds Green-10.

from sligocki.github.io.

@IIjIl from Discord just shared this page in which Wythagoras (of BB(7) fame) claims better bounds for 13-15 states: https://googology.fandom.com/wiki/User:Wythagoras/Rado's_sigma_function#Bounds_for_%5C(%5CSigma(n,2)%5C)_and_%5C(S(n,2)%5C) Specifically:

• Sigma(13) > 3 ↑^{2046} 3
• Sigma(14) > 3 ↑^{10 ↑ 18267} 3
• Sigma(15) > 3 ↑^{10 ↑↑ 5 [↑ 7]} 3

from sligocki.github.io.