User blog comment:LittlePeng9/Random Turing machines/@comment-10429372-20140808191119

I have another 1 state reduction on your 3 color hydra machine.

If we combine 4 and 4' instead of 3 and 4, we can combine state 3 and 25.

Also (I said this before) we don't need state 24 (reduced version). It just keeps in state 24 before it halts. So we can just change the transition leading to state 24 to the transition leading to halt.

So, now we have proven Sigma(39,3) > f_e_0(n) for large n. Yay!