1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC

1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC (bbch) is a halting BB(3,4) TM. It was discovered in April 2024 by Pavel Kropitz. It achieves a sigma score of exactly $(2{\uparrow }^{15}5)+14$, making it the current BB(3,4) champion. Shawn Ligocki confirmed the TM's score.

Another long running TM, 1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA (bbch), is a permutation of this TM, obtained by starting it in state B and then converting to TNF and achieves a sigma score of exactly $(2{\uparrow }^{6}5)+5$.

Analysis

Let $B(k,n,m)=$ 0^inf 3^(2*m+1) 2^k A> 1^n

Then $B(k,n,m)\to B(k,0,g_{k-1}^n(m))$ if $k\ge 1$

where $2g_k(m)+4=2{\uparrow }^{k-1}(2m+4)$

Start -> B(16,3,0)+2 -> B(16,0,(2{15}5)/2-2)+2 -> Halt