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. In Novmber 2026, the machines score was verified in Coq by Jeff Ketchersid using Claude.

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