User:MrSolis/Playground

5-state busy beaver winner (Remake)

The 5-state busy beaver (BB(5)) winner is 1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA (bbch). Discovered by Heiner Marxen and Jürgen Buntrock in 1989, this machine proved that $\operatorname {BB} (5)\geq 47176870{\phantom {}}$ and $\Sigma (5)\geq 4098$ at the time.

Analysis

Let $g(x):=0^{\infty }\;{\textrm {<A}}\,1^{x}\;0^{\infty }$. Then,

$${\begin{array}{lll}g(3x)&{\phantom {}}\xrightarrow {5x^{2}+19x+15} &g(5x+6),\\g(3x+1)&{\phantom {}}\xrightarrow {5x^{2}+25x+27} &g(5x+9),\\g(3x+2){\phantom {}}&\xrightarrow {6x+12} &0^{\infty }\;1\;{\textrm {Z>}}\;01\;001^{x+1}\;1\;0^{\infty }\end{array}}$$