1RB0LB_1LC0RE_1LA1LD_0LC---_0RB0RF_1RE1RB

Unsolved problem:

Does this TM run forever?

This is a probviously non-halting BB(6) Cryptid found by @racheline and shared on Discord on 25 Nov 2024.

Rules

 start: (4,124)
 (a+1,3n+0) --> (a+7,4n+4)
 (a+1,3n+1) --> (a+0,4n+7)
 (a+1,3n+2) --> (a+5,4n+4)
 (0,3(27n+21)+1) --> halt

 (a,n) := 0^inf 10 01^a 0^n <A 11011 0^inf

Plot of the first entry in (x,y) over the first 100k steps of this TM. The TM enters a new phase (or halts) if x hits 0. This is extremely unlikely.

For simplicity only one potential halting rule is shown. In fact, it also has the potential to become a translated cycler or bouncer when it reaches (0,n).