1RB0LC_1LC0RD_1LF1LA_1LB1RE_1RB1LE_---0LE
1RB0LC_1LC0RD_1LF1LA_1LB1RE_1RB1LE_---0LE (bbch) is a probviously halting tetrational BB(6) Cryptid found by Racheline on 23 Nov 2024 (Discord link).
1RB0LC_1LC0RD_1LF1LA_1LB1RE_1RB1LE_---0LE is a tetrational probviously halting cryptid. the lower bound for when it halts is around 10^10^120395, and with each exponentiation it has a 1/4 chance of halting, so i think the expected halting time is around 10^10^10^10^10^120395 sadly we won't be able to run it any further, it uses the hydra map which we don't have a way to accelerate
On 21 Sep 2025, mxdys has shown that this machine is in an equivalence class of 3 machines:
1RB0LC_1LC0RD_1LF1LA_1LB1RE_1RB1LE_---0LE(bbch)1RB1LA_1LC0RE_1LF1LD_1RB0LC_1LB1RA_---0LA(bbch)1RB1LA_1LC0RE_1LF1LD_0RA0LC_1LB1RA_---0LA(bbch)
Some analysis by Opus 4.7 / DrDisentangle
Dominant 3-step cycle E → B → D → E (≈ 16,737 fires per 100k
steps). E-runs of length 3 are the modal run, corresponding to the
"E sweeps left over exactly two 1s then fires" pattern.
Let [b₁, b₂, ..., bₙ, (1)] denote the tape at an
E-turnaround (all observed turnarounds have rightmost block = 1):
0^inf 1^b₁ 0 1^b₂ 0 ... 0 1^bₙ 0 1 E> 0 0^inf
E-right-blank events (blocks read L-to-R, rightmost is always 1): step 6 dt= 6 blocks=[1, 1] step 26 dt= 20 blocks=[2, 2, 1] step 76 dt= 50 blocks=[6, 2, 1] step 190 dt= 114 blocks=[2, 10, 2, 1] step 752 dt= 562 blocks=[2, 25, 2, 1] step 18240 dt=17488 blocks=[2, 124, 4, 2, 1]
These events are rare; between consecutive events the machine performs a non-trivial restructure that also grows the active region. Rate of growth is super-linear, consistent with a "shift-overflow counter" character.
In addition to the E-turnaround, the only proven macro-regime configurations are mid-run states used by the bump family:
M_Config L K j M— head = 1 on the 2nd cell (from left) of the middle 1-block. Tape shape:
L 0 1^K 0 1 [E,1]1^j 0 1^M 0 0^inf
(Block 2 has size j + 2. Used as the loop invariant of the 5-step bump cycle.)
S_Config L K M— head = 0 on the 0-separator between a size-1 block 2 and block 3. Tape shape:
L 0 1^K 0 1 [E,0]1^M 0 0^inf
(Post-iteration state, one 5-step bump before the final finish.)
R_Config L K— 3-block E-turnaround at blocks[K, 2, 1]:
L 0 1^K 0 1^2 0 1 [E,0] 0^inf
R4_Config L K— 4-block E-turnaround at blocks[2, K, 2, 1]:
L 0 1^2 0 1^K 0 1^2 0 1 [E,0] 0^inf
--- 5-step bump family (middle block shrinks by 1 per cycle) ---
Generic form: the head at the 2nd cell of block 2 acts as a
shift register; each 5-step cycle transfers one 1 from the
middle block to the left block, via:
1. E,1 -> 1LE (pop 1 from left of head)
2. E,1 -> 1LE (pop the block-1/block-2 boundary 1)
3. E,0 -> 1RB (extend left block by 1, now on 1)
4. B,1 -> 0RD (write new 0 separator)
5. D,1 -> 1RE (re-enter E-state)
All rules in this family hold for any L : Side (fully local).
Bump5: M_Config L K (j+1) M -> M_Config L (K+1) j M
(shifts one 1 from block 2 into block 1)
in 5 steps. [bump5]
Term5: M_Config L K 0 M -> S_Config L (K+1) M
(block 2 collapses to size 1; head lands on 0-sep)
in 5 steps. [bump5_term]
Iter: M_Config L K (j+n) M -> M_Config L (K+n) j M
in 5n steps. [bump5_iter]
IterTerm: M_Config L K n M -> S_Config L (K+n+1) M
in 5(n+1) steps. [bump5_iter_term]
Finish3: S_Config L K 2 -> R_Config L K
(3-step E->B->D->E mini-cycle landing at right blank)
in 3 steps. [finish3_M2]
Full: M_Config L K n 2 -> R_Config L (K + n + 1)
(blocks [..., K, n+2, 2] -> [..., K+n+1, 2, 1])
in 5(n+1) + 3 = 5n + 8 steps. [macro_to_R]
These rules have been proven in Lean[1].