1RB0LF_1RC1RA_0RD0RB_1LE---_0LA1LE_1RD1LA

1RB0LF_1RC1RA_0RD0RB_1LE---_0LA1LE_1RD1LA (bbch) is a BB(6) potential Cryptid found by Marco Dos Santos using Gemini and reported in his paper At the Limits of Computability: Steps Towards Autonomous AI Discovery on the Busy Beaver Frontier. The probvious behavior of these TMs has not yet been analyzed.

Analysis by Marco Dos Santos

Consider:
J(u, v, w) = 0^inf 1^5 10^u 1 A> 11 01^v 1^w 01 0^inf
S_E(b, m, k) = 0^inf 1^5 10^b E> 1 1101^m 1^6 11^k 01 0^inf
S_{E,0}(b, m) = 0^inf 1^5 10^b E> 1 1101^m 1101 0^inf
S_{E,1}(b, m, n) = 0^inf 1^5 10^b E> 1 1101^m 111 01^n 01001 0^inf

J(0, v, 0) -> S_{E,0}(v+3, 0)
J(0, v, 1) -> S_{E,1}(v+2, 0, 0)
J(0, v, 2) -> S_E(v+2, 0, 0)
J(0, v, w) -> J(v+3, 0, w-3) if w >= 3
J(1, v, 0) -> S_E(0, 0, v+3)
J(u, v, 0) -> S_{E,1}(u-2, 0, v+2) if u >= 2
J(1, v, 1) -> Halt
J(u, v, 1) -> S_E(u-2, 0, v+2) if u >= 2
J(u, v, w) -> J(u-1, v+2, w-2) if u >= 1 and w >= 2

S_E(0, 0, k) -> J(0, 0, 2k+6)
S_E(0, m, k) -> J(2, 2m+2, 2k+1) if m >= 1
S_E(1, m, k) -> J(0, 2m+3, 2k+1)
S_E(b, m, k) -> S_E(b-2, m+1, k) if b >= 2

S_{E,0}(0, m) -> S_E(2, 0, 2m)
S_{E,0}(1, m) -> S_E(0, 0, 2m+1)
S_{E,0}(b, m) -> S_{E,0}(b-2, m+1) if b >= 2

S_{E,1}(0, m, n) -> S_E(2, 0, 2m+n+2)
S_{E,1}(1, m, n) -> S_E(0, 0, 2m+n+3)
S_{E,1}(b, m, n) -> S_{E,1}(b-2, m+1, n) if b >= 2

Start: J(0, 0, 0), reached after 35 raw TM steps

This can be simplified to:

Consider:
J(u, v, w) = 0^inf 1^5 10^u 1 A> 11 01^v 1^w 01 0^inf

J(0, v, 0) -> J(0, 0, 2v+12) if v is even
J(0, v, 0) -> J(2, 4, 2v+7) if v is odd
J(0, v, 1) -> J(2, 4, 2v+9) if v is even
J(0, v, 1) -> J(0, 0, 2v+14) if v is odd
J(0, v, 2) -> J(2, v+4, 1) if v is even
J(0, v, 2) -> J(0, v+4, 1) if v is odd
J(0, v, w) -> J(v+3, 0, w-3) if w >= 3

J(1, v, 0) -> J(0, 0, 2v+12)
J(u, v, 0) -> J(2, 4, 2u+2v+5) if u >= 2 and u is even
J(u, v, 0) -> J(0, 0, 2u+2v+10) if u >= 3 and u is odd

J(1, v, 1) -> Halt
J(2, v, 1) -> J(0, 0, 2v+10)
J(u, v, 1) -> J(2, u, 2v+5) if u >= 4 and u is even
J(u, v, 1) -> J(0, u, 2v+5) if u >= 3 and u is odd

J(u, v, w) -> J(u-1, v+2, w-2) if u >= 1 and w >= 2

Start: J(0, 0, 0), reached after 35 raw TM steps