View source for 1RB0LC 0LC1RF 1LE1RD 0RC1RC 0LA1LA ---1RA

{{machine|1RB0LC_0LC1RF_1LE1RD_0RC1RC_0LA1LA_---1RA}}
{{TM|1RB0LC_0LC1RF_1LE1RD_0RC1RC_0LA1LA_---1RA}} is a [[BB(6)]] potential [[Cryptid]] found by Marco Dos Santos using Gemini and reported in his paper [https://arxiv.org/abs/2610.22603 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 ==
<pre>
Consider:
E(a, k, c) = 0^inf 1^a A> 0 11^k 0 1^c 0^inf
M_1(a, k, z) = 0^inf 1^a 0 11^k 1 0 C> 1^z 0^inf
M_0(n, z) = 0^inf 1^n 1 0 C> 1^z 0^inf

E(a, 0, c) -> M_0(a, c)
E(a, 1, 2m) -> E(a+3, m, 0)
E(a, 1, 1) -> Halt
E(a, 1, 2j+3) -> M_0(a+5, 2j)
E(a, k+2, 0) -> M_0(a+2, 2k+1)
E(a, k+2, c) -> M_1(a+3, k, c) if c >= 1

M_1(a, k, 2j+1) -> E(a+3, k, 2j+1)
M_1(a, k, 2) -> E(a, 1, 2k+2)
M_1(a, k, 2j+4) -> E(a+3, k+1, 2j+2)

M_0(n, 0) -> E(3, 0, n+2)
M_0(2m, 2j+1) -> E(3, m, 2j+1)
M_0(2m+1, 2j+1) -> E(4, m+1, 2j+1)
M_0(2m, 2) -> E(0, 1, 2m+2)
M_0(2m+1, 2) -> E(1, 1, 2m+4)
M_0(2m, 2j+4) -> E(3, m+1, 2j+2)
M_0(2m+1, 2j+4) -> E(4, m+2, 2j+2)

Start: E(3, 0, 2), reached after 23 raw TM steps
</pre>

This can be simplified to:

<pre>
Consider:
E(a, k, c) = 0^inf 1^a A> 0 11^k 0 1^c 0^inf

E(a, 0, 0) -> E(3, 0, a+2)
E(2m, 0, 2j+1) -> E(3, m, 2j+1)
E(2m+1, 0, 2j+1) -> E(4, m+1, 2j+1)
E(2m, 0, 2) -> E(0, 1, 2m+2)
E(2m+1, 0, 2) -> E(1, 1, 2m+4)
E(2m, 0, 2j+4) -> E(3, m+1, 2j+2)
E(2m+1, 0, 2j+4) -> E(4, m+2, 2j+2)

E(a, 1, 2m) -> E(a+3, m, 0)
E(a, 1, 1) -> Halt
E(a, 1, 3) -> E(3, 0, a+7)
E(2m, 1, 5) -> E(1, 1, 2m+8)
E(2m+1, 1, 5) -> E(0, 1, 2m+8)
E(2m, 1, 2j+7) -> E(4, m+4, 2j+2)
E(2m+1, 1, 2j+7) -> E(3, m+4, 2j+2)

E(2m, k+2, 0) -> E(3, m+1, 2k+1)
E(2m+1, k+2, 0) -> E(4, m+2, 2k+1)
E(a, k+2, 2j+1) -> E(a+6, k, 2j+1)
E(a, k+2, 2) -> E(a+3, 1, 2k+2)
E(a, k+2, 2j+4) -> E(a+6, k+1, 2j+2)

Start: E(3, 0, 2), reached after 23 raw TM steps
</pre>

[[Category:BB(6)]][[Category:Potential Cryptids]]