BusyBeaverWiki - User contributions [en]

User:Hipparcos

2025-10-08T06:58:52Z

Hipparcos: test

I am @hipparcos on Discord.

Some of my Turing machine code: [https://github.com/jhuang97/turing%20machine https://github.com/jhuang97/turing_machine].

testing math rendering...

<math>a+b \mathrel{\textrm{A}} c</math>

Hydra

2025-10-07T16:46:03Z

Hipparcos: fix some directed heads

{{machine|1RB3RB---3LA1RA_2LA3RA4LB0LB0LA}}{{unsolved|Does Hydra run forever?}}
{{TM|1RB3RB---3LA1RA_2LA3RA4LB0LB0LA|undecided}}, called '''Hydra''', is a [[BB(2,5)]] [[Cryptid]]. Its high-level rules were first reported [https://discord.com/channels/960643023006490684/1084047886494470185/1231110668288135208 on Discord] by Daniel Yuan on 20 April 2024, who also gave Hydra said name. Later on, a 6-state, 2-symbol [[Turing machine]] was discovered and named [[Antihydra]] for having similar behaviour to Hydra, making the study of this machine important to the study of that one.

Hydra is known to not generate Sturmian words<ref>Dubickas A. On Integer Sequences Generated by Linear Maps. ''Glasgow Mathematical Journal''. 2009; 51(2): 243-252. doi:[https://doi.org/10.1017/S0017089508004655 10.1017/S0017089508004655]</ref> (Corollary 4).
<div style="width: fit-content; text-align: center; margin-left: auto; margin-right: auto;">
{|class="wikitable" style="margin-left: auto; margin-right: auto;"
! !!0!!1!!2!!3!!4
|-
!A
|1RB
|3RB
| ---
|3LA
|1RA
|-
!B
|2LA
|3RA
|4LB
|0LB
|0LA
|}
The transition table of Hydra.</div>
== Analysis ==
Let <math>C(a,b):=0^\infty <\!\!\text{A}\;2\;0^a\;3^b\;2\;0^\infty</math>. Then,<ref>S. Ligocki, "[https://www.sligocki.com/2024/05/10/bb-2-5-is-hard.html BB(2, 5) is Hard (Hydra)] (2024). Accessed 22 July 2024.</ref>
<math display="block">\begin{array}{|lll|}\hline
C(2a,0)&\xrightarrow{6a^2+20a+4}&0^\infty\;3^{3a+1}\;1\;\text{A}\!\!> 2\;0^\infty,\\
C(2a,b+1)&\xrightarrow{6a^2+23a+10}&C(3a+3,b),\\
C(2a+1,b)&\xrightarrow{4b+6a^2+23a+26}&C(3a+3,b+2).\\\hline
\end{array}</math>
<div class="toccolours mw-collapsible mw-collapsed">'''Proof'''<div class="mw-collapsible-content">
Consider the partial configuration <math>P(m,n):=0^\infty\;3^m\;\text{A}\!\!>02\;0^n</math>. After 14 steps this configuration becomes
<math>0^\infty\;3^{m+3}<\!\!\text{A}\;2\;0^{n-2}</math>. We note the following shift rule:
<math display="block">\begin{array}{|c|}\hline3^s<\!\!\text{A}\xrightarrow{s}\;<\!\!\text{A}\;3^s\\\hline\end{array}</math>
Using this shift rule, we get <math>0^\infty<\!\!\text{A}\;3^{m+3}\;2\;0^{n-2}</math> in <math>m+3</math> steps. From here, we can observe that <math>\text{A}\!\!>0\;3^s</math> turns into <math>3\;\text{A}\!\!>0\;3^{s-1}</math> in three steps if <math>s\ge 1</math>. By repeating this process, we acquire this transition rule:
<math display="block">\begin{array}{|c|}\hline\text{A}\!\!>0\;3^s\xrightarrow{3s}3^s\;\text{A}\!\!>0\\\hline\end{array}</math>
With this rule, it takes <math>3m+9</math> steps to reach the configuration <math>0^\infty\;3^{m+3}\;\text{A}\!\!>02\;0^{n-2}</math>, which is the same configuration as <math>P(m+3,n-2)</math>. To summarize:
<math display="block">\begin{array}{|c|}\hline P(m,n)\xrightarrow{4m+26}P(m+3,n-2)\text{ if }n\ge 2.\\\hline\end{array}</math>
With <math>C(a,b)</math> we have <math>P(0,a)</math>. As a result, we can apply this rule <math display="inline">\big\lfloor\frac{1}{2}a\big\rfloor</math> times, which creates two possible scenarios:
#If <math>a\equiv0\ (\operatorname{mod}2)</math>, then in <math>\sum_{i=0}^{(a/2)-1}(4\times 3i+26)=\textstyle\frac{3}{2}a^2+10a</math> steps we arrive at <math display="inline">P\Big(\frac{3}{2}a,0\Big)</math>. The matching complete configuration is <math>0^\infty\;3^{(3/2)a}\;\text{A}\!\!>02\;3^b\;2\;0^\infty</math>, which in four steps becomes <math>0^\infty\;3^{(3/2)a+1}\;1\;\text{A}\!\!>3^b\;2\;0^\infty.</math> If <math>b=0</math> then we have reached the undefined <code>A2</code> transition in <math display="inline">\frac{3}{2}a^2+10a+4</math> steps total. Otherwise, continuing for three steps gives us <math>0^\infty\;3^{(3/2)+2}<\!\!\text{B}\;0\;3^{b-1}\;2\;0^\infty</math>. Another shift rule is required here:<math display="block">\begin{array}{|c|}\hline3^s<\!\!\text{B}\xrightarrow{s}\;<\!\!\text{B}\;0^s\\\hline\end{array}</math>This means the configuration becomes <math>0^\infty<\!\!\text{B}\;0^{(3/2)a+3}\;3^{b-1}\;2\;0^\infty</math> in <math display="inline">\frac{3}{2}a+2</math> steps, and <math>0^\infty<\!\!\text{A}\;2\;0^{(3/2)a+3}\;3^{b-1}\;2\;0^\infty</math>, equal to <math display="inline">C\Big(\frac{3}{2}a+3,b-1\Big)</math>, one step later. This gives a total of <math display="inline">\frac{3}{2}a^2+\frac{23}{2}a+10</math> steps.
#If <math>a\equiv1\ (\operatorname{mod}2)</math>, then in <math display="inline">\frac{3}{2}a^2+7a-\frac{17}{2}</math> steps we arrive at <math display="inline">P\Big(\frac{3a-3}{2},1\Big)</math>. The matching complete configuration is <math>0^\infty\;3^{(3a-3)/2}\;\text{A}\!\!>020\;3^b\;2\;0^\infty</math>, which in four steps becomes <math>0^\infty\;3^{(3a-1)/2}\;1\;\text{A}\!\!>0\;3^b\;2\;0^\infty</math>, and then <math>0^\infty\;3^{(3a-1)/2}\;1\;3^b\;\text{A}\!\!>02\;0^\infty</math> in <math>3b</math> steps. After 14 steps, we see the configuration <math>0^\infty\;3^{(3a-1)/2}\;1\;3^{b+3}<\!\!\text{A}\;2\;0^\infty</math>, which turns into <math>0^\infty\;3^{(3a-1)/2}\;1<\!\!\text{A}\;3^{b+3}\;2\;0^\infty</math> in <math>b+3</math> steps. In two steps we get <math>0^\infty\;3^{(3a+1)/2}<\!\!\text{B}\;0\;3^{b+2}\;2\;0^\infty</math>, followed by <math>0^\infty<\!\!\text{B}\;0^{(3a+3)/2}\;3^{b+2}\;2\;0^\infty</math> after <math display="inline">\frac{3a+1}{2}</math> more steps. We conclude with <math>0^\infty<\!\!\text{A}\;2\;0^{(3a+3)/2}\;3^{b+2}\;2\;0^\infty</math>, equal to <math display="inline">C\Big(\frac{3a+3}{2},b+2\Big)</math>, one step later. This gives a total of <math display="inline">4b+\frac{3}{2}a^2+\frac{17}{2}a+16</math> steps.
The information above can be summarized as
<math display="block">C(a,b)\rightarrow\begin{cases}0^\infty\;3^{(3/2)a+1}\;1\;\text{A}\!\!>2\;0^\infty&\text{if }a\equiv0\pmod{2}\text{ and }b=0,\\C\Big(\frac{3}{2}a+3,b-1\Big)&\text{if }a\equiv0\pmod{2}\text{ and }b>0,\\C\Big(\frac{3a+3}{2},b+2\Big)&\text{if }a\equiv1\pmod2.\end{cases}</math>
Substituting <math>a\leftarrow 2a</math> for the first two cases and <math>a\leftarrow 2a+1</math> for the third yields the final result.
</div></div>
In effect, the halting problem for Hydra is about whether repeatedly applying the function <math display="inline">f(n)=3\big\lfloor\frac{n}{2}\big\rfloor+3</math> will at some point produce more even values of <math>n</math> than twice the number of odd values.

An alternative version of these rules exists that makes the connection to Antihydra more apparent by using the function <math display="inline">H(n)=\Big\lfloor\frac{3}{2}n\Big\rfloor</math>, or the [[Hydra function]].<ref>S. Ligocki, "[https://www.sligocki.com/2024/07/06/bb-6-2-is-hard.html BB(6) is Hard (Antihydra)]" (2024). Accessed 22 July 2024.</ref>

== Trajectory ==
It takes 20 steps to reach the configuration <math>C(3,0)</math>, and from there, the [[Collatz-like]] rules are repeatedly applied. Simulating Hydra has shown that after 4000000 rule steps, we have <math>b=2005373</math>. Here are the first few:
<math display="block">\begin{array}{|c|}\hline C(3,0)\xrightarrow{55}C(6,2)\xrightarrow{133}C(12,1)\xrightarrow{364}C(21,0)\xrightarrow{856}C(33,2)\xrightarrow{1938}C(51,4)\xrightarrow{4367}C(78,6)\rightarrow\cdots\\\hline\end{array}</math>
The heuristic argument that suggests Antihydra is a [[probviously]] non-halting machine can be applied here. This means that if <math>b</math> is to be thought of as moving randomly, then the probability of Hydra halting is <math display="inline">{\Big(\frac{\sqrt{5}-1}{2}\Big)}^{2005374}\approx 4.168\times 10^{-419099}</math>.

== Code ==

Fast Hydra/[[Antihydra]] simulation code by Greg Kuperberg (who said it could be made faster using FLINT):<syntaxhighlight lang="python2" line="1">
# Python script to demonstrate almost linear time hydra simulation
# using fast multiplication.
# by Greg Kuperberg

import time
from gmpy2 import mpz,bit_mask

# Straight computation of t steps of hydra
def simple(n,t):
for s in range(t): n += n>>1
return n

# Accelerated computation of 2**e steps of hydra
def hydra(n,e):
if e < 9: return simple(n,1<<e)
t = 1<<(e-1)
(p3t,m) = (mpz(3)**t,bit_mask(t))
n = p3t*(n>>t) + hydra(n&m,e-1)
return p3t*(n>>t) + hydra(n&m,e-1)

def elapsed():
(last,elapsed.mark) = (elapsed.mark,time.process_time())
return elapsed.mark-last
elapsed.mark = 0

(n,e) = (mpz(3),25)

elapsed()
print('hydra: steps=%d hash=%016x time=%.6fs'
% (1<<e,hash(hydra(n,e)),elapsed()))

# Quadratic time algorithm for comparison
# print('simple: steps=%d hash=%016x time=%.6fs'
# % (1<<e,hash(simple(n,1<<e)),elapsed()))
</syntaxhighlight>

==References==
[[Category:BB(2,5)]][[Category:Cryptids]]

1RB0RA 1LC1LF 1RD0LB 1RA1LE 1RZ0LC 1RG1LD 0RG0RF

2025-10-07T16:22:24Z

Hipparcos: try to fix math rendering issues with directed heads and \textrm -> \text

{{machine|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF|halt}} is the current [[BB(7)]] [[champion]], running for over <math>2 \uparrow^{11} 2 \uparrow^{11} 3</math> steps before it halts. It was discovered by Pavel Kropitz on 10 May 2025 ([https://discord.com/channels/960643023006490684/1369339127652159509/1370678203395604562 Discord link]) and analyzed by Shawn Ligocki (here) on 13 May 2025.

== Analysis by Shawn Ligocki ==
Consider general configurations matching the regex:

<math display="block">0^\infty \; 11 \; (1 \; (01)^*)^* \; 0011100 \; \text{A}\!\! > 0^\infty</math>

=== Low level rules ===
<pre>
01 1 01^n 0011100 A> 00 --> 1 01^n+2 0011100 A>
01^3 11 01^n 0011100 A> 0^6 --> 1 01^n+5 1 01 0011100 A>
01^3 (1 01)^k+1 11 01^n 0011100 A> 0^6 --> 1 01^n+6 (1 01)^k 11 01 0011100 A>
011 (1 01)^k 11 01^n 0011100 A> 0^2 --> 1 Z> 111 01^n+1 00 101^k+2
</pre>

=== Mid level rules ===
Let

<math display="block">
B(a; b, c, ..., z) = 0^\infty \; 111 \; (01)^{3z+1} \; 1 \; \cdots \; 1 (01)^{3c+1} \; 1 \; (01)^{3b+1} \; 1 \; (01)^0 \; 1 \; (01)^{3a+1} \; 0011100 \; \text{A}\!\! > 0^\infty
</math>

and let <code>B(a; [x]*k, y, ...)</code> = <math>B(a; \underbrace{x, \cdots, x}_k, y, ...)</math> (In other words, <code>[x]*k</code> represents k repeats of the value x in a config).

then

<pre>
B(a; b+1, ...) -> B(2a+4; b, ...)
B(a; [0]*k, 0, n+1, ...) -> B(0; [0]*k, a+2, n, ...)
B(a; [0]*k) -> Halt(3a + 2k + 9)

Start at step 8178: B(2, [1]*12)
</pre>

=== High level rule ===
Let

<math display="block">\begin{array}{l}
g_0(x) & = & 2x + 4 \\
g_{k+1}(x) & = & g_k^{x+2}(0) \\
\end{array}</math>

then

<math display="block">
B(a; \underbrace{0, \cdots, 0}_k, n, ...) \to B(g_k^n(a); \underbrace{0, \cdots, 0}_k, 0, ...)
</math>

=== Bound ===
Let

<math display="block">\begin{array}{l}
a_0 & = & 2 \\
a_{k+1} & = & g_k(a_k) \\
\end{array}
</math>

then

<math display="block">
B(a_0; \underbrace{1, \cdots, 1}_k)
\to B(a_k, \underbrace{0, \cdots, 0}_k)
\to \text{Halt}(3 a_k + 2 k + 9)
</math>and

<math display="block">
\text{Start} \to B(a_0; \underbrace{1, \cdots, 1}_{12})
</math>

and so this TM halts with a sigma score of <math> \sigma = 3 a_{12} + 33 </math>

Note that <math>g_k(x) = (2 \uparrow^k (x+4)) - 4</math> and so for <math>k \ge 2</math>,

<math display="block">
a_{k+1} + 4 > 2 \uparrow^k 2 \uparrow^k 3
</math>

and so this TM halts with sigma score <math>\sigma > 2 \uparrow^{11} 2 \uparrow^{11} 3</math>.

This bound is pretty tight: <math>\sigma < 2 \uparrow^{11} 2 \uparrow^{11} 4 = 2 \uparrow^{12} 4</math>.
[[Category:BB(7)]]

User:Hipparcos/Status by BB domain

2025-07-15T15:14:06Z

Hipparcos: add cryptids

I am seeing if it makes sense to summarize Busy Beaver progress in a table:

{| class="wikitable"
|+ Experimental BB Status Panel
|-
! scope="row"| Domain
! scope="col"| [[BB(2)]]
! scope="col"| [[BB(3,2)|BB(3)]]
! scope="col"| [[BB(2,3)]]
![[BB(4)]]
![[BB(2,4)]]
![[BB(5)]]
![[BB(3,3)]]
![[BB(2,5)]]
![[BB(6)]]
![[BB(7)]]
|-
! scope="row"| Maximum<ref>Shows max shift (S) and max score (Σ) values if known. In some cases, only max score is shown. See [[Busy Beaver Functions]].</ref>
| 6
4
|21
6
|38
9
|107
13
|3,932,964
2050
|47,176,870
4098
|<math>>10^{17}</math>
<math>>10^8</math>
|<math>>10 \uparrow \uparrow 4</math>
|<math>>2 \uparrow \uparrow \uparrow 5</math>
|<math>> 2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|-
! scope="row"| Cryptids
|
|
|
|
|
|
|Bigfoot
|Hydra
Bonus Cryptid
|~1000-2500,
incl. Antihydra,
Lucy's Moonlight
|
|-
! scope="row"| Holdouts
| style="background-color: #9EFF9E;" |
| style="background-color: #9EFF9E;" |
| style="background-color: #9EFF9E;" |
| style="background-color: #9EFF9E;" |
| style="background-color: #9EFF9E;" |
| style="background-color: #9EFF9E;" |
| style="background-color: #CFC;" |6 (manual)
19 (Rocq)
| style="background-color: #CFC;" |83
| style="background-color: #FE7;" |2891
| style="background-color: #FFC7C7;" |~108
|-
! scope="row"|Enumeration<ref># of TMs in [[TNF-1RB]]</ref>
| style="background-color: #9EFF9E;" | 41
| style="background-color: #9EFF9E;" |4057
| style="background-color: #9EFF9E;" |
| style="background-color: #9EFF9E;" |620,621
| style="background-color: #9EFF9E;" |
| style="background-color: #9EFF9E;" |126,891,605
| style="background-color: #9EFF9E;" |
| style="background-color: #9EFF9E;" |
| style="background-color: #FFC;" |~33,436,000,000
| style="background-color: #FE7;" |informal, ongoing
|-
!Sporadic<ref>Number of TMs requiring dedicated proofs.</ref>
|
|
|
|
|
|13
|
|
|
|
|-
! scope="row" |Deciders used
|Loop
|Loop
CPS
|Loop
CPS

RepWL
|Loop
CPS

RepWL
|Loop
CPS

RepWL
|Loop
CPS

RepWL

FAR

WFAR
|
|
|
|
|}

<references />

User:Hipparcos/Status by BB domain

2025-07-15T15:08:45Z

Hipparcos: add more info; reorder rows

I am seeing if it makes sense to summarize Busy Beaver progress in a table:

{| class="wikitable"
|+ Experimental BB Status Panel
|-
! scope="row"| Domain
! scope="col"| [[BB(2)]]
! scope="col"| [[BB(3,2)|BB(3)]]
! scope="col"| [[BB(2,3)]]
![[BB(4)]]
![[BB(2,4)]]
![[BB(5)]]
![[BB(3,3)]]
![[BB(2,5)]]
![[BB(6)]]
![[BB(7)]]
|-
! scope="row"| Maximum<ref>Shows max shift (S) and max score (Σ) values if known. In some cases, only max score is shown. See [[Busy Beaver Functions]].</ref>
| 6
4
|21
6
|38
9
|107
13
|3,932,964
2050
|47,176,870
4098
|<math>>10^{17}</math>
<math>>10^8</math>
|<math>>10 \uparrow \uparrow 4</math>
|<math>>2 \uparrow \uparrow \uparrow 5</math>
|<math>> 2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|-
! scope="row"| Cryptids
|
|
|
|
|
|
|Bigfoot
|Hydra
Bonus Cryptid
|1000-2500?
|
|-
! scope="row"| Holdouts
| style="background-color: #9EFF9E;" |
| style="background-color: #9EFF9E;" |
| style="background-color: #9EFF9E;" |
| style="background-color: #9EFF9E;" |
| style="background-color: #9EFF9E;" |
| style="background-color: #9EFF9E;" |
| style="background-color: #CFC;" |6 (manual)
19 (Rocq)
| style="background-color: #CFC;" |83
| style="background-color: #FE7;" |2891
| style="background-color: #FFC7C7;" |~108
|-
! scope="row"|Enumeration<ref># of TMs in [[TNF-1RB]]</ref>
| style="background-color: #9EFF9E;" | 41
| style="background-color: #9EFF9E;" |4057
| style="background-color: #9EFF9E;" |
| style="background-color: #9EFF9E;" |620,621
| style="background-color: #9EFF9E;" |
| style="background-color: #9EFF9E;" |126,891,605
| style="background-color: #9EFF9E;" |
| style="background-color: #9EFF9E;" |
| style="background-color: #FFC;" |~33,436,000,000
| style="background-color: #FE7;" |informal, ongoing
|-
!Sporadic<ref>Number of TMs requiring dedicated proofs.</ref>
|
|
|
|
|
|13
|
|
|
|
|-
! scope="row" |Deciders used
|Loop
|Loop
CPS
|Loop
CPS

RepWL
|Loop
CPS

RepWL
|Loop
CPS

RepWL
|Loop
CPS

RepWL

FAR

WFAR
|
|
|
|
|}

<references />

Busy Beaver Challenge

2025-07-15T14:56:05Z

Hipparcos: improve flow of sentence

The '''Busy Beaver Challenge''' (or '''bbchallenge''') is an online community founded in 2022 with the goal of solving [[BB(5)]]. This goal was accomplished in 2024. Since then the community has focussed on many different goals, including searching through unsolved domains (currently [[BB(6)]], [[BB(3,3)]], [[BB(2,5)]] and [[BB(7)]]) for new [[champions]] and [[cryptids]] and reducing [[holdout]] lists. Most of the interaction happens on our public Discord.

== See Also ==

* Main Website: https://bbchallenge.org/

User:Hipparcos/Status by BB domain

2025-07-15T14:48:53Z

Hipparcos: add more TNF tree sizes

I am seeing if it makes sense to summarize Busy Beaver progress in a table:

{| class="wikitable"
|+ Experimental BB Status Panel
|-
! scope="row"| Domain
! scope="col"| [[BB(2)]]
! scope="col"| [[BB(3,2)|BB(3)]]
! scope="col"| [[BB(2,3)]]
![[BB(4)]]
![[BB(2,4)]]
![[BB(5)]]
![[BB(3,3)]]
![[BB(2,5)]]
![[BB(6)]]
![[BB(7)]]
|-
! scope="row"| Cryptids
|
|
|
|
|
|
|Bigfoot
|Hydra
Bonus Cryptid
|1000-2500?
|
|-
! scope="row"| Holdouts
|
|
|
|
|
|
|6 (manual)
19 (Rocq)
|83
|2891
|
|-
! scope="row"| Maximum<ref>Shows max shift (S) and max score (Σ) values if known. In some cases, only max score is shown. See [[Busy Beaver Functions]].</ref>
| 6
4
|21
6
|38
9
|107
13
|3,932,964
2050
|47,176,870
4098
|<math>>10^{17}</math>
<math>>10^8</math>
|<math>>10 \uparrow \uparrow 4</math>
|
|
|-
! scope="row"|Enumeration<ref># of TMs in [[TNF-1RB]]</ref>
| style="background-color: #9EFF9E;" | 41
| style="background-color: #9EFF9E;" |4057
| style="background-color: #9EFF9E;" |
| style="background-color: #9EFF9E;" |620,621
| style="background-color: #9EFF9E;" |
| style="background-color: #9EFF9E;" |126,891,605
| style="background-color: #CFC;" |
| style="background-color: #CFC;" |
| style="background-color: #FFC;" |~33,436,000,000
| style="background-color: #FE7;" |
|-
!Sporadic<ref>Number of TMs requiring dedicated proofs.</ref>
|
|
|
|
|
|13
|
|
|
|
|-
! scope="row" |Deciders used
|Loop
|Loop
CPS
|Loop
CPS

RepWL
|Loop
CPS

RepWL
|Loop
CPS

RepWL
|Loop
CPS

RepWL

FAR

WFAR
|
|
|
|
|}

<references />

User:Hipparcos/Status by BB domain

2025-07-15T14:38:53Z

Hipparcos: add footnotes

I am seeing if it makes sense to summarize Busy Beaver progress in a table:

{| class="wikitable"
|+ Experimental BB Status Panel
|-
! scope="row"| Domain
! scope="col"| [[BB(2)]]
! scope="col"| [[BB(3,2)|BB(3)]]
! scope="col"| [[BB(2,3)]]
![[BB(4)]]
![[BB(2,4)]]
![[BB(5)]]
![[BB(3,3)]]
![[BB(2,5)]]
![[BB(6)]]
![[BB(7)]]
|-
! scope="row"| Cryptids
|
|
|
|
|
|
|Bigfoot
|Hydra
Bonus Cryptid
|1000-2500?
|
|-
! scope="row"| Holdouts
|
|
|
|
|
|
|6 (manual)
19 (Rocq)
|83
|2891
|
|-
! scope="row"| Maximum<ref>Shows max shift (S) and max score (Σ) values if known. In some cases, only max score is shown. See [[Busy Beaver Functions]].</ref>
| 6
4
|21
6
|38
9
|107
13
|3,932,964
2050
|47,176,870
4098
|<math>>10^{17}</math>
<math>>10^8</math>
|<math>>10 \uparrow \uparrow 4</math>
|
|
|-
! scope="row"|Enumeration<ref># of TMs in [[TNF-1RB]]</ref>
| style="background-color: #9EFF9E;" | 41
| style="background-color: #9EFF9E;" |4057
| style="background-color: #9EFF9E;" |
| style="background-color: #9EFF9E;" |620,621
| style="background-color: #9EFF9E;" |
| style="background-color: #9EFF9E;" |
| style="background-color: #CFC;" |
| style="background-color: #CFC;" |
| style="background-color: #FFC;" |
| style="background-color: #FE7;" |
|-
!Sporadic<ref>Number of TMs requiring dedicated proofs.</ref>
|
|
|
|
|
|13
|
|
|
|
|-
! scope="row" |Deciders used
|Loop
|Loop
CPS
|Loop
CPS

RepWL
|Loop
CPS

RepWL
|Loop
CPS

RepWL
|Loop
CPS

RepWL

FAR

WFAR
|
|
|
|
|}

<references />

Module:Sandbox/Hipparcos

2025-07-15T14:11:17Z

Hipparcos: module test

local p = {}
p.main = function(frame)
local args = frame.args
local out = ''
-- some code here

return out
end
return p

Module:Sandbox/doc

2025-07-15T14:09:57Z

Hipparcos: adapt Module:Sandbox/doc from Wikipedia

This page is not itself a sandbox. If you want to test a module, see the instructions below; do not edit this page itself.

== Scribunto testing area ==

This is not an actual [https://en.wikipedia.org/wiki/Wikipedia:Lua Lua] module. It exists to provide a convenient pseudo-namespace for code testing, hopefully preventing the main Module: namespace from becoming littered with experiments, as Lua modules cannot exist as subpages in the User: namespace.

Please name your experimental modules in the following format to help keep things tidy:

Module:Sandbox/<var>Your User Name</var>
<inputbox>
type=create
preload=Module:Sandbox/new
editintro=Template:New module editintro
prefix=Module:Sandbox/
placeholder=Insert your username here
button label=Create new sandbox module
</inputbox>
If you need more Module sandboxes, create subpages of the sandbox thus created.

Module:Sandbox

2025-07-15T14:00:04Z

Hipparcos: copy over Wikipedia's Module:Sandbox

--[[
Please do not edit this page. This page serves as a root for the sandbox.

The following below is some starter code that you may use to get started with module writing and testing. Please feel free to take this to get started on your module.

Remember to remove this top notice when copying and pasting from here to your module sandbox.
]]--

local p = {}
p.main = function(frame)
local args = frame.args
local out = ''
-- some code here

return out
end
return p

User:Hipparcos/Status by BB domain

2025-07-15T13:53:28Z

Hipparcos: formatting; types of holdouts

User:Hipparcos/Status by BB domain

2025-07-15T13:50:02Z

Hipparcos: add a color background to indicate status of enumeration

User:Hipparcos/Status by BB domain

2025-07-15T03:08:49Z

Hipparcos: worked on BB status table some more

User:Hipparcos/Status by BB domain

2025-07-15T01:56:46Z

Hipparcos: trying a format for Busy Beaver status panel

I am seeing if it makes sense to summarize Busy Beaver progress in a table:

{| class="wikitable"
|+ Experimental BB Status Panel
|-
! scope="row"| Domain
! scope="col"| [[BB(2)]]
! scope="col"| [[BB(3,2)]]
! scope="col"| [[BB(2,3)]]
|-
! scope="row"| Cryptids
|
|
|
|-
! scope="row"| Holdouts
|
|
|
|-
! scope="row"| High score
| 6, 4
|
|
|-
! scope="row"|Enumeration
| style="background-color: #9EFF9E;" | 41
|
|
|-
! scope="row"|Deciders used
|Loops
|
|
|}

User:Hipparcos

2025-07-15T01:15:03Z

Hipparcos: create my user page

I am @hipparcos on Discord.

Some of my Turing machine code: [https://github.com/jhuang97/turing%20machine https://github.com/jhuang97/turing_machine].

BB(7)

2025-06-18T03:29:53Z

Hipparcos: /* Current Progress */ 71xxxx results

The 7-state, 2-symbol Busy Beaver problem '''BB(7)''' is a mostly unexplored domain with only preliminary information.

The current BB(7) champion is {{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}} discovered by Pavel Kropitz in 2025 proving the lower bound:<math display="block">S(7) > \Sigma(7) > 2 \uparrow^{11} 2 \uparrow^{11} 3</math>

== History ==
Before 2025, the only known BB(7) champions were produced by hand, not by search. Example, Milton Green designed a machine in 1964 that had [[sigma score]] 22,961 and Wythagoras modified a BB(6) champion in 2014 to produce a machine that had sigma score <math>> 10 \uparrow\uparrow 5</math>.

In May 2025, mxdys shared [https://github.com/ccz181078/TM C++ code] that breaks up the BB(7) enumeration into 1 million subtasks which each run for about 2 minutes and leave ~100 holdouts each. Various folks on Discord have been investigating different sections of this domain to search for champions.

Within three days of the code's release, the Ligockis found three champions after applying their deciders to enumerator output. Shawn Ligocki found the first two, {{TM|1RB0RF_1LC0RE_1RD1LB_1LA1LD_0RA0LE_1RG0LB_1RZ1RB}} and {{TM|1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC}}, with sigma scores of approximately 10 ↑↑ 22 and 10 ↑↑ 35. That evening, Terry Ligocki found {{TM|1RB0LG_1RC0RF_1LD1RZ_1LF0LE_1RA1LD_1LG1RE_0LB0LB}}, with sigma score ~10 ↑↑ 46. These were all outpaced by Pavel's champion.

== Top Halters ==
Based on limited search through a subset of the 1 million subtasks from mxdys's code, the top 20 scoring known machines are:
{| class="wikitable"
!TM
!Approximate sigma score
!Discoverer
|-
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE}}
|10 ↑↑ 519.20
|Andrew Ducharme
|-
|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}}
|10 ↑↑ 286.17
|Terry Ligocki
|-
|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD}}
|10 ↑↑ 246.32
|@Iijil
|-
|{{TM|1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RC0LD}}
|10 ↑↑ 192.67
|Andrew Ducharme
|-
|{{TM|1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RG0LD}}
|10 ↑↑ 192.67
|Terry Ligocki
|-
|{{TM|1RB1LA_1LC0RE_0LD1LB_1RD0LA_1RF0RA_0RG0LA_1RB1RZ}}
|10 ↑↑ 192.67
|Terry Ligocki
|-
|{{TM|1RB1LA_1LC0RE_0LD1LB_1RD0LA_1RF0RA_1RG0LA_0LE1RZ}}
|10 ↑↑ 192.67
|Terry Ligocki
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG}}
|10 ↑↑ 192.67
|Terry Ligocki
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RG0LG_1RB1LG}}
|10 ↑↑ 192.67
|Terry Ligocki
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LG_1RF0RG_0RA0LG_1RB1LG}}
|10 ↑↑ 192.67
|Terry Ligocki
|-
|{{TM|1RB1RZ_1LC0RF_0LD1LB_1RD0LE_1RB1LE_1RG0RE_0RA0LE}}
|10 ↑↑ 192.67
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_1LG1RE_1LD0RF_0RA1RE_1RZ0RA}}
|10 ↑↑ 188.28
|@XnoobSpeakable, @Peacemaker II
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0LF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LF0RF_0RA1RE_1RZ0RE}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LF0RF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_1LG1RE_0RF0LF_0RA1RE_1RZ0LE}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_1LG1RE_0RF0LF_0RA1RE_1RZ0RA}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_1LG1RE_1LF0RF_0RA1RE_1RZ0RA}}
|10 ↑↑ 188.28
|Terry Ligocki
|}

The top 20 known halters with unique scores are:

{| class="wikitable"
!TM
!Approximate sigma score
!Discoverer
|-
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE}}
|10 ↑↑ 519.20
|Andrew Ducharme
|-
|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}}
|10 ↑↑ 286.17
|Terry Ligocki
|-
|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD}}
|10 ↑↑ 246.32
|@Iijil
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG}}
|10 ↑↑ 192.67
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC0LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LC}}
|10 ↑↑ 140.28
|@stokastic
|-
|{{TM|1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG}}
|10 ↑↑ 133.85
|@poppuncher
|-
|{{TM|1RB1RZ_1RC0RF_1LD1RB_1RG0LE_1LD0RA_1RE0LD_0RC1LF}}
|10 ↑↑ 129.24
|@Iijil
|-
|{{TM|1RB0LC_1RC0RG_1RD0LF_1RE0RF_1LA1RG_1LE1LF_1RZ1RD}}
|10 ↑↑ 126.20
|@stokastic
|-
|{{TM|1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ}}
|10 ↑↑ 116.98
|Terry Ligocki
|-
|{{TM|1RB0RD_1RC0LA_0LA0LE_1RE1RZ_1RF0RA_1LG0LE_1LC0LG}}
|10 ↑↑ 116.05
|
|-
|{{TM|1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ}}
|10 ↑↑ 115.52
|@prurq
|-
|{{TM|1RB0RF_1RC0RB_0RD0RF_1LE0LG_1LC0RD_1LA0LD_1LF1RZ}}
|10 ↑↑ 114.61
|Andrew Ducharme
|-
|{{TM|1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ}}
|10 ↑↑ 114.60
|Shawn Ligocki
|-
|{{TM|1RB0RE_0RC1LC_0LD1LF_1LE0LG_1RA0RC_0LB1LA_1LB1RZ}}
|10 ↑↑ 114.57
|Andrew Ducharme
|-
|{{TM|1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ}}
|10 ↑↑ 113.38
|Terry Ligocki
|-
|{{TM|1RB1RZ_1RC1RA_1RD0RB_1LE0RC_1LF0LD_1RG0LF_1RC0LG}}
|10 ↑↑ 108.77
|Terry Ligocki
|-
|{{TM|1RB0LA_1RC0RA_0RD0RB_1LE0RC_0LD1LF_0LA1LG_0LC1RZ}}
|10 ↑↑ 105.37
|Terry Ligocki
|-
|{{TM|1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG}}
|10 ↑↑ 93.81
|Andrew Ducharme
|}

== Current Progress ==
This is a summary of the 1 million subtasks from mxdys's code that have been processed, including further processing by Shawn Ligocki's linear rule code ("TBD" = "To Be Determined", "TBE" = "To Be Entered"):
{| class="wikitable defaultleft"
!rowspan="2"|Task range
!rowspan="2"|Done by
!colspan="2"|Completed
!rowspan="2"|# holdouts
!rowspan="2"|Maximum Score TM
!rowspan="2"|~Sigma
!rowspan="2"|Source
|-
!enumeration
!linear rule
|-
|00xxxx
|rowspan="10"|@Iijil
|Yes
|Yes
|728,495
|{{TM|1RB0RF_1RC1LF_0RD0RD_1LE0LB_1RA1RZ_1LG1RA_1LD0RC}}
|10 ↑↑ 45.64
|rowspan="10"|[https://drive.google.com/drive/folders/1wniwrAuvsHfkvro8Tg65WAMNZEuIekzD Google Drive folder]
|-
|01xxxx
|Yes
|Yes
|817,178
|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD}}
|10 ↑↑ 246.32
|-
|02xxxx
|Yes
|No
|963,486
|TBD
|TBD
|-
|03xxxx
|Yes
|No
|1,052,504
|TBD
|TBD
|-
|04xxxx
|Yes
|No
|955,711
|TBD
|TBD
|-
|05xxxx
|Yes
|No
|1,056,745
|TBD
|TBD
|-
|06xxxx
|Yes
|No
|950,271
|TBD
|TBD
|-
|07xxxx
|Yes
|No
|1,053,750
|TBD
|TBD
|-
|08xxxx
|Yes
|No
|951,114
|TBD
|TBD
|-
|09xxxx
|Yes
|No
|1,052,362
|TBD
|TBD
|-
|13xxxx
|Shawn Ligocki
|Yes
|Yes
|1,192,442
|{{TM|1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ}}
|10 ↑↑ 114.60
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|
20xxxx - 
22xxxx
|@C7X
|Yes
|No
|2,972,747
|TBD
|TBD
|[https://drive.google.com/drive/folders/11iGTKsvu2Y7aFrwOcWS1LYvcN6i_7-JM?usp=sharing Google Drive folder]
|-
|243308
|@uni
|Yes
|No
|TBE
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|[https://discord.com/channels/960643023006490684/1369339127652159509/1373660959960469545 Discord post]
|-
|25xxxx
|rowspan="10"|@stokastic
|Yes
|Yes
|815,919
|{{TM|1RB1RZ_1LC0LE_0LD0LC_0RE1LB_1RF0RG_0LD1RB_1RD1RA}}
|10 ↑↑ 31.33
|rowspan="10"|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|26xxxx
|Yes
|Yes
|731,995
|{{TM|1RB1RZ_0LC1RB_0LE0LD_1LE1LD_0RF0LC_0RG1RF_1RD0RA}}
|10 ↑↑ 36.26
|-
|27xxxx
|Yes
|Yes
|811,486
|{{TM|1RB0RG_1LC1LB_0RE0LD_0LC1RF_0RA1RE_0LF0LB_1RF1RZ}}
|10 ↑↑ 63.56
|-
|28xxxx
|Yes
|Yes
|956,935
|{{TM|1RB1RZ_0LC1RC_0RE1RD_0RB1RG_1RF0RA_1LG0LC_1LB0LF}}
|10 ↑↑ 114.57
|-
|29xxxx
|Yes
|Yes
|1,052,415
|{{TM|1RB1LA_1RC1RD_0LA1LG_1RZ0LE_1RB1RF_1RE0LC_0RE1LF}}
|10 ↑↑ 31.67
|-
|30xxxx
|Yes
|Yes
|1,032,095
|{{TM|1RB0LC_1RC0RG_1RD0LF_1RE0RF_1LA1RG_1LE1LF_1RZ1RD}}
|10 ↑↑ 126.20
|-
|31xxxx
|Yes
|Yes
|1,436,970
|{{TM|1RB1LD_1LC0RF_0RA0LB_0LE1RZ_1LA0LE_1RG1LA_0RC0RF}}
|10 ↑↑ 50.27
|-
|32xxxx
|Yes
|Yes
|1,036,950
|{{TM|1RB1RD_1LC0RF_0LE0LD_1LE1LE_1RF0LB_1RB0RG_1RA1RZ}}
|10 ↑↑ 50.28
|-
|33xxxx
|Yes
|Yes
|1,432,081
|{{TM|1RB0LC_1LC0LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LC}}
|10 ↑↑ 140.28
|-
|34xxxx
|Yes
|Yes
|1,032,970
|{{TM|1RB0RA_1LC0LE_0LD0LB_1RE0RD_0RA0LF_1RD1RG_0RF1RZ}}
|10 ↑↑ 72.69
|-
|
35xxxx - 
39xxxx
|Terry Ligocki
|Yes
|Yes
|4,894,047
|{{TM|1RB1RZ_1LC0RF_0LD1LB_1RD0LE_1RB1LE_1RG0RE_0RA0LE}}
|10 ↑↑ 192.67
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|40xxxx
| rowspan="8" |Andrew Ducharme
|Yes
|Yes
|730,310
|{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE}}
|10 ↑↑ 519.20
| rowspan="8" |[https://drive.google.com/drive/folders/16uDjgOahkhAMWv3v-YWmxJG7xxsBvj4h?usp=sharing Google Drive folder]
|-
|41xxxx
|Yes
|Yes
|814,075
|{{TM|1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RC0LD}}
|10 ↑↑ 192.67
|-
|42xxxx
|Yes
|Yes
|739,729
|{{TM|1RB1LD_0RC1RF_1LD0LE_0LE0LA_1LA1LE_1RG0LA_1RZ1RA}}
|10 ↑↑ 46.26
|-
|43xxxx
|Yes
|Yes
|817,332
|{{TM|1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG}}
|10 ↑↑ 93.81
|-
|44xxxx
|Yes
|Yes
|729,686
|{{TM|1RB1LC_1RC0RC_1RD1LA_0RE1RF_1LC0LG_1LA1LE_1RZ1LF}}
|10 ↑↑ 76.36
|-
|45xxxx
|Yes
|Yes
|812,973
|{{TM|1RB0RE_0RC1LC_0LD1LF_1LE0LG_1RA0RC_0LB1LA_1LB1RZ}}
|10 ↑↑ 114.57
|-
|46xxxx
|Yes
|Yes
|725,102
|{{TM|1RB1RA_0LC0RE_0LD1LC_1LA0LF_0RB0RA_1LG1RZ_0RE1LG}}
|10 ↑↑ 36.26
|-
|47xxxx
|No
|No
|TBD
|TBD
|TBD
|-
|48xxxx
| rowspan="2" |Tobiáš Brichta
|No
|No
|TBD
|TBD
|TBD
| rowspan="2" |[https://drive.google.com/drive/folders/1-csgJ5uSIX3SKlqTkSnhkUuEYLKgCw81 Google Drive folder]
|-
|49xxxx
|No
|No
|TBD
|TBD
|TBD
|-
|500xxx
|rowspan="2"|@prurq
|Yes
|Yes
|120,520
|{{TM|1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ}}
|10 ↑↑ 115.52
|rowspan="2"|[https://drive.google.com/drive/folders/145H4sT4F9KJYGSrlIETZdBOIMR7krLQm Google Drive folder]
|-
|501xxx
|Yes
|No
|96,102
|TBD
|TBD
|-
|60xxxx
| rowspan="5" |@gerbil5709
|Yes
|No
|957,769
|TBD
|TBD
| rowspan="5" |[https://drive.google.com/drive/folders/1kAvBebeF09CEVocCk5bGKlDJfRN8co_i?usp=sharing Google Drive folder]
|-
|61xxxx
|Yes
|No
|1,052,047
|TBD
|TBD
|-
|62xxxx
|Yes
|No
|959,753
|TBD
|TBD
|-
|63xxxx
|Yes
|No
|1,051,882
|TBD
|TBD
|-
|64xxxx
|No
|No
|TBD
|TBD
|TBD
|-
|
65xxxx - 
68xxxx
|Terry Ligocki
|Yes
|Yes
|3,076,778
|{{TM|1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RG0LD}}
|10 ↑↑ 192.67
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|69xxxx
|@poppuncher
|Yes
|Yes
|1,053,119
|{{TM|1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG}}
|10 ↑↑ 133.85
|[https://drive.google.com/drive/folders/1KlCZqXxqVPuBPkDcCBocuMPA8paq9b8P?usp=drive_link Google Drive folder]
|-
|70xxxx
|@hipparcos
|Yes
|Yes
|798,304
|
{{TM|1RB0LF_1RC1LE_0RD1RA_1RE1RG_0LA1LB_1LE1RG_0RC1RZ}}
|
10 ↑↑ 33.81
|[https://github.com/jhuang97/bb7x2/releases/tag/70xxxx Github release]
|-
|71xxxx
|@hipparcos
|Yes
|Yes
|1,100,790
|{{TM|1RB1RZ_1LC1RD_0LD0LC_1LE1RA_1LF0LE_1RF0RG_1RG0RD}}
|10 ↑↑ 77.50
|[https://github.com/jhuang97/bb7x2/releases/tag/71xxxx Github release]
|-
|75xxxx
|Terry Ligocki
|Yes
|Yes
|1,103,089
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0LF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188.28
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|79xxxx
|Terry Ligocki
|Yes
|No
|1,438,112
|TBD
|TBD
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|80xxxx
|@xnoobspeakable
|Yes
|No
|964,396
|TBD
|TBD
| rowspan="2" |[https://drive.google.com/drive/folders/1TpuEC7KottEmvsFnCREugnlVMPaY5ZHi?usp=sharing Google Drive folder]
|-
|81xxxx
|@xnoobspeakable
|No
|No
|TBD
|TBD
|TBD
|-
|
82xxxx - 
99xxxx
|Terry Ligocki
|Yes
|Yes
|15,673,786
|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}}
|10 ↑↑ 286.17
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|}
[[Category:BB Domain]]

BB(7)

2025-06-07T04:24:16Z

Hipparcos: /* Current Progress */ started working on 71xxxx

The 7-state, 2-symbol Busy Beaver problem '''BB(7)''' is a mostly unexplored domain with only preliminary information.

The current BB(7) champion is {{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}} discovered by Pavel Kropitz in 2025 proving the lower bound:<math display="block">S(7) > \Sigma(7) > 2 \uparrow^{11} 2 \uparrow^{11} 3</math>

== History ==
Before 2025, the only known BB(7) champions were produced by hand, not by search. Example, Milton Green designed a machine in 1964 that had [[sigma score]] 22,961 and Wythagoras modified a BB(6) champion in 2014 to produce a machine that had sigma score <math>> 10 \uparrow\uparrow 5</math>.

In May 2025, mxdys shared [https://github.com/ccz181078/TM C++ code] that breaks up the BB(7) enumeration into 1 million subtasks which each run for about 2 minutes and leave ~100 holdouts each. Various folks on Discord have been investigating different sections of this domain to search for champions.

Within three days of the code's release, the Ligockis found three champions after applying their deciders to enumerator output. Shawn Ligocki found the first two, {{TM|1RB0RF_1LC0RE_1RD1LB_1LA1LD_0RA0LE_1RG0LB_1RZ1RB}} and {{TM|1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC}}, with sigma scores of approximately 10 ↑↑ 22 and 10 ↑↑ 35. That evening, Terry Ligocki found {{TM|1RB0LG_1RC0RF_1LD1RZ_1LF0LE_1RA1LD_1LG1RE_0LB0LB}}, with sigma score ~10 ↑↑ 46. These were all outpaced by Pavel's champion.

== Top Halters ==
Based on limited search through a subset of the 1 million subtasks from mxdys's code, the top 20 scoring known machines are:
{| class="wikitable"
!TM
!Approximate sigma score
!Discoverer
|-
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE}}
|10 ↑↑ 519.20
|Andrew Ducharme
|-
|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}}
|10 ↑↑ 286.17
|Terry Ligocki
|-
|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD}}
|10 ↑↑ 246.32
|@Iijil
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG}}
|10 ↑↑ 192.67
|Terry Ligocki
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LG_1RF0RG_0RA0LG_1RB1LG}}
|10 ↑↑ 192.67
|Terry Ligocki
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RG0LG_1RB1LG}}
|10 ↑↑ 192.67
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LF0RF_0RA1RE_1RZ0RE}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LF0RF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_1LG1RE_1LF0RF_0RA1RE_1RZ0RA}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_1LG1RE_1LD0RF_0RA1RE_1RZ0RA}}
|10 ↑↑ 188.28
|@XnoobSpeakable, @Peacemaker II
|-
|{{TM|1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG}}
|10 ↑↑ 133.85
|@poppuncher
|-
|{{TM|1RB1RZ_1RC0RF_1LD1RB_1RG0LE_1LD0RA_1RE0LD_0RC1LF}}
|10 ↑↑ 129.24
|@Iijil
|-
|{{TM|1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ}}
|10 ↑↑ 116.97
|Terry Ligocki
|-
|{{TM|1RB0RD_1RC0LA_0LA0LE_1RE1RZ_1RF0RA_1LG0LE_1LC0LG}}
|10 ↑↑ 116.05
|
|-
|{{TM|1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ}}
|10 ↑↑ 115.52
|@prurq
|-
|{{TM|1RB0RF_1RC0RB_0RD0RF_1LE0LG_1LC0RD_1LA0LD_1LF1RZ}}
|10 ↑↑ 114.61
|Andrew Ducharme
|-
|{{TM|1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ}}
|10 ↑↑ 114.60
|Shawn Ligocki
|-
|{{TM|1RB0RE_0RC1LC_0LD1LF_1LE0LG_1RA0RC_0LB1LA_1LB1RZ}}
|10 ↑↑ 114.57
|Andrew Ducharme
|-
|{{TM|1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ}}
|10 ↑↑ 113.37
|Terry Ligocki
|}
The top 20 known halters with unique scores are:
{| class="wikitable"
!TM
!Approximate sigma score
!Discoverer
|-
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE}}
|10 ↑↑ 519.20
|Andrew Ducharme
|-
|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}}
|10 ↑↑ 286.17
|Terry Ligocki
|-
|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD}}
|10 ↑↑ 246.32
|@Iijil
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG}}
|10 ↑↑ 192.67
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG}}
|10 ↑↑ 133.85
|@poppuncher
|-
|{{TM|1RB1RZ_1RC0RF_1LD1RB_1RG0LE_1LD0RA_1RE0LD_0RC1LF}}
|10 ↑↑ 129.24
|@Iijil
|-
|{{TM|1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ}}
|10 ↑↑ 116.97
|Terry Ligocki
|-
|{{TM|1RB0RD_1RC0LA_0LA0LE_1RE1RZ_1RF0RA_1LG0LE_1LC0LG}}
|10 ↑↑ 116.05
|
|-
|{{TM|1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ}}
|10 ↑↑ 115.52
|@prurq
|-
|{{TM|1RB0RF_1RC0RB_0RD0RF_1LE0LG_1LC0RD_1LA0LD_1LF1RZ}}
|10 ↑↑ 114.61
|Andrew Ducharme
|-
|{{TM|1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ}}
|10 ↑↑ 114.60
|Shawn Ligocki
|-
|{{TM|1RB0RE_0RC1LC_0LD1LF_1LE0LG_1RA0RC_0LB1LA_1LB1RZ}}
|10 ↑↑ 114.57
|Andrew Ducharme
|-
|{{TM|1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ}}
|10 ↑↑ 113.37
|Terry Ligocki
|-
|{{TM|1RB1RZ_1RC1RA_1RD0RB_1LE0RC_1LF0LD_1RG0LF_1RC0LG}}
|10 ↑↑ 108.77
|Terry Ligocki
|-
|{{TM|1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG}}
|10 ↑↑ 93.81
|Andrew Ducharme
|-
|{{TM|1RB0RF_1LC0LD_1RC0LB_1LE1RG_1RA1RE_1RD0RD_0RA1RZ}}
|10 ↑↑ 93.78
|Terry Ligocki
|-
|{{TM|1RB1LB_1LC1RE_1RD1RC_0RE0RD_1LF0RB_1LF1LG_1RZ0LA}}
|10 ↑↑ 86.40
|Terry Ligocki
|-
|{{TM|1RB1LC_1RC0LG_1RD0RG_0LE0RA_1LC0LF_0LD1LF_1RZ1RA}}
|10 ↑↑ 82.44
|Terry Ligocki
|}

== Current Progress ==
This is a summary of the 1 million subtasks from mxdys's code that have been processed, including further processing by Shawn Ligocki's linear rule code ("TBD" = "To Be Determined", "TBE" = "To Be Entered"):
{| class="wikitable defaultleft"
!rowspan="2"|Task range
!rowspan="2"|Done by
!colspan="2"|Completed
!rowspan="2"|# holdouts
!rowspan="2"|Maximum Score TM
!rowspan="2"|~Sigma
!rowspan="2"|Source
|-
!enumeration
!linear rule
|-
|00xxxx
|@Iijil
|Yes
|Yes
|728,495
|{{TM|1RB0RF_1RC1LF_0RD0RD_1LE0LB_1RA1RZ_1LG1RA_1LD0RC}}
|10 ↑↑ 45.64
| rowspan="10" |[https://drive.google.com/drive/folders/1wniwrAuvsHfkvro8Tg65WAMNZEuIekzD Google Drive folder]
|-
|01xxxx
|@Iijil
|Yes
|Yes
|1,056,253
|TBD
|TBD
|-
|02xxxx
|@Iijil
|Yes
|No
|963,486
|TBD
|TBD
|-
|03xxxx
|@Iijil
|Yes
|No
|1,052,504
|TBD
|TBD
|-
|04xxxx
|@Iijil
|Yes
|No
|955,711
|TBD
|TBD
|-
|05xxxx
|@Iijil
|Yes
|No
|TBD
|TBD
|TBD
|-
|06xxxx
|@Iijil
|Yes
|No
|TBD
|TBD
|TBD
|-
|07xxxx
|@Iijil
|Yes
|No
|TBD
|TBD
|TBD
|-
|08xxxx
|@Iijil
|Yes
|No
|TBD
|TBD
|TBD
|-
|09xxxx
|@Iijil
|Yes
|No
|TBD
|TBD
|TBD
|-
|13xxxx
|Shawn Ligocki
|Yes
|Yes
|1,192,442
|{{TM|1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ}}
|10 ↑↑ 114.60
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|20xxxx - 
21xxxx
|@C7X
|Yes
|No
|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/11iGTKsvu2Y7aFrwOcWS1LYvcN6i_7-JM?usp=sharing Google Drive folder]
|-
|243308
|@uni
|Yes
|No
|TBE
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|[https://discord.com/channels/960643023006490684/1369339127652159509/1373660959960469545 Discord post]
|-
|25xxxx
|@stokastic
|Yes
|No
|1,056,591
|{{TM|1RB1RZ_1LC0LE_0LD0LC_0RE1LB_1RF0RG_0LD1RB_1RD1RA}}
|10 ↑↑ 31.33
| rowspan="10" |[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|26xxxx
|@stokastic
|Yes
|No
|958,289
|1RB1RZ_0LC1RB_0LE0LD_1LE1LD_0RF0LC_0RG1RF_1RD0RA ([https://bbchallenge.org/1RB1RZ_0LC1RB_0LE0LD_1LE1LD_0RF0LC_0RG1RF_1RD0RA bbch])
|10 ↑↑ 36.26
|-
|27xxxx
|@stokastic
|Yes
|No
|1,052,946
|1RB0RG_1LC1LB_0RE0LD_0LC1RF_0RA1RE_0LF0LB_1RF1RZ ([https://bbchallenge.org/1RB0RG_1LC1LB_0RE0LD_0LC1RF_0RA1RE_0LF0LB_1RF1RZ bbch])
|10 ↑↑ 63.56
|-
|28xxxx
|@stokastic
|Yes
|No
|956,935
|TBD
|TBD
|-
|29xxxx
|@stokastic
|Yes
|No
|1,052,415
|TBD
|TBD
|-
|30xxxx
|@stokastic
|Yes
|No
|1,032,095
|TBD
|TBD
|-
|31xxxx
|@stokastic
|Yes
|No
|1,436,970
|TBD
|TBD
|-
|32xxxx
|@stokastic
|Yes
|No
|1,036,950
|TBD
|TBD
|-
|33xxxx
|@stokastic
|Yes
|No
|1,432,081
|TBD
|TBD
|-
|34xxxx
|@stokastic
|Yes
|No
|1,032,970
|TBD
|TBD
|-
|35xxxx
|rowspan="5"|Terry Ligocki
|Yes
|No
|1,437,841
|TBD
|TBD
|rowspan="5"|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|36xxxx
|Yes
|Yes
|798,364
|{{TM|1RB1LD_0LC1LE_1RD1LB_1RD0RA_1LB0RF_0RG1RE_1RZ0RA}}
|10 ↑↑ 26.82
|-
|37xxxx
|Yes
|Yes
|1,098,681
|{{TM|1RB0LA_1RC0LB_1RD0RF_1LE0RC_1LA0LD_1RC1RG_1RF1RZ}}
|10 ↑↑ 108.77
|-
|38xxxx
|Yes
|Yes
|801,308
|{{TM|1RB1RZ_1RC1RA_1RD0RB_1LE0RC_1LF0LD_1RG0LF_1RC0LG}}
|10 ↑↑ 108.77
|-
|39xxxx
|Yes
|Yes
|1,093,938
|{{TM|1RB1LA_1LC0RE_0LD1LB_1RD0LA_1RF0RA_0RG0LA_1RB1RZ}}
|10 ↑↑ 192.67
|-
|40xxxx
| rowspan="6" |Andrew Ducharme
|Yes
|Yes
|730,310
|{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE}}
|10 ↑↑ 519.20
| rowspan="6" |[https://drive.google.com/drive/folders/16uDjgOahkhAMWv3v-YWmxJG7xxsBvj4h?usp=sharing Google Drive folder]
|-
|41xxxx
|No
|No
|TBD
|TBD
|TBD
|-
|42xxxx
|No
|No
|TBD
|TBD
|TBD
|-
|43xxxx
|Yes
|Yes
|817,332
|{{TM|1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG}}
|10 ↑↑ 93.81
|-
|44xxxx
|Yes
|Yes
|729,686
|{{TM|1RB1LC_1RC0RC_1RD1LA_0RE1RF_1LC0LG_1LA1LE_1RZ1LF}}
|10 ↑↑ 76.36
|-
|45xxxx
|Yes
|Yes
|812,973
|{{TM|1RB0RE_0RC1LC_0LD1LF_1LE0LG_1RA0RC_0LB1LA_1LB1RZ}}
|10 ↑↑ 114.57
|-
|49xxxx
|Tobiáš Brichta
|No
|No
|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/1-csgJ5uSIX3SKlqTkSnhkUuEYLKgCw81 Google Drive folder]
|-
|500xxx
|@prurq
|Yes
|No
|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/145H4sT4F9KJYGSrlIETZdBOIMR7krLQm Google Drive folder]
|-
|60xxxx
|rowspan="3"|@gerbil5709
|Yes
|No
|TBD
|TBD
|TBD
| rowspan="3" |[https://drive.google.com/drive/folders/1kAvBebeF09CEVocCk5bGKlDJfRN8co_i?usp=sharing Google Drive folder]
|-
|61xxxx
|No
|No
|TBD
|TBD
|TBD
|-
|62xxxx
|No
|No
|TBD
|TBD
|TBD
|-
|69xxxx
|@poppuncher
|Yes
|No
|TBD
|{{TM|1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG}}
|10 ↑↑ 133.85
|[https://drive.google.com/drive/folders/1KlCZqXxqVPuBPkDcCBocuMPA8paq9b8P?usp=drive_link Google Drive folder]
|-
|70xxxx
|@hipparcos
|Yes
|Yes
|798,304
|
{{TM|1RB0LF_1RC1LE_0RD1RA_1RE1RG_0LA1LB_1LE1RG_0RC1RZ}} 
{{TM|1RB0LF_1LC1LE_1RE0LD_0LC0LA_1LB1RA_0LG0RC_1RZ0LA}}
|
10 ↑↑ 33.81 
10 ↑↑ 26.63
|[https://github.com/jhuang97/bb7x2/releases/tag/70xxxx Github release]
|-
|71xxxx
|@hipparcos
|No
|No
|TBD
|TBD
|TBD
|
|-
|75xxxx
|Terry Ligocki
|Yes
|Yes
|1,103,089
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0LF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188.28
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|80xxxx
|@xnoobspeakable
|Yes
|No
|964,396
|TBD
|TBD
| rowspan="2" |[https://drive.google.com/drive/folders/1TpuEC7KottEmvsFnCREugnlVMPaY5ZHi?usp=sharing Google Drive folder]
|-
|81xxxx
|@xnoobspeakable
|No
|No
|TBD
|TBD
|TBD
|-
|
85xxxx - 
9xxxxx
|Terry Ligocki
|Yes
|Yes
|13,396,923
|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}}
|10 ↑↑ 286.17
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|}
[[Category:BB Domain]]

BB(7)

2025-06-05T16:44:02Z

Hipparcos: /* Current Progress */ add link to 70xxxx results

The 7-state, 2-symbol Busy Beaver problem '''BB(7)''' is a mostly unexplored domain with only preliminary information.

The current BB(7) champion is {{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}} discovered by Pavel Kropitz in 2025 proving the lower bound:<math display="block">S(7) > \Sigma(7) > 2 \uparrow^{11} 2 \uparrow^{11} 3</math>

== History ==
Before 2025, the only known BB(7) champions were produced by hand, not by search. Example, Milton Green designed a machine in 1964 that had [[sigma score]] 22,961 and Wythagoras modified a BB(6) champion in 2014 to produce a machine that had sigma score <math>> 10 \uparrow\uparrow 5</math>.

In May 2025, mxdys shared [https://github.com/ccz181078/TM C++ code] that breaks up the BB(7) enumeration into 1 million subtasks which each run for about 2 minutes and leave ~100 holdouts each. Various folks on Discord have been investigating different sections of this domain to search for champions.

== Top Halters ==
Based on limited search through a subset of the 1 million subtasks from mxdys's code, the top 20 scoring known machines are:
{| class="wikitable"
!TM
!Approximate sigma score
!Discoverer
|-
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|Pavel Kropitz
|-
|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}}
|10 ↑↑ 286.17
|Terry Ligocki
|-
|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD}}
|10 ↑↑ 246.32
|@Iijil
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG}}
|10 ↑↑ 192.67
|Terry Ligocki
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LG_1RF0RG_0RA0LG_1RB1LG}}
|10 ↑↑ 192.67
|Terry Ligocki
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RG0LG_1RB1LG}}
|10 ↑↑ 192.67
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LF0RF_0RA1RE_1RZ0RE}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LF0RF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_1LG1RE_1LF0RF_0RA1RE_1RZ0RA}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_1LG1RE_1LD0RF_0RA1RE_1RZ0RA}}
|10 ↑↑ 188.28
|@XnoobSpeakable, @Peacemaker II
|-
|{{TM|1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG}}
|10 ↑↑ 133
|@poppuncher
|-
|{{TM|1RB1RZ_1RC0RF_1LD1RB_1RG0LE_1LD0RA_1RE0LD_0RC1LF}}
|10 ↑↑ 129.24
|@Iijil
|-
|{{TM|1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ}}
|10 ↑↑ 116.97
|Terry Ligocki
|-
|{{TM|1RB0RD_1RC0LA_0LA0LE_1RE1RZ_1RF0RA_1LG0LE_1LC0LG}}
|10 ↑↑ 116.05
|
|-
|{{TM|1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ}}
|10 ↑↑ 115.52
|@prurq
|-
|{{TM|1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ}}
|10 ↑↑ 114.60
|Shawn Ligocki
|-
|{{TM|1RB0RE_0RC1LC_0LD1LF_1LE0LG_1RA0RC_0LB1LA_1LB1RZ}}
|10 ↑↑ 114.57
|Andrew Ducharme
|-
|{{TM|1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ}}
|10 ↑↑ 113.37
|Terry Ligocki
|-
|{{TM|1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG}}
|10 ↑↑ 93.81
|Andrew Ducharme
|}
The top 20 known halters with unique scores are:
{| class="wikitable"
!TM
!Approximate sigma score
!Discoverer
|-
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|Pavel Kropitz
|-
|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}}
|10 ↑↑ 286.17
|Terry Ligocki
|-
|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD}}
|10 ↑↑ 246.32
|@Iijil
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG}}
|10 ↑↑ 192.67
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG}}
|10 ↑↑ 133
|@poppuncher
|-
|{{TM|1RB1RZ_1RC0RF_1LD1RB_1RG0LE_1LD0RA_1RE0LD_0RC1LF}}
|10 ↑↑ 129.24
|@Iijil
|-
|{{TM|1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ}}
|10 ↑↑ 116.97
|Terry Ligocki
|-
|{{TM|1RB0RD_1RC0LA_0LA0LE_1RE1RZ_1RF0RA_1LG0LE_1LC0LG}}
|10 ↑↑ 116.05
|
|-
|{{TM|1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ}}
|10 ↑↑ 115.52
|@prurq
|-
|{{TM|1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ}}
|10 ↑↑ 114.60
|Shawn Ligocki
|-
|{{TM|1RB0RE_0RC1LC_0LD1LF_1LE0LG_1RA0RC_0LB1LA_1LB1RZ}}
|10 ↑↑ 114.57
|Andrew Ducharme
|-
|{{TM|1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ}}
|10 ↑↑ 113.37
|Terry Ligocki
|-
|{{TM|1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG}}
|10 ↑↑ 93.81
|Andrew Ducharme
|-
|{{TM|1RB0RF_1LC0LD_1RC0LB_1LE1RG_1RA1RE_1RD0RD_0RA1RZ}}
|10 ↑↑ 93.78
|Terry Ligocki
|-
|{{TM|1RB1LB_1LC1RE_1RD1RC_0RE0RD_1LF0RB_1LF1LG_1RZ0LA}}
|10 ↑↑ 86.40
|Terry Ligocki
|-
|{{TM|1RB1LC_1RC0LG_1RD0RG_0LE0RA_1LC0LF_0LD1LF_1RZ1RA}}
|10 ↑↑ 82.44
|Terry Ligocki
|-
|{{TM|1RB1LG_1RC0LA_1LD0RF_0LE0LD_1RE0RB_0LB1LF_1RZ1LC}}
|10 ↑↑ 80.18
|Andrew Ducharme
|-
|{{TM|1RB1LC_1RC0RC_1RD1LA_0RE1RF_1LC0LG_1LA1LE_1RZ1LF}}
|10 ↑↑ 76.36
|Andrew Ducharme
|-
|{{TM|1RB0LD_1RC0RF_0RD1RA_1LE0RB_0LA0LB_1RA1RG_0RA1RZ}}
|10 ↑↑ 64.03
|Terry Ligocki
|}

== Current Progress ==
This is a summary of the 1 million subtasks from mxdys's code that have been processed, including further processing by Shawn Ligocki's linear rule code ("TBD" = "To Be Determined", "TBE" = "To Be Entered"):
{| class="wikitable defaultleft"
!rowspan="2"|Task range
!rowspan="2"|Done by
!colspan="2"|Completed
!rowspan="2"|# holdouts
!rowspan="2"|Maximum Score TM
!rowspan="2"|~Sigma
!rowspan="2"|Source
|-
!enumeration
!linear rule
|-
|00xxxx
|@Iijil
|Yes
|Yes
|728,495
|{{TM|1RB0RF_1RC1LF_0RD0RD_1LE0LB_1RA1RZ_1LG1RA_1LD0RC}}
|10 ↑↑ 46
| rowspan="10" |[https://drive.google.com/drive/folders/1wniwrAuvsHfkvro8Tg65WAMNZEuIekzD Google Drive folder]
|-
|01xxxx
|@Iijil
|Yes
|Yes
|1,056,253
|TBD
|TBD
|-
|02xxxx
|@Iijil
|Yes
|No
|963,486
|TBD
|TBD
|-
|03xxxx
|@Iijil
|Yes
|No
|1,052,504
|TBD
|TBD
|-
|04xxxx
|@Iijil
|Yes
|No
|955,711
|TBD
|TBD
|-
|05xxxx
|@Iijil
|Yes
|No
|TBD
|TBD
|TBD
|-
|06xxxx
|@Iijil
|Yes
|No
|TBD
|TBD
|TBD
|-
|07xxxx
|@Iijil
|Yes
|No
|TBD
|TBD
|TBD
|-
|08xxxx
|@Iijil
|Yes
|No
|TBD
|TBD
|TBD
|-
|09xxxx
|@Iijil
|Yes
|No
|TBD
|TBD
|TBD
|-
|13xxxx
|Shawn Ligocki
|Yes
|Yes
|1,192,442
|{{TM|1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ}}
|10 ↑↑ 114.60
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|20xxxx - 
21xxxx
|@C7X
|Yes
|No
|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/11iGTKsvu2Y7aFrwOcWS1LYvcN6i_7-JM?usp=sharing Google Drive folder]
|-
|243308
|@uni
|Yes
|No
|TBE
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|[https://discord.com/channels/960643023006490684/1369339127652159509/1373660959960469545 Discord post]
|-
|25xxxx
|@stokastic
|Yes
|No
|1,056,591
|{{TM|1RB1RZ_1LC0LE_0LD0LC_0RE1LB_1RF0RG_0LD1RB_1RD1RA}}
|10↑↑31.33
| rowspan="10" |[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|26xxxx
|@stokastic
|Yes
|No
|958,289
|TBD
|TBD
|-
|27xxxx
|@stokastic
|Yes
|No
|1,052,946
|TBD
|TBD
|-
|28xxxx
|@stokastic
|Yes
|No
|956,935
|TBD
|TBD
|-
|29xxxx
|@stokastic
|Yes
|No
|1,052,415
|TBD
|TBD
|-
|30xxxx
|@stokastic
|Yes
|No
|1,032,095
|TBD
|TBD
|-
|31xxxx
|@stokastic
|Yes
|No
|1,436,970
|TBD
|TBD
|-
|32xxxx
|@stokastic
|Yes
|No
|1,036,950
|TBD
|TBD
|-
|33xxxx
|@stokastic
|Yes
|No
|1,432,081
|TBD
|TBD
|-
|34xxxx
|@stokastic
|Yes
|No
|1,032,970
|TBD
|TBD
|-
|
35xxxx - 
38xxxx
|Terry Ligocki
|No
|No
|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|39xxxx
|Terry Ligocki
|Yes
|Yes
|1,093,938
|{{TM|1RB1LA_1LC0RE_0LD1LB_1RD0LA_1RF0RA_0RG0LA_1RB1RZ}}
|10 ↑↑ 193
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|40xxxx
| rowspan="6" |Andrew Ducharme
|No
|No
|TBD
|TBD
|TBD
| rowspan="6" |[https://drive.google.com/drive/folders/16uDjgOahkhAMWv3v-YWmxJG7xxsBvj4h?usp=sharing Google Drive folder]
|-
|41xxxx
|No
|No
|TBD
|TBD
|TBD
|-
|42xxxx
|No
|No
|TBD
|TBD
|TBD
|-
|43xxxx
|Yes
|Yes
|817,332
|{{TM|1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG}}
|10 ↑↑ 93.81
|-
|44xxxx
|Yes
|Yes
|729,686
|{{TM|1RB1LC_1RC0RC_1RD1LA_0RE1RF_1LC0LG_1LA1LE_1RZ1LF}}
|10 ↑↑ 76.36
|-
|45xxxx
|Yes
|Yes
|812,973
|{{TM|1RB0RE_0RC1LC_0LD1LF_1LE0LG_1RA0RC_0LB1LA_1LB1RZ}}
|10 ↑↑ 114.57
|-
|49xxxx
|Tobiáš Brichta
|No
|No
|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/1-csgJ5uSIX3SKlqTkSnhkUuEYLKgCw81 Google Drive folder]
|-
|500xxx
|@prurq
|Yes
|No
|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/145H4sT4F9KJYGSrlIETZdBOIMR7krLQm Google Drive folder]
|-
|60xxxx
|@gerbil5709
|Yes
|No
|TBD
|TBD
|TBD
| rowspan="2" |[https://drive.google.com/drive/folders/1kAvBebeF09CEVocCk5bGKlDJfRN8co_i?usp=sharing Google Drive folder]
|-
|61xxxx
|@gerbil5709
|No
|No
|TBD
|TBD
|TBD
|-
|69xxxx
|@poppuncher
|Yes
|No
|TBD
|{{TM|1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG}}
|10 ↑↑ 133
|[https://drive.google.com/drive/folders/1KlCZqXxqVPuBPkDcCBocuMPA8paq9b8P?usp=drive_link Google Drive folder]
|-
|70xxxx
|@hipparcos
|Yes
|Yes
|798,304
|{{TM|1RB0LF_1RC1LE_0RD1RA_1RE1RG_0LA1LB_1LE1RG_0RC1RZ}} 
{{TM|1RB0LF_1LC1LE_1RE0LD_0LC0LA_1LB1RA_0LG0RC_1RZ0LA}}
|10↑↑33.81 
10↑↑26.63
|[https://github.com/jhuang97/bb7x2/releases/tag/70xxxx Github release]
|-
|75xxxx
|Terry Ligocki
|Yes
|Yes
|1,103,089
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0LF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|80xxxx
|@xnoobspeakable
|Yes
|No
|964,396
|TBD
|TBD
| rowspan="2" |[https://drive.google.com/drive/folders/1TpuEC7KottEmvsFnCREugnlVMPaY5ZHi?usp=sharing Google Drive folder]
|-
|81xxxx
|@xnoobspeakable
|No
|No
|TBD
|TBD
|TBD
|-
|
85xxxx - 
9xxxxx
|Terry Ligocki
|Yes
|Yes
|13,396,923
|
{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}} 
{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG}} 
{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA}} 
{{TM|1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ}} 
{{TM|1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ}}
|
10 ↑↑ 286 
10 ↑↑ 193 
10 ↑↑ 188 
10 ↑↑ 117 
10 ↑↑ 113
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|}
[[Category:BB Domain]]

BB(7)

2025-06-05T07:22:50Z

Hipparcos: /* Current Progress */ 70xxxx result update

The 7-state, 2-symbol Busy Beaver problem '''BB(7)''' is a mostly unexplored domain with only preliminary information.

The current BB(7) champion is {{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}} discovered by Pavel Kropitz in 2025 proving the lower bound:<math display="block">S(7) > \Sigma(7) > 2 \uparrow^{11} 2 \uparrow^{11} 3</math>

== History ==
Before 2025, the only known BB(7) champions were produced by hand, not by search. Example, Milton Green designed a machine in 1964 that had [[sigma score]] 22,961 and Wythagoras modified a BB(6) champion in 2014 to produce a machine that had sigma score <math>> 10 \uparrow\uparrow 5</math>.

In May 2025, mxdys shared [https://github.com/ccz181078/TM C++ code] that breaks up the BB(7) enumeration into 1 million subtasks which each run for about 2 minutes and leave ~100 holdouts each. Various folks on Discord have been investigating different sections of this domain to search for champions.

== Top Halters ==
Based on limited search through a subset of the 1 million subtasks from mxdys's code, the top 20 scoring known machines are:
{| class="wikitable"
!TM
!Approximate sigma score
!Discoverer
|-
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|Pavel Kropitz
|-
|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}}
|10 ↑↑ 286.17
|Terry Ligocki
|-
|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD}}
|10 ↑↑ 246.32
|@Iijil
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG}}
|10 ↑↑ 192.67
|Terry Ligocki
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LG_1RF0RG_0RA0LG_1RB1LG}}
|10 ↑↑ 192.67
|Terry Ligocki
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RG0LG_1RB1LG}}
|10 ↑↑ 192.67
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LF0RF_0RA1RE_1RZ0RE}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LF0RF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_1LG1RE_1LF0RF_0RA1RE_1RZ0RA}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_1LG1RE_1LD0RF_0RA1RE_1RZ0RA}}
|10 ↑↑ 188.28
|@XnoobSpeakable, @Peacemaker II
|-
|{{TM|1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG}}
|10 ↑↑ 133
|@poppuncher
|-
|{{TM|1RB1RZ_1RC0RF_1LD1RB_1RG0LE_1LD0RA_1RE0LD_0RC1LF}}
|10 ↑↑ 129.24
|@Iijil
|-
|{{TM|1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ}}
|10 ↑↑ 116.97
|Terry Ligocki
|-
|{{TM|1RB0RD_1RC0LA_0LA0LE_1RE1RZ_1RF0RA_1LG0LE_1LC0LG}}
|10 ↑↑ 116.05
|
|-
|{{TM|1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ}}
|10 ↑↑ 115.52
|@prurq
|-
|{{TM|1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ}}
|10 ↑↑ 114.60
|Shawn Ligocki
|-
|{{TM|1RB0RE_0RC1LC_0LD1LF_1LE0LG_1RA0RC_0LB1LA_1LB1RZ}}
|10 ↑↑ 114.57
|Andrew Ducharme
|-
|{{TM|1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ}}
|10 ↑↑ 113.37
|Terry Ligocki
|-
|{{TM|1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG}}
|10 ↑↑ 93.81
|Andrew Ducharme
|}
The top 20 known halters with unique scores are:
{| class="wikitable"
!TM
!Approximate sigma score
!Discoverer
|-
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|Pavel Kropitz
|-
|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}}
|10 ↑↑ 286.17
|Terry Ligocki
|-
|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD}}
|10 ↑↑ 246.32
|@Iijil
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG}}
|10 ↑↑ 192.67
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG}}
|10 ↑↑ 133
|@poppuncher
|-
|{{TM|1RB1RZ_1RC0RF_1LD1RB_1RG0LE_1LD0RA_1RE0LD_0RC1LF}}
|10 ↑↑ 129.24
|@Iijil
|-
|{{TM|1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ}}
|10 ↑↑ 116.97
|Terry Ligocki
|-
|{{TM|1RB0RD_1RC0LA_0LA0LE_1RE1RZ_1RF0RA_1LG0LE_1LC0LG}}
|10 ↑↑ 116.05
|
|-
|{{TM|1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ}}
|10 ↑↑ 115.52
|@prurq
|-
|{{TM|1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ}}
|10 ↑↑ 114.60
|Shawn Ligocki
|-
|{{TM|1RB0RE_0RC1LC_0LD1LF_1LE0LG_1RA0RC_0LB1LA_1LB1RZ}}
|10 ↑↑ 114.57
|Andrew Ducharme
|-
|{{TM|1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ}}
|10 ↑↑ 113.37
|Terry Ligocki
|-
|{{TM|1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG}}
|10 ↑↑ 93.81
|Andrew Ducharme
|-
|{{TM|1RB0RF_1LC0LD_1RC0LB_1LE1RG_1RA1RE_1RD0RD_0RA1RZ}}
|10 ↑↑ 93.78
|Terry Ligocki
|-
|{{TM|1RB1LB_1LC1RE_1RD1RC_0RE0RD_1LF0RB_1LF1LG_1RZ0LA}}
|10 ↑↑ 86.40
|Terry Ligocki
|-
|{{TM|1RB1LC_1RC0LG_1RD0RG_0LE0RA_1LC0LF_0LD1LF_1RZ1RA}}
|10 ↑↑ 82.44
|Terry Ligocki
|-
|{{TM|1RB1LG_1RC0LA_1LD0RF_0LE0LD_1RE0RB_0LB1LF_1RZ1LC}}
|10 ↑↑ 80.18
|Andrew Ducharme
|-
|{{TM|1RB1LC_1RC0RC_1RD1LA_0RE1RF_1LC0LG_1LA1LE_1RZ1LF}}
|10 ↑↑ 76.36
|Andrew Ducharme
|-
|{{TM|1RB0LD_1RC0RF_0RD1RA_1LE0RB_0LA0LB_1RA1RG_0RA1RZ}}
|10 ↑↑ 64.03
|Terry Ligocki
|}

== Current Progress ==
This is a summary of the 1 million subtasks from mxdys's code that have been processed, including further processing by Shawn Ligocki's linear rule code ("TBD" = "To Be Determined", "TBE" = "To Be Entered"):
{| class="wikitable defaultleft"
!rowspan="2"|Task range
!rowspan="2"|Done by
!colspan="2"|Completed
!rowspan="2"|# holdouts
!rowspan="2"|Maximum Score TM
!rowspan="2"|~Sigma
!rowspan="2"|Source
|-
!enumeration
!linear rule
|-
|00xxxx
|@Iijil
|Yes
|Yes
|728,495
|{{TM|1RB0RF_1RC1LF_0RD0RD_1LE0LB_1RA1RZ_1LG1RA_1LD0RC}}
|10 ↑↑ 46
| rowspan="10" |[https://drive.google.com/drive/folders/1wniwrAuvsHfkvro8Tg65WAMNZEuIekzD Google Drive folder]
|-
|01xxxx
|@Iijil
|Yes
|Yes
|1,056,253
|TBD
|TBD
|-
|02xxxx
|@Iijil
|Yes
|No
|963,486
|TBD
|TBD
|-
|03xxxx
|@Iijil
|Yes
|No
|1,052,504
|TBD
|TBD
|-
|04xxxx
|@Iijil
|Yes
|No
|955,711
|TBD
|TBD
|-
|05xxxx
|@Iijil
|Yes
|No
|TBD
|TBD
|TBD
|-
|06xxxx
|@Iijil
|Yes
|No
|TBD
|TBD
|TBD
|-
|07xxxx
|@Iijil
|Yes
|No
|TBD
|TBD
|TBD
|-
|08xxxx
|@Iijil
|Yes
|No
|TBD
|TBD
|TBD
|-
|09xxxx
|@Iijil
|Yes
|No
|TBD
|TBD
|TBD
|-
|13xxxx
|Shawn Ligocki
|Yes
|Yes
|1,192,442
|{{TM|1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ}}
|10 ↑↑ 114.60
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|20xxxx - 
21xxxx
|@C7X
|Yes
|No
|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/11iGTKsvu2Y7aFrwOcWS1LYvcN6i_7-JM?usp=sharing Google Drive folder]
|-
|243308
|@uni
|Yes
|No
|TBE
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|[https://discord.com/channels/960643023006490684/1369339127652159509/1373660959960469545 Discord post]
|-
|25xxxx
|@stokastic
|Yes
|No
|1,056,591
|{{TM|1RB1RZ_1LC0LE_0LD0LC_0RE1LB_1RF0RG_0LD1RB_1RD1RA}}
|10↑↑31.33
| rowspan="10" |[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|26xxxx
|@stokastic
|Yes
|No
|958,289
|TBD
|TBD
|-
|27xxxx
|@stokastic
|Yes
|No
|1,052,946
|TBD
|TBD
|-
|28xxxx
|@stokastic
|Yes
|No
|956,935
|TBD
|TBD
|-
|29xxxx
|@stokastic
|Yes
|No
|1,052,415
|TBD
|TBD
|-
|30xxxx
|@stokastic
|Yes
|No
|1,032,095
|TBD
|TBD
|-
|31xxxx
|@stokastic
|Yes
|No
|1,436,970
|TBD
|TBD
|-
|32xxxx
|@stokastic
|Yes
|No
|1,036,950
|TBD
|TBD
|-
|33xxxx
|@stokastic
|Yes
|No
|1,432,081
|TBD
|TBD
|-
|34xxxx
|@stokastic
|Yes
|No
|1,032,970
|TBD
|TBD
|-
|
35xxxx - 
38xxxx
|Terry Ligocki
|No
|No
|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|39xxxx
|Terry Ligocki
|Yes
|Yes
|1,093,938
|{{TM|1RB1LA_1LC0RE_0LD1LB_1RD0LA_1RF0RA_0RG0LA_1RB1RZ}}
|10 ↑↑ 193
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|40xxxx
| rowspan="6" |Andrew Ducharme
|No
|No
|TBD
|TBD
|TBD
| rowspan="6" |[https://drive.google.com/drive/folders/16uDjgOahkhAMWv3v-YWmxJG7xxsBvj4h?usp=sharing Google Drive folder]
|-
|41xxxx
|No
|No
|TBD
|TBD
|TBD
|-
|42xxxx
|No
|No
|TBD
|TBD
|TBD
|-
|43xxxx
|Yes
|Yes
|817,332
|{{TM|1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG}}
|10 ↑↑ 93.81
|-
|44xxxx
|Yes
|Yes
|729,686
|{{TM|1RB1LC_1RC0RC_1RD1LA_0RE1RF_1LC0LG_1LA1LE_1RZ1LF}}
|10 ↑↑ 76.36
|-
|45xxxx
|Yes
|Yes
|812,973
|{{TM|1RB0RE_0RC1LC_0LD1LF_1LE0LG_1RA0RC_0LB1LA_1LB1RZ}}
|10 ↑↑ 114.57
|-
|49xxxx
|Tobiáš Brichta
|No
|No
|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/1-csgJ5uSIX3SKlqTkSnhkUuEYLKgCw81 Google Drive folder]
|-
|500xxx
|@prurq
|Yes
|No
|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/145H4sT4F9KJYGSrlIETZdBOIMR7krLQm Google Drive folder]
|-
|60xxxx
|@gerbil5709
|Yes
|No
|TBD
|TBD
|TBD
| rowspan="2" |[https://drive.google.com/drive/folders/1kAvBebeF09CEVocCk5bGKlDJfRN8co_i?usp=sharing Google Drive folder]
|-
|61xxxx
|@gerbil5709
|No
|No
|TBD
|TBD
|TBD
|-
|69xxxx
|@poppuncher
|Yes
|No
|TBD
|{{TM|1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG}}
|10 ↑↑ 133
|[https://drive.google.com/drive/folders/1KlCZqXxqVPuBPkDcCBocuMPA8paq9b8P?usp=drive_link Google Drive folder]
|-
|70xxxx
|@hipparcos
|Yes
|Yes
|798,304
|{{TM|1RB0LF_1RC1LE_0RD1RA_1RE1RG_0LA1LB_1LE1RG_0RC1RZ}} 
{{TM|1RB0LF_1LC1LE_1RE0LD_0LC0LA_1LB1RA_0LG0RC_1RZ0LA}}
|10↑↑33.81 
10↑↑26.63
|TBE
|-
|75xxxx
|Terry Ligocki
|Yes
|Yes
|1,103,089
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0LF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|80xxxx
|@xnoobspeakable
|Yes
|No
|964,396
|TBD
|TBD
| rowspan="2" |[https://drive.google.com/drive/folders/1TpuEC7KottEmvsFnCREugnlVMPaY5ZHi?usp=sharing Google Drive folder]
|-
|81xxxx
|@xnoobspeakable
|No
|No
|TBD
|TBD
|TBD
|-
|
85xxxx - 
9xxxxx
|Terry Ligocki
|Yes
|Yes
|13,396,923
|
{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}} 
{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG}} 
{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA}} 
{{TM|1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ}} 
{{TM|1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ}}
|
10 ↑↑ 286 
10 ↑↑ 193 
10 ↑↑ 188 
10 ↑↑ 117 
10 ↑↑ 113
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|}
[[Category:BB Domain]]

1RB2LC1RC 2LC---2RB 2LA0LB0RA

2025-04-07T06:04:46Z

Hipparcos: /* Timings */ change section title

{{machine|1RB2LC1RC_2LC---2RB_2LA0LB0RA}}{{unsolved|Does this TM halt? If so, how many steps does it take to halt?}}
{{TM|1RB2LC1RC_2LC---2RB_2LA0LB0RA|undecided}}

This is a [[BB(3,3)]] [[holdout]] which appears to [[probviously]] halt. If can be proven to halt, it will be the BB(3,3) champion, in terms of both steps and tape symbols. However, it could also turn out to be a probviously halting [[Cryptid]].

This is holdout #758 on Justin's 3x3 mugshots. After about 1.8 million steps and up to some relabelling, it is equivalent to holdout #153: {{TM|1RB0LB0RC_2LC2LA1RA_1RA1LC---}}. And if you start in state C it is a [[permutation]] of the same machine. Together, they simulate a complex set of Collatz-like rules with two decreasing parameters.

After active exploration on the #bb3x3 channel by LegionMammal and dyuan, LegionMammal found (and dyuan confirmed) a configuration A(1,c) (defined [https://discord.com/channels/960643023006490684/1259770474897080380/1259968221218607145 here]) which halts and for which a huge "wall" of previous A(1, c') values all reach it. This gives strong evidence that the TM probviosly halts since jumping over this wall is very "unlikely".

NOTE: As of 16 Jul 2024 there is a lot more active work on the #bb3x3 channel with LegionMammal and dyuan not reflected here.

== dyuan01's Rules ==
https://discord.com/channels/960643023006490684/1084047886494470185/1224457633176486041

<pre>
A_1(a, b, c) = 0^inf 1 2^a <C (22)^b (20)^c 0^inf
A_2(a, b, c) = 0^inf 1 2^a <A2 (22)^b (20)^c 0^inf
B(a, b) = 0^inf 1 2^a <B0 (20)^b 0^inf
</pre>

{| class="wikitable"
! From !! To
|-
| A1(0, b, 2n) || A2(1, b+2n+1, 0)
|-
| A1(0, b, 2n+1) || A1(1, 0, b+2n+3)
|-
| A1(m+1, b, 0) || A1(m, 0, b+2)
|-
| A1(m+1, b, n+1) || A2(m, b+1, n)
|-
| A2(0, b, 2n) || A1(2b+3, 0, 2n+1)
|-
| A2(0, b, 2n+1) || A2(2b+3, 2n+1, 0)
|-
| A2(m+1, b, 0) || B(m, b+2)
|-
| A2(m+1, b, n+1) || A1(m, b+2, n)
|-
| B(0, b) || Halt
|-
| B(m+1, 2n) || A2(m, 2n+1, 0)
|-
| B(m+1, 2n+1) || A1(m, 0, 2n+3)
|}
Starting from A1(0, 0, 1) (at step 2).

== savask's Rules ==
https://discord.com/channels/960643023006490684/1084047886494470185/1254085725138190336

Let <code>(m, b, n) = A2(m, b, n) = 0^inf 1 2^m <A2 (22)^b (20)^n 0^inf</code>

<pre>
(0, b, n) -> (2b+2, 1, n) if n is even
-> (2b, 1, n+3) if n is odd

(1, b, 0) -> Halt

(2, b, 0) -> (0, b+3, 0) if b is even
-> (0, 1, b+5) if b is odd

(m, b, 0) -> (m-2, b+3, 0) if b is even
-> (m-3, 1, b+3) if b is odd

(1, b, n) -> (0, 1, n+b+2) if n is even
-> Halt if n is odd

(2, b, 1) -> Halt if b is even
-> (0, 1, b+5) if b is odd

(m, b, 1) -> (m-3, 1, b+3)

(m, b, n) -> (m-2, b+3, n-2)
</pre>

https://discord.com/channels/960643023006490684/1084047886494470185/1254306301786198116

<pre>
step (A2 0 b n) | even n = A2 (2*b+2) 1 n
| otherwise = A2 (2*b) 1 (n+3)
-- From now on m > 0
step (A2 1 b 0) = error $ "Halt A2 1 " ++ show b ++ " 0"
step (A2 2 b 0) | even b = A2 0 (b+3) 0
| otherwise = A2 0 1 (b+5)
step (A2 m b 0) | even b = A2 (m-2) (b+3) 0
| otherwise = A2 (m-3) 1 (b+3)
-- From now on n > 0
step (A2 1 b n) | even n = A2 0 1 (n+b+2)
| otherwise = error $ "Halt A2 1 " ++ show b ++ " " ++ show n
step (A2 2 b 1) | even b = error $ "Halt A2 2 " ++ show b ++ " 1"
| otherwise = A2 0 1 (b+5)
step (A2 m b 1) = A2 (m-3) 1 (b+3)
-- Here m > 1, n > 1
step (A2 m b n) = let d2 = (min m n) `div` 2 in A2 (m - 2*d2) (b + 3*d2) (n - 2*d2) -- Accelerated
</pre>

== Shawn's Rules ==
https://discord.com/channels/960643023006490684/1084047886494470185/1254307091863048264

We can reduce the set of rules from savask's list a bit by noticing that we can evaluate so that all rules end with c even:

<pre>
(0, b, 2c) -> (2b+2, 1, 2c)

(1, b, 0) -> Halt
(1, 2b, 2c) -> (0, 1, 2(b+c+1))
(1, 2b+1, 2c) -> (2, 1, 2(b+c+3))

(a, 2b, 0) -> (a-2, 2b+3, 0)
(2, 2b+1, 0) -> (0, 1, 2b+6)
(a, 2b+1, 0) -> (a-3, 1, 2b+4)

(a, b, c) -> (a-2, b+3, c-2)
</pre>

=== Phases ===
We can think of this going through two different phases. "Even Phase" (where <code>a</code> is even) and "Odd Phase" (where <code>a</code> is odd).

<pre>
Even Phase: a,c even:
(0, b, 2c) -> (2b+2, 1, 2c)
(2a+2, 2b, 0) -> (2a, 2b+3, 0)
(2, 2b+1, 0) -> (0, 1, 2(b+3))

To Odd Phase:
(2a+4, 2b+1, 0) -> (2a+1, 1, 2b+4)

Odd Phase: a odd, c even
To Halt:
(1, b, 0) -> Halt
(3, 2b, 0) -> (1, 2b+3, 0) -> Halt

To Even Phase:
(1, 2b, 2c+2) -> (0, 1, 2(b+c+2))
(1, 2b+1, 2c+2) -> (0, 1, 2b+2c+5) -> (2, 1, 2(b+c+4))

(2a+5, 2b, 0) -> (2a+3, 2b+3, 0) -> (2a, 1, 2b+6)
(2a+3, 2b+1, 0) -> (2a, 1, 2b+4)
</pre>

So the only way for this to halt is if it is in "Even Phase" and hits (2k+8, 2k+1, 0) or (4k+12, 4k+3, 0) (which will lead to (1, b, 0) or (3, 2b, 0) eventually).
If <code>a</code> is bigger or smaller, then "Odd Phase" will end going back to "Even Phase" again.

=== Repeated (0, b, 2c) ===

Let <math>f(n) = 3n+4</math>, then<math display="block">(0, b, 2c) \to (0, f(b), 2(c - b - 1))</math> Let<math display="block">h(n) = f^n(1) + 1 = 3^{n+1} - 1</math><math display="block">g(n) = \sum_{k=0}^{n-1} h(k) = \frac{3}{2} (3^n - 1) - n</math>

Then if <math>c > g(n)</math>:<math display="block">(0, 1, 2c) \to (0, f^n(1), 2 (c-g(n))) \to (2 h(n), 1, 2 (c-g(n)))</math>

=== Repeated (0, 1, 2c) ===
https://discord.com/channels/960643023006490684/1084047886494470185/1254635277020954705

Let <math>C(n) = (0, 1, 2n)</math> = <code>0^inf 1 <A2 22 (20)^2n 0^inf</code>

<math display="block">C(g(n) + 8k+1) \to C(g(n) + 8k+1 + n+9)</math><math display="block">\forall k: \frac{h(n) - 45}{65} < k < \frac{h(n) - 22}{38}</math>

Notably, when 8 divides (n+1) then this rule can potentially be applied repeatedly.

Ex: if n = 7, then we get:<math display="block">\forall k \in [101, 172]: C(3273 + 8k) \to C(3273 + 8(k+2))</math>

And we see this starting with <math>C(4137) = C(3273 + 8 \cdot 108)</math> which repeats this rule until we get to <math>C(4665) = C(3273 + 8 \cdot 174)</math>.

And as n gets way bigger, these ranges of repeat will increase exponentially.

== A(a, c) Rules and Timings ==

Let A(a, c) = A1(a, 0, c) = <code>0^∞ 1 2^a <C (20)^c 0^∞</code>, where A1(a, b, c) comes from dyuan01's rules. Then the TM satisfies the following rules once it reaches A(0, 1) after 2 steps. Note that rules (a) and (g) aren't actually reachable from the initial condition.

{| class="wikitable" style="text-align:left"
|+ Rules and associated step counts ([https://discord.com/channels/960643023006490684/1259770474897080380/1324065684677988505 source])
! !! style="text-align:left" | A(a, c) → !! Conditions !! Step count
|-
! style="text-align:right" | (a)
| A(a−c−1, 3c/2+2) || c ≤ a−1, c ≡ 0 (mod 2) || 3c2+8c+5
|-
! style="text-align:right" | (b)
| A(a−c−2, 3(c−1)/2+5) || c ≤ a−2, c ≡ 1 (mod 4) || (6c2+31c+37)/2
|-
! style="text-align:right" | (c)
| A(a−c−4, 3(c−1)/2+8) || c ≤ a−4, c ≡ 3 (mod 4) || 3c2+29c+65
|-
! style="text-align:right" | (d)
| Halt(3(c−1)/2+7) || c = a−3, c ≡ 3 (mod 4) || (6c2+43c+75)/2
|-
! style="text-align:right" | (e)
| A(3c+8, 1) || c = a−2, c ≡ 3 (mod 4) || (6c2+37c+63)/2
|-
! style="text-align:right" | (f)
| Halt(3(c−1)/2+4) || c = a−1, c ≡ 1 (mod 2) || 3c2+8c+6
|-
! style="text-align:right" | (g)
| Halt(a/2+c+4) || c ≥ a, a ≡ 0, c ≡ 0 (mod 2) || 3a2+5a+9c+24
|-
! style="text-align:right" | (h)
| A(1, a/2+c+2) || c ≥ a, a ≡ 0, c ≡ 1 (mod 2) || 3a2+3a+5c+11
|-
! style="text-align:right" | (i)
| A(3a, c−a+4) || c ≥ a, a ≡ 1, c ≡ 0 (mod 2) || 3a2−9a+14c+30
|-
! style="text-align:right" | (j)
| A(3a+2, c−a+1) || c ≥ a, a ≡ 1, c ≡ 1 (mod 2) || 3a2+5c+6
|}

== Equivalence to 1RB0LB0RC_2LC2LA1RA_1RA1LC--- ==
{{TM|1RB0LB0RC_2LC2LA1RA_1RA1LC---}}, #153, eventually becomes equivalent to this machine. As found by [https://discord.com/channels/960643023006490684/1259770474897080380/1260244842999709726 @Legion], after running the #153 machine for 1,790,901 steps, if one permutes the states A,C, and B and exchanges 1 for 2 and L for R, it has the same configuration as TM #758 after it has run 1,841,608 steps.