BusyBeaverWiki - User contributions [en]

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

2025-07-03T10:07:30Z

Axolotldailyweek: Undo revision 2260 by Axolotldailyweek (talk)

{{machine|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}} is a halting [[BB(7)]] TM which runs for over <math>2 \uparrow^{11} 2 \uparrow^{11} 3</math> steps. 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 \; \textrm{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 \; \textrm{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">
\textrm{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>.

BB(7)

2025-07-01T18:40:04Z

Axolotldailyweek: /* Current Progress */

The 7-state, 2-symbol Busy Beaver problem, '''BB(7)''', refers to the unsolved 7th value of the [[Busy Beaver function]]. With the compilation of the [[Cryptid]] machine [[Bigfoot]] into a 7-state, 2-symbol machine in May 2024, we now know that we must solve a [[Collatz-like]] problem in order to solve BB(7).

The current BB(7) champion {{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}} was discovered by Pavel Kropitz in May 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. For 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.

Pavel's champion is enumerated in subtask 243308.

== 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|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_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|1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ}}
|10 ↑↑ 228.78
|Terry Ligocki
|-
|{{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|1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RC0LD}}
|10 ↑↑ 192.67
|Andrew Ducharme
|-
|{{TM|1RB1LA_1LC0RE_0LD1LB_1RE1LG_1RF0LG_0RA0LA_0RF1RZ}}
|10 ↑↑ 192.67
|Andrew Ducharme
|-
|{{TM|1RB1LA_1LC0RF_0LD0RD_1RF1LE_1LB1RZ_1RG0RA_0RA0LA}}
|10 ↑↑ 192.67
|@C7X
|-
|{{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
|}

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|1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ}}
|10 ↑↑ 228.78
|Terry Ligocki
|-
|{{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|1RB0LD_1RC1RA_0RD1RG_1LE1LF_0LF1LE_0RA0LD_0RA1RZ}}
|10 ↑↑ 124.86
|Terry Ligocki
|-
|{{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|1RB0RG_1LC0LE_1LD0LB_0LE1RE_0RA1RF_0RD1RC_1RD1RZ}}
|10 ↑↑ 114.83
|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|1RB0RC_1LC1LD_1RA0RD_0LF1LE_0LB1LA_0RE0LG_1LB1RZ}}
|10 ↑↑ 114.37
|@C7X
|-
|<code>1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ</code> (bbch)
|10 ↑↑ 113.38
|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"). Cells which are in '''bold font''' have already had the listed subtasks enumerated with mxdys's code, but have not been filtered by the Ligocki code. You can help! Download the enumerated TMs from the linked source in the far right column, put your name alongside the enumerator's in the "Done by" column, and return with the number of holdouts, the maximum score TM, and its approximate sigma value when you're done.

After downloading the Ligocki codebase busy-beaver-main [https://github.com/sligocki/busy-beaver here], you can install the dependencies by running `python3 -m pip install -r requirements.txt`, then perform the filtering on holdouts from subtasks between start_number and end_number by running the below command.<syntaxhighlight lang="bash">
for x in {start_number..end_number}; do busy-beaver-main/Code/Enumerate.py --infile your-path-to-holdouts/holdouts_${x}.txt --outfile your-save-path/bb7_${x}.out.pb -r --no-steps --exp-linear-rules --max-loops=100_000 --block-mult=2 --force --save-freq=100; done
</syntaxhighlight>
{| 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="2" |@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
|@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'''
|1,056,745
|TBD
|TBD
|-
|06xxxx
|@Iijil
|Yes
|'''No'''
|950,271
|TBD
|TBD
|-
|07xxxx
|@Iijil
|Yes
|'''No'''
|1,053,750
|TBD
|TBD
|-
|08xxxx
|@Iijil
|Yes
|'''No'''
|951,114
|TBD
|TBD
|-
|09xxxx
|@Iijil
|Yes
|'''No'''
|1,052,362
|TBD
|TBD
|-
|10xxxx
| rowspan="3" |Andrew Ducharme
|Yes
|Yes
|802,059
|{{TM|1RB0LG_1RC0RA_1LD0LE_1LG1LC_1LF0RB_0LC0RC_1LA1RZ}}
|10 ↑↑ 40.79
| rowspan="3" |[https://drive.google.com/drive/folders/16uDjgOahkhAMWv3v-YWmxJG7xxsBvj4h?usp=sharing Google Drive folder]
|-
|11xxxx
|Yes
|Yes
|1,105,947
|{{TM|1RB0RG_1LC0LE_1LD0LB_0LE1RE_0RA1RF_0RD1RC_1RD1RZ}}
|10 ↑↑ 114.83
|-
|12xxxx
|Yes
|Yes
|800,882
|{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD1LF_1LB0LE}}
|10 ↑↑ 519.20
|-
|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]
|-
|14xxxx
| rowspan="3" |Andrew Ducharme
|Yes
|Yes
|797,532
|{{TM|1RB0LC_1LC0LD_1LA1LB_0LG1RE_0RF0LD_0RA1RE_1RZ1LC}}
|10 ↑↑ 140.28
| rowspan="3" |[https://drive.google.com/drive/folders/16uDjgOahkhAMWv3v-YWmxJG7xxsBvj4h?usp=sharing Google Drive folder]
|-
|15xxxx
|Yes
|No
|TBD
|TBD
|TBD
|-
|16xxxx
|No
|No
|TBD
|TBD
|TBD
|-
|'''17xxxx'''
|
|'''No'''
|'''No'''
|
|
|
|
|-
|'''18xxxx'''
|
|'''No'''
|'''No'''
|
|
|
|
|-
|19xxxx
|@isokate
|No
|No
|TBD
|TBD
|TBD
|
|-
|
20xxxx
| rowspan="2" | @C7X
|Yes
|Yes
|728,510
|{{TM|1RB1LA_1LC0RF_0LD0RD_1RF1LE_1LB1RZ_1RG0RA_0RA0LA}}
|10↑↑192.67
| rowspan="2" | [https://drive.google.com/drive/folders/11iGTKsvu2Y7aFrwOcWS1LYvcN6i_7-JM?usp=sharing Google Drive folder]
|-
|
21xxxx - 
23xxxx
|Yes
|No
|3,065,946
|TBD
|TBD
|-
|24xxxx
|Andrew Ducharme
|Yes
|Yes
|712,356
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}*
|<math>2 \uparrow^{11} 2 \uparrow^{11} 3^*</math>
|[https://drive.google.com/drive/folders/16uDjgOahkhAMWv3v-YWmxJG7xxsBvj4h?usp=sharing Google Drive folder]
|-
|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
|Yes
|Yes
|812120
|{{TM|1RB1LA_1LC0RE_0LD1LB_1RE1LG_1RF0LG_0RA0LA_0RF1RZ}}
|10 ↑↑ 192.67
|-
|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
|-
|50xxxx
|@prurq
|No
|No
|~1.08M
|{{TM|1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ}}
|10 ↑↑ 115.52
|[https://drive.google.com/drive/folders/145H4sT4F9KJYGSrlIETZdBOIMR7krLQm Google Drive folder]
|-
|51xxxx
|@gerbil5709
|Yes
|'''No'''
|1,436,814
|TBD
|TBD
| rowspan="2" |[https://drive.google.com/drive/folders/1kAvBebeF09CEVocCk5bGKlDJfRN8co_i?usp=sharing Google Drive folder]
|-
|52xxxx
|@gerbil5709
|No
|'''No'''
|TBD
|TBD
|TBD
|-
|'''53xxxx'''
|
|'''No'''
|'''No'''
|
|
|
|-
|'''54xxxx'''
|
|'''No'''
|'''No'''
|
|
|
|-
|'''55xxxx'''
|
|'''No'''
|'''No'''
|
|
|
|-
|56xxxx
|Terry Ligocki
|No
|No
|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|57xxxx
|Terry Ligocki
|Yes
|Yes
|1,100,748
|{{TM|1RB1RC_0RC0RB_0RD0RE_1LD0LE_1LF0RG_1LG1RZ_1LA0LG}}
|10 ↑↑ 69.85
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|58xxxx
|Terry Ligocki
|Yes
|Yes
|795,772
|{{TM|1RB0RD_1RC0RA_1LA1LD_0LF1LE_0LC1LB_1LA0LG_1LC1RZ}}
|10 ↑↑ 115.32
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|59xxxx
|Terry Ligocki
|Yes
|Yes
|1,094,678
|{{TM|1RB0LF_0LC0RA_1LA1RD_0RE1RZ_1RC0RE_1LG1RC_0LB1RA}}
|10 ↑↑ 124.12
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|60xxxx
|@gerbil5709
|Yes
|'''No'''
|957,769
|TBD
|TBD
| rowspan="5" |[https://drive.google.com/drive/folders/1kAvBebeF09CEVocCk5bGKlDJfRN8co_i?usp=sharing Google Drive folder]
|-
|61xxxx
|@gerbil5709
|Yes
|'''No'''
|1,052,047
|TBD
|TBD
|-
|62xxxx
|@gerbil5709
|Yes
|'''No'''
|959,753
|TBD
|TBD
|-
|63xxxx
|@gerbil5709
|Yes
|'''No'''
|1,051,882
|TBD
|TBD
|-
|64xxxx
|@gerbil5709
|Yes
|'''No'''
|957,669
|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]
|-
|
72xxxx - 
79xxxx
|Terry Ligocki
|Yes
|Yes
|7,627,514
|{{TM|1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ}}
|10 ↑↑ 228.78
|[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]
|}
<nowiki>*</nowiki>The current BB(7) champion TM {{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}* was discovered by Pavel Kropitz in the enumeration of subtask 243308. The remaining subtasks in the 24xxxx range were enumerated and filtered by Andrew Ducharme.
[[Category:BB Domain]]

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

2025-06-24T20:36:37Z

Axolotldailyweek:

{{machine|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}} is a halting [[BB(7)]] TM which runs for over <math>2 \uparrow^{11} 2 \uparrow^{11} 3</math> (or <math>2 \uparrow^{11} 2 \uparrow^{10} 4</math>) steps. 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 \; \textrm{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 \; \textrm{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">
\textrm{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>.

BB(7)

2025-06-20T04:02:57Z

Axolotldailyweek: /* Current Progress */

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
[https://discord.com/channels/960643023006490684/1369339127652159509/1370678203395604562 in May 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.

Pavel's champion is enumerated in subtask 243308.

== 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 22 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|1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ}}
|10 ↑↑ 228.78
|Terry Ligocki
|-
|{{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|1RB0LD_1RC1RA_0RD1RG_1LE1LF_0LF1LE_0RA0LD_0RA1RZ}}
|10 ↑↑ 124.86
|Terry Ligocki
|-
|{{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 - 
23xxxx
|@C7X
|Yes
|No
|4,021,884
|TBD
|TBD
|[https://drive.google.com/drive/folders/11iGTKsvu2Y7aFrwOcWS1LYvcN6i_7-JM?usp=sharing Google Drive folder]
|-
|24xxxx
|Andrew Ducharme
|No
|No
|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/16uDjgOahkhAMWv3v-YWmxJG7xxsBvj4h?usp=sharing Google Drive folder]
|-
|243308
|@uni
|N/A
|N/A
|N/A
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|[https://discord.com/channels/960643023006490684/1369339127652159509/1370678203395604562 Discord May 2025]
|-
|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
|Yes
|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]
|-
|77xxxx
|Terry Ligocki
|Yes
|No
|1,435,026
|TBD
|TBD
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|78xxxx
|Terry Ligocki
|Yes
|Yes
|800,141
|{{TM|1RB0LD_1RC1RA_0RD1RG_1LE1LF_0LF1LE_0RA0LD_0RA1RZ}}
|10 ↑↑ 124.86
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|79xxxx
|Terry Ligocki
|Yes
|Yes
|1,104,247
|{{TM|1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ}}
|10 ↑↑ 228.78
|[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)

2025-06-06T06:31:31Z

Axolotldailyweek: /* Top Halters */

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 ↑↑ 133.85
|@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|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
|}
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 ↑↑ 133.85
|@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|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
|-
|{{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
|}

== 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
|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
|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
|No
|1,032,318
|TBD
|TBD
|-
|37xxxx
|Yes
|No
|1,432,632
|TBD
|TBD
|-
|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
|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 ↑↑ 133.85
|[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]
|-
|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)

2025-06-06T06:16:24Z

Axolotldailyweek: /* Top Halters */

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 ↑↑ 133.85
|@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|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
|
|}
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 ↑↑ 133.85
|@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|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
|
|-
|{{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
|}

== 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
|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
|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
|No
|1,032,318
|TBD
|TBD
|-
|37xxxx
|Yes
|No
|1,432,632
|TBD
|TBD
|-
|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
|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 ↑↑ 133.85
|[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]
|-
|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)

2025-06-06T06:15:53Z

Axolotldailyweek: /* Top Halters */

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 ↑↑ 133.85
|@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|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
|
|}
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 ↑↑ 133.85
|@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|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
|
|{{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
|}

== 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
|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
|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
|No
|1,032,318
|TBD
|TBD
|-
|37xxxx
|Yes
|No
|1,432,632
|TBD
|TBD
|-
|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
|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 ↑↑ 133.85
|[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]
|-
|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]]

Collatz-like

2025-06-05T06:08:43Z

Axolotldailyweek: I think fixed now

A '''Collatz-like function''' is a partial function defined piecewise depending on the remainder of an input modulo some number. The canonical example is the original Collatz function:<math display="block">\begin{array}{l}
c(2k) & = & k \\
c(2k+1) & = & 3k+2 \\
\end{array}</math>

A '''Collatz-like problem''' is a question about the behavior of iterating a Collatz-like function. Collatz-like problems are famously difficult.

Many [[Busy Beaver Champions]] have '''Collatz-like behavior''', meaning that their behavior can be concisely described via the iterated values of a Collatz-like function.

== Examples ==

=== BB(5,2) Champion ===
Consider the [[5-state busy beaver winner|BB(5,2) Champion]] and the generalized configuration:

<math display="block">M(n) = 0^\infty \; \textrm{<A} \; 1^n \; 0^\infty</math>Pascal Michel showed that:

<math display="block">\begin{array}{lcl}
0^\infty \; \textrm{<A} \; 0^\infty & = & M(0) \\
M(3k) & \xrightarrow{5 k^2 + 19 k + 15} & M(5k+6) \\
M(3k+1) & \xrightarrow{5 k^2 + 25 k + 27} & M(5k+9) \\
M(3k+2) & \xrightarrow{6k +12} & 0^\infty \;\; 1 \;\; \textrm{H>} \;\; 01 \;\; {(001)}^{k+1} \;\; 1 \;\; 0^\infty \\
\end{array}</math>

Starting on a blank tape <math>M(0)</math>, these rules iterate 15 times before reaching the halt config.<ref>[https://bbchallenge.org/~pascal.michel/beh#tm52a Pascal Michel's Analysis of the BB(5, 2) Champion]</ref>

=== Hydra ===
Consider [[Hydra]] (a [[Cryptids|Cryptid]]) and the generalized configuration:

<math display="block">C(a, b) = 0^\infty \; \textrm{ 
Daniel Yuan showed that:<math display="block">\begin{array}{l}
\\
0^\infty \; \textrm{A>} \; 0^\infty & & \xrightarrow{19} & C(3, 0) \\
C(2n, & 0) & \to & \text{Halt}(9n-6) \\
C(2n, & b+1) & \to & C(3n, & b) \\
C(2n+1, & b) & \to & C(3n+1, & b+2) \\
\end{array}</math>

Where <math>\textrm{Halt}(n)</math> is a halting configuration with <math>n</math> non-zero symbols on the tape.

Starting from config <math>C(3, 0)</math> this simulates a pseudo-random walk along the <math>b</math> parameter, increasing it by 2 every time <math>a</math> is odd, decreasing by 1 every time it's even. Deciding whether or not Hydra halts requires being able to prove a detailed question about the trajectory of the Collatz-like function<math display="block">\begin{array}{l}
h(2n) & = & 3n \\
h(2n+1) & = & 3n+1 \\
\end{array}</math>starting from 3:

<math display="block">\begin{array}{l}
\\
3 \xrightarrow{O} 4 \xrightarrow{E} 6\xrightarrow{E} 9 \xrightarrow{O} 13 \xrightarrow{O} 19 \xrightarrow{O} 28 \xrightarrow{E} 42 \xrightarrow{E} 63 \cdots \\
\end{array}
</math>

Specifically, will it ever reach a point where the cumulative number of <code>E</code> (even transitions) applied is greater than twice the number of <code>O</code> (odd transitions) applied?<ref>Shawn Ligocki. [https://www.sligocki.com/2024/05/10/bb-2-5-is-hard.html BB(2, 5) is Hard (Hydra)]. 10 May 2024.</ref>

=== Exponential Collatz ===
Consider the current [[1RB0LD_1RC0RF_1LC1LA_0LE1RZ_1LF0RB_0RC0RE|BB(6,2) Champion]] (discovered by Pavel Kropitz in May 2022) and consider the general configuration:<math display="block">K(n) = 0^\infty \; 1 \; 0^n \; 11 \; 0^5 \; \textrm{C>} \; 0^\infty</math>Shawn Ligocki showed that:
<math display="block">\begin{array}{l}
\\
0^\infty \; \textrm{A>} \; 0^\infty & \xrightarrow{45} & K(5) \\
K(4k) & \to & \text{Halt}(\frac{3^{k+3} - 11}{2}) \\
K(4k+1) & \to & K(\frac{3^{k+3} - 11}{2}) \\
K(4k+2) & \to & K(\frac{3^{k+3} - 11}{2}) \\
K(4k+3) & \to & K(\frac{3^{k+3} + 1}{2}) \\
\end{array}</math>

Demonstrating Collatz-like behavior with exponential piecewise component functions.

Starting from config <math>K(5)</math>, these rules iterate 15 times before reaching the halt config leaving over <math>10 \uparrow\uparrow 15</math> non-zero symbols on the tape.<ref>Shawn Ligocki. [https://www.sligocki.com/2022/06/21/bb-6-2-t15.html BB(6, 2) > 10↑↑15]. 21 Jun 2022.</ref>

== References ==
<references />
[[Category:Zoology]]

Collatz-like

2025-06-05T06:08:23Z

Axolotldailyweek: I think fixed now

A '''Collatz-like function''' is a partial function defined piecewise depending on the remainder of an input modulo some number. The canonical example is the original Collatz function:<math display="block">\begin{array}{l}
c(2k) & = & k \\
c(2k+1) & = & 6k+2 \\
\end{array}</math>

A '''Collatz-like problem''' is a question about the behavior of iterating a Collatz-like function. Collatz-like problems are famously difficult.

Many [[Busy Beaver Champions]] have '''Collatz-like behavior''', meaning that their behavior can be concisely described via the iterated values of a Collatz-like function.

== Examples ==

=== BB(5,2) Champion ===
Consider the [[5-state busy beaver winner|BB(5,2) Champion]] and the generalized configuration:

<math display="block">M(n) = 0^\infty \; \textrm{<A} \; 1^n \; 0^\infty</math>Pascal Michel showed that:

<math display="block">\begin{array}{lcl}
0^\infty \; \textrm{<A} \; 0^\infty & = & M(0) \\
M(3k) & \xrightarrow{5 k^2 + 19 k + 15} & M(5k+6) \\
M(3k+1) & \xrightarrow{5 k^2 + 25 k + 27} & M(5k+9) \\
M(3k+2) & \xrightarrow{6k +12} & 0^\infty \;\; 1 \;\; \textrm{H>} \;\; 01 \;\; {(001)}^{k+1} \;\; 1 \;\; 0^\infty \\
\end{array}</math>

Starting on a blank tape <math>M(0)</math>, these rules iterate 15 times before reaching the halt config.<ref>[https://bbchallenge.org/~pascal.michel/beh#tm52a Pascal Michel's Analysis of the BB(5, 2) Champion]</ref>

=== Hydra ===
Consider [[Hydra]] (a [[Cryptids|Cryptid]]) and the generalized configuration:

<math display="block">C(a, b) = 0^\infty \; \textrm{ 
Daniel Yuan showed that:<math display="block">\begin{array}{l}
\\
0^\infty \; \textrm{A>} \; 0^\infty & & \xrightarrow{19} & C(3, 0) \\
C(2n, & 0) & \to & \text{Halt}(9n-6) \\
C(2n, & b+1) & \to & C(3n, & b) \\
C(2n+1, & b) & \to & C(3n+1, & b+2) \\
\end{array}</math>

Where <math>\textrm{Halt}(n)</math> is a halting configuration with <math>n</math> non-zero symbols on the tape.

Starting from config <math>C(3, 0)</math> this simulates a pseudo-random walk along the <math>b</math> parameter, increasing it by 2 every time <math>a</math> is odd, decreasing by 1 every time it's even. Deciding whether or not Hydra halts requires being able to prove a detailed question about the trajectory of the Collatz-like function<math display="block">\begin{array}{l}
h(2n) & = & 3n \\
h(2n+1) & = & 3n+1 \\
\end{array}</math>starting from 3:

<math display="block">\begin{array}{l}
\\
3 \xrightarrow{O} 4 \xrightarrow{E} 6\xrightarrow{E} 9 \xrightarrow{O} 13 \xrightarrow{O} 19 \xrightarrow{O} 28 \xrightarrow{E} 42 \xrightarrow{E} 63 \cdots \\
\end{array}
</math>

Specifically, will it ever reach a point where the cumulative number of <code>E</code> (even transitions) applied is greater than twice the number of <code>O</code> (odd transitions) applied?<ref>Shawn Ligocki. [https://www.sligocki.com/2024/05/10/bb-2-5-is-hard.html BB(2, 5) is Hard (Hydra)]. 10 May 2024.</ref>

=== Exponential Collatz ===
Consider the current [[1RB0LD_1RC0RF_1LC1LA_0LE1RZ_1LF0RB_0RC0RE|BB(6,2) Champion]] (discovered by Pavel Kropitz in May 2022) and consider the general configuration:<math display="block">K(n) = 0^\infty \; 1 \; 0^n \; 11 \; 0^5 \; \textrm{C>} \; 0^\infty</math>Shawn Ligocki showed that:
<math display="block">\begin{array}{l}
\\
0^\infty \; \textrm{A>} \; 0^\infty & \xrightarrow{45} & K(5) \\
K(4k) & \to & \text{Halt}(\frac{3^{k+3} - 11}{2}) \\
K(4k+1) & \to & K(\frac{3^{k+3} - 11}{2}) \\
K(4k+2) & \to & K(\frac{3^{k+3} - 11}{2}) \\
K(4k+3) & \to & K(\frac{3^{k+3} + 1}{2}) \\
\end{array}</math>

Demonstrating Collatz-like behavior with exponential piecewise component functions.

Starting from config <math>K(5)</math>, these rules iterate 15 times before reaching the halt config leaving over <math>10 \uparrow\uparrow 15</math> non-zero symbols on the tape.<ref>Shawn Ligocki. [https://www.sligocki.com/2022/06/21/bb-6-2-t15.html BB(6, 2) > 10↑↑15]. 21 Jun 2022.</ref>

== References ==
<references />
[[Category:Zoology]]

BB(7)

2025-05-30T22:33:24Z

Axolotldailyweek:

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 some of the top known halting machines are:
{| class="wikitable"
!TM
!Approximate sigma score
|-
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|-
|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}}
|10 ↑↑ 286
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG}}
|10 ↑↑ 193
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LF0RF_0RA1RE_1RZ0RE}}
|10 ↑↑ 188
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LF0RF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_1LG1RE_1LF0RF_0RA1RE_1RZ0RA}}
|10 ↑↑ 188
|-
|{{TM|1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ}}
|10 ↑↑ 117
|-
|{{TM|1RB0RD_1RC0LA_0LA0LE_1RE1RZ_1RF0RA_1LG0LE_1LC0LG}}
|10 ↑↑ 116.05
|-
|{{TM|1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ}}
|10 ↑↑ 114.60
|-
|{{TM|1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ}}
|10 ↑↑ 113
|-
|{{TM|1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG}}
|10 ↑↑ 93.81
|-
|{{TM|1RB0RF_1LC0LD_1RC0LB_1LE1RG_1RA1RE_1RD0RD_0RA1RZ}}
|10 ↑↑ 93.78
|-
|{{TM|1RB1RF_1LC1LB_0RE0LD_0LC0LB_0RA1RE_1RG1RZ_0LG0RA}}
{{TM|1RB1RF_1LC1LB_0RE0LD_0LC0LB_0RA1RE_1RG1RZ_0LG0LE}}
|10 ↑↑ 63
|-
|{{TM|1RB0RE_1LC0RB_1LD0RC_1LE0LF_1RA0LD_1LD1LG_1LF1RZ}}
|10 ↑↑ 55
|-
|{{TM|1RB0RG_0RC0RF_1LD0RA_0LE0LA_1RA0LC_0LG1LC_1RE1RZ}}
|10 ↑↑ 51
|-
|{{TM|1RB1RZ_1RC0RG_0RD1RB_0LE0RB_0LF0RA_1LB1RF_1RE1LD}}
|10 ↑↑ 50
|-
|{{TM|1RB0RF_1RC1LF_0RD0RD_1LE0LB_1RA1RZ_1LG1RA_1LD0RC}}
|10 ↑↑ 46
|-
|{{TM|1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC}}
|10 ↑↑ 35
|}

== 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"
!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
|style="text-align:right;"|728495
|{{TM|1RB0RF_1RC1LF_0RD0RD_1LE0LB_1RA1RZ_1LG1RA_1LD0RC}}
|10 ↑↑ 46
|rowspan="5"|[https://drive.google.com/drive/folders/1wniwrAuvsHfkvro8Tg65WAMNZEuIekzD Google Drive folder]
|-
|01xxxx
|@Iijil
|Yes
|No
|style="text-align:right;"|1,056,253
|TBD
|TBD
|-
|02xxxx
|@Iijil
|Yes
|No
|style="text-align:right;"|963,486
|TBD
|TBD
|-
|03xxxx
|@Iijil
|Yes
|No
|style="text-align:right;"|1,052,504
|TBD
|TBD
|-
|04xxxx
|@Iijil
|Yes
|No
|style="text-align:right;"|955,711
|TBD
|TBD
|-
|13xxxx
|Shawn Ligocki
|Yes
|Yes
|style="text-align:right;"|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
|@C7X
|Yes
|No
|style="text-align:center;"|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/11iGTKsvu2Y7aFrwOcWS1LYvcN6i_7-JM?usp=sharing Google Drive folder]
|-
|243308
|@uni
|Yes
|No
|style="text-align:center;"|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
|style="text-align:right;"|1,056,591
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|26xxxx
|@stokastic
|Yes
|No
|style="text-align:right;"|958,289
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|27xxxx
|@stokastic
|Yes
|No
|style="text-align:right;"|1,052,946
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|28xxxx
|@stokastic
|Yes
|No
|style="text-align:right;"|956,935
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|29xxxx
|@stokastic
|Yes
|No
|style="text-align:right;"|1,052,415
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|30xxxx
|@stokastic
|Yes
|No
|style="text-align:center;"|1,032,095
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|31xxxx
|@stokastic
|Yes
|No
|1,436,970
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|43xxxx
| rowspan="2" |Andrew Ducharme
|Yes
|Yes
|style="text-align:right;"|817,332
|{{TM|1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG}}
|10 ↑↑ 93
| rowspan="2" |[https://drive.google.com/drive/folders/16uDjgOahkhAMWv3v-YWmxJG7xxsBvj4h?usp=sharing Google Drive folder]
|-
|44xxxx
|No
|No
|TBD
|TBD
|TBD
|-
|49xxxx
|Tobiáš Brichta
|No
|No
|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/1-csgJ5uSIX3SKlqTkSnhkUuEYLKgCw81 Google Drive folder]
|-
|500xxx
|@prurq
|Yes
|No
|style="text-align:center;"|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/145H4sT4F9KJYGSrlIETZdBOIMR7krLQm Google Drive folder]
|-
|69xxxx
|@poppuncher
|Yes
|No
|1,053,119
|TBD
|TBD
|[https://drive.google.com/drive/folders/1KlCZqXxqVPuBPkDcCBocuMPA8paq9b8P?usp=drive_link Google Drive folder]
|-
|
700xxx -
701xxx
|@hipparcos
|Yes
|Yes
|style="text-align:right;"|160,792
|{{TM|1RB0LF_1LC1LE_1RE0LD_0LC0LA_1LB1RA_0LG0RC_1RZ0LA}}
|10 ↑↑ 26
|[https://discord.com/channels/960643023006490684/1369339127652159509/1372088267364634704 Posted to Discord]
|-
|
80xxxx
|@xnoobspeakable
|Yes
|No
|style="text-align:right;"|964,396
|TBD
|TBD
|[https://drive.google.com/drive/folders/1TpuEC7KottEmvsFnCREugnlVMPaY5ZHi?usp=sharing Google Drive folder]
|-
|85xxxx
|Terry Ligocki
|Yes
|No
|style="text-align:center;"|1,050,753
|TBD
|TBD
|rowspan="6"|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|86xxxx
|Terry Ligocki
|Yes
|No
|style="text-align:right;"|952,102
|TBD
|TBD
|-
|87xxxx
|Terry Ligocki
|Yes
|Yes
|style="text-align:right;"|813,349
|{{TM|1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ}}
|10 ↑↑ 117
|-
|88xxxx
|Terry Ligocki
|Yes
|Yes
|style="text-align:right;"|727,990
|{{TM|1RB0RE_1LC0RB_1LD0RC_1LE0LF_1RA0LD_1LD1LG_1LF1RZ}}
|10 ↑↑ 55
|-
|89xxxx
|Terry Ligocki
|Yes
|Yes
|style="text-align:right;"|804,470
|{{TM|1RB1LD_1LC1RE_0RA0LB_1LA0LE_1RC0RF_0RC1RG_1RZ0RB}}
|10 ↑↑ 32
|-
|9xxxxx
|Terry Ligocki
|Yes
|Yes
|style="text-align:right;"|9,516,852
|
{{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|1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ}}
|
10 ↑↑ 286 
10 ↑↑ 193 
10 ↑↑ 188 
10 ↑↑ 113
|}
[[Category:BB Domain]]

BB(7)

2025-05-30T09:39:16Z

Axolotldailyweek: /* Top Halters */

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 some of the top known halting machines are:
{| class="wikitable"
!TM
!Approximate sigma score
|-
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|-
|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}}
|10 ↑↑ 286
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG}}
|10 ↑↑ 193
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LF0RF_0RA1RE_1RZ0RE}}
|10 ↑↑ 188
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LF0RF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_1LG1RE_1LF0RF_0RA1RE_1RZ0RA}}
|10 ↑↑ 188
|-
|{{TM|1RB0RD_1RC0LA_0LA0LE_1RE1RZ_1RF0RA_1LG0LE_1LC0LG}}
|10 ↑↑ 116.05
|-
|{{TM|1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ}}
|10 ↑↑ 114.60
|-
|{{TM|1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ}}
|10 ↑↑ 113
|-
|{{TM|1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG}}
|10 ↑↑ 93.81
|-
|{{TM|1RB0RF_1LC0LD_1RC0LB_1LE1RG_1RA1RE_1RD0RD_0RA1RZ}}
|10 ↑↑ 93.78
|-
|{{TM|1RB1RF_1LC1LB_0RE0LD_0LC0LB_0RA1RE_1RG1RZ_0LG0RA}}
{{TM|1RB1RF_1LC1LB_0RE0LD_0LC0LB_0RA1RE_1RG1RZ_0LG0LE}}
|10 ↑↑ 63
|-
|{{TM|1RB0RE_1LC0RB_1LD0RC_1LE0LF_1RA0LD_1LD1LG_1LF1RZ}}
|10 ↑↑ 55
|-
|{{TM|1RB0RG_0RC0RF_1LD0RA_0LE0LA_1RA0LC_0LG1LC_1RE1RZ}}
|10 ↑↑ 51
|-
|{{TM|1RB1RZ_1RC0RG_0RD1RB_0LE0RB_0LF0RA_1LB1RF_1RE1LD}}
|10 ↑↑ 50
|-
|{{TM|1RB0RF_1RC1LF_0RD0RD_1LE0LB_1RA1RZ_1LG1RA_1LD0RC}}
|10 ↑↑ 46
|-
|{{TM|1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC}}
|10 ↑↑ 35
|}

== 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"
!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
|style="text-align:right;"|728495
|{{TM|1RB0RF_1RC1LF_0RD0RD_1LE0LB_1RA1RZ_1LG1RA_1LD0RC}}
|10 ↑↑ 46
| rowspan="5" |[https://drive.google.com/drive/folders/1wniwrAuvsHfkvro8Tg65WAMNZEuIekzD Google Drive folder]
|-
|01xxxx
|@Iijil
|Yes
|No
|style="text-align:right;"|1,056,253
|TBD
|TBD
|-
|02xxxx
|@Iijil
|Yes
|No
|style="text-align:right;"|963,486
|TBD
|TBD
|-
|03xxxx
|@Iijil
|Yes
|No
|style="text-align:right;"|1,052,504
|TBD
|TBD
|-
|04xxxx
|@Iijil
|Yes
|No
|style="text-align:right;"|955,711
|TBD
|TBD
|-
|13xxxx
|Shawn Ligocki
|Yes
|Yes
|style="text-align:right;"|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
|@C7X
|Yes
|No
|style="text-align:center;"|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/11iGTKsvu2Y7aFrwOcWS1LYvcN6i_7-JM?usp=sharing Google Drive folder]
|-
|243308
|@uni
|Yes
|No
|style="text-align:center;"|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
|style="text-align:right;"|1,056,591
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|26xxxx
|@stokastic
|Yes
|No
|style="text-align:right;"|958,289
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|27xxxx
|@stokastic
|Yes
|No
|style="text-align:right;"|1,052,946
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|28xxxx
|@stokastic
|Yes
|No
|style="text-align:right;"|956,935
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|29xxxx
|@stokastic
|Yes
|No
|style="text-align:right;"|1,052,415
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|30xxxx
|@stokastic
|Yes
|No
|style="text-align:center;"|1,032,095
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|31xxxx
|@stokastic
|Yes
|No
|1,436,970
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|43xxxx
|Andrew Ducharme
|Yes
|Yes
|style="text-align:right;"|817,332
|{{TM|1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG}}
|10 ↑↑ 93
|[https://drive.google.com/drive/folders/16uDjgOahkhAMWv3v-YWmxJG7xxsBvj4h?usp=sharing Google Drive folder]
|-
|49xxxx
|Tobiáš Brichta
|No
|No
|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/1-csgJ5uSIX3SKlqTkSnhkUuEYLKgCw81 Google Drive folder]
|-
|500xxx
|@prurq
|Yes
|No
|style="text-align:center;"|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/145H4sT4F9KJYGSrlIETZdBOIMR7krLQm Google Drive folder]
|-
|69xxxx
|@poppuncher
|Yes
|No
|1,053,119
|TBD
|TBD
|[https://drive.google.com/drive/folders/1KlCZqXxqVPuBPkDcCBocuMPA8paq9b8P?usp=drive_link Google Drive folder]
|-
|
700xxx -
701xxx
|@hipparcos
|Yes
|Yes
|style="text-align:right;"|160,792
|{{TM|1RB0LF_1LC1LE_1RE0LD_0LC0LA_1LB1RA_0LG0RC_1RZ0LA}}
|10 ↑↑ 26
|[https://discord.com/channels/960643023006490684/1369339127652159509/1372088267364634704 Posted to Discord]
|-
|
80xxxx
|@xnoobspeakable
|Yes
|No
|style="text-align:right;"|964,396
|TBD
|TBD
|[https://drive.google.com/drive/folders/1TpuEC7KottEmvsFnCREugnlVMPaY5ZHi?usp=sharing Google Drive folder]
|-
|85xxxx
|Terry Ligocki
|Yes
|No
|style="text-align:center;"|1,050,753
|TBD
|TBD
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|86xxxx
|Terry Ligocki
|Yes
|No
|style="text-align:right;"|952,102
|TBD
|TBD
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|87xxxx
|Terry Ligocki
|Yes
|No
|style="text-align:right;"|1,049,036
|TBD
|TBD
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|88xxxx
|Terry Ligocki
|Yes
|Yes
|style="text-align:right;"|727,990
|{{TM|1RB0RE_1LC0RB_1LD0RC_1LE0LF_1RA0LD_1LD1LG_1LF1RZ}}
|10 ↑↑ 55
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|89xxxx
|Terry Ligocki
|Yes
|Yes
|style="text-align:right;"|804,470
|{{TM|1RB1LD_1LC1RE_0RA0LB_1LA0LE_1RC0RF_0RC1RG_1RZ0RB}}
|10 ↑↑ 32
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|9xxxxx
|Terry Ligocki
|Yes
|Yes
|style="text-align:right;"|9,516,852
|
{{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|1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ}}
|
10 ↑↑ 286 
10 ↑↑ 193 
10 ↑↑ 188 
10 ↑↑ 113
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|}
[[Category:BB Domain]]

BB(7)

2025-05-22T19:19:53Z

Axolotldailyweek: /* Top Halters */

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 some of the top known halting machines are:
{| class="wikitable"
!TM
!Approximate sigma score
|-
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|-
|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}}
|10 ↑↑ 286
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG}}
|10 ↑↑ 193
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LF0RF_0RA1RE_1RZ0RE}}
|10 ↑↑ 188
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LF0RF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_1LG1RE_1LF0RF_0RA1RE_1RZ0RA}}
|10 ↑↑ 188
|-
|{{TM|1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ}}
|10 ↑↑ 113
|-
|{{TM|1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG}}
|10 ↑↑ 93.81
|-
|{{TM|1RB0RF_1LC0LD_1RC0LB_1LE1RG_1RA1RE_1RD0RD_0RA1RZ}}
|10 ↑↑ 93.78
|-
|{{TM|1RB1RF_1LC1LB_0RE0LD_0LC0LB_0RA1RE_1RG1RZ_0LG0RA}}
{{TM|1RB1RF_1LC1LB_0RE0LD_0LC0LB_0RA1RE_1RG1RZ_0LG0LE}}
|10 ↑↑ 63
|-
|{{TM|1RB0RG_0RC0RF_1LD0RA_0LE0LA_1RA0LC_0LG1LC_1RE1RZ}}
|10 ↑↑ 51
|-
|{{TM|1RB1RZ_1RC0RG_0RD1RB_0LE0RB_0LF0RA_1LB1RF_1RE1LD}}
|10 ↑↑ 50
|-
|{{TM|1RB0RF_1RC1LF_0RD0RD_1LE0LB_1RA1RZ_1LG1RA_1LD0RC}}
|10 ↑↑ 46
|-
|{{TM|1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC}}
|10 ↑↑ 35
|}

== 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"
!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
|style="text-align:right;"|728495
|{{TM|1RB0RF_1RC1LF_0RD0RD_1LE0LB_1RA1RZ_1LG1RA_1LD0RC}}
|10 ↑↑ 46
| rowspan="5" |[https://drive.google.com/drive/folders/1wniwrAuvsHfkvro8Tg65WAMNZEuIekzD Google Drive folder]
|-
|01xxxx
|@Iijil
|Yes
|No
|style="text-align:right;"|1,056,253
|TBD
|TBD
|-
|02xxxx
|@Iijil
|Yes
|No
|style="text-align:right;"|963,486
|TBD
|TBD
|-
|03xxxx
|@Iijil
|Yes
|No
|style="text-align:right;"|1,052,504
|TBD
|TBD
|-
|04xxxx
|@Iijil
|Yes
|No
|style="text-align:right;"|955,711
|TBD
|TBD
|-
|13xxxx
|Shawn Ligocki
|Yes
|Yes
|style="text-align:right;"|1,437,978
|{{TM|1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC}}
|10 ↑↑ 35
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|20xxxx
|@C7X
|Yes
|No
|style="text-align:center;"|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/11iGTKsvu2Y7aFrwOcWS1LYvcN6i_7-JM?usp=sharing Google Drive folder]
|-
|243308
|@uni
|Yes
|No
|style="text-align:center;"|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
|No
|No
|style="text-align:center;"|1,056,591
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|43xxxx
|Andrew Ducharme
|No
|No
|style="text-align:center;"|TBD
|{{TM|1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG}}
|10 ↑↑ 93
|[https://drive.google.com/drive/folders/16uDjgOahkhAMWv3v-YWmxJG7xxsBvj4h?usp=sharing Google Drive folder]
|-
|500xxx
|@prurq
|Yes
|No
|style="text-align:center;"|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/145H4sT4F9KJYGSrlIETZdBOIMR7krLQm Google Drive folder]
|-
|700xxx
701xxx
|@hipparcos
|Yes
|Yes
|style="text-align:right;"|160,792
|{{TM|1RB0LF_1LC1LE_1RE0LD_0LC0LA_1LB1RA_0LG0RC_1RZ0LA}}
|10 ↑↑ 26
|[https://discord.com/channels/960643023006490684/1369339127652159509/1372088267364634704 Posted to Discord]
|-
|90xxxx
|Terry Ligocki
|Yes
|No
|style="text-align:right;"|1,025,733
|TBD
|TBD
| rowspan="10" |[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|91xxxx
|Terry Ligocki
|Yes
|No
|style="text-align:right;"|1,437,031
|TBD
|TBD
|-
|92xxxx
|Terry Ligocki
|Yes
|Yes
|style="text-align:right;"|806,127
|{{TM|1RB1RZ_1RC1RA_1RD0RB_1LE0RF_1LG0LD_1RD1RB_0LB0LG}}
|10 ↑↑ 48
|-
|93xxxx
|Terry Ligocki
|Yes
|Yes
|style="text-align:right;"|1,101,660
|{{TM|1RB1RA_1LC1RF_1LD1LB_1RE1LG_1LF0LE_0RA0RB_1LE1RZ}}
|10 ↑↑ 41
|-
|94xxxx
|Terry Ligocki
|Yes
|No
|style="text-align:right;"|1,040,565
|TBD
|TBD
|-
|95xxxx-99xxxx
|Terry Ligocki
|Yes
|Yes
|style="text-align:right;"|6,381,012
|
{{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|1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ}} 
{{TM|1RB0RF_1LC0LD_1RC0LB_1LE1RG_1RA1RE_1RD0RD_0RA1RZ}}
|
10 ↑↑ 286 
10 ↑↑ 193 
10 ↑↑ 188 
10 ↑↑ 113 
10 ↑↑ 94
|}
[[Category:BB Domain]]

BB(7)

2025-05-22T19:19:35Z

Axolotldailyweek:

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 some of the top known halting machines are:
{| class="wikitable"
!TM
!Approximate sigma score
|-
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|-
|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}}
|10 ↑↑ 286
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG}}
|10 ↑↑ 193
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LF0RF_0RA1RE_1RZ0RE}}
|10 ↑↑ 188
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LF0RF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_1LG1RE_1LF0RF_0RA1RE_1RZ0RA}}
|10 ↑↑ 188
|-
|{{TM|1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ}}
|10 ↑↑ 113
|-
|{{TM|1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG}}
|10 ↑↑ 93.81
|-
|{{TM|1RB0RF_1LC0LD_1RC0LB_1LE1RG_1RA1RE_1RD0RD_0RA1RZ}}
|10 ↑↑ 93.78
|-
|{{TM|1RB1RF_1LC1LB_0RE0LD_0LC0LB_0RA1RE_1RG1RZ_0LG0RA}}
{{TM|1RB1RF_1LC1LB_0RE0LD_0LC0LB_0RA1RE_1RG1RZ_0LG0LE}}
|10 ↑↑ 63
|-
|{{TM|1RB0RG_0RC0RF_1LD0RA_0LE0LA_1RA0LC_0LG1LC_1RE1RZ}}
|10 ↑↑ 51
|-
|{{TM|1RB1RZ_1RC0RG_0RD1RB_0LE0RB_0LF0RA_1LB1RF_1RE1LD}}
|10 ↑↑ 50
|-
|{{TM|1RB0RF_1RC1LF_0RD0RD_1LE0LB_1RA1RZ_1LG1RA_1LD0RC}}*
|10 ↑↑ 46
|-
|{{TM|1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC}}
|10 ↑↑ 35
|}

== 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"
!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
|style="text-align:right;"|728495
|{{TM|1RB0RF_1RC1LF_0RD0RD_1LE0LB_1RA1RZ_1LG1RA_1LD0RC}}
|10 ↑↑ 46
| rowspan="5" |[https://drive.google.com/drive/folders/1wniwrAuvsHfkvro8Tg65WAMNZEuIekzD Google Drive folder]
|-
|01xxxx
|@Iijil
|Yes
|No
|style="text-align:right;"|1,056,253
|TBD
|TBD
|-
|02xxxx
|@Iijil
|Yes
|No
|style="text-align:right;"|963,486
|TBD
|TBD
|-
|03xxxx
|@Iijil
|Yes
|No
|style="text-align:right;"|1,052,504
|TBD
|TBD
|-
|04xxxx
|@Iijil
|Yes
|No
|style="text-align:right;"|955,711
|TBD
|TBD
|-
|13xxxx
|Shawn Ligocki
|Yes
|Yes
|style="text-align:right;"|1,437,978
|{{TM|1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC}}
|10 ↑↑ 35
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|20xxxx
|@C7X
|Yes
|No
|style="text-align:center;"|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/11iGTKsvu2Y7aFrwOcWS1LYvcN6i_7-JM?usp=sharing Google Drive folder]
|-
|243308
|@uni
|Yes
|No
|style="text-align:center;"|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
|No
|No
|style="text-align:center;"|1,056,591
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|43xxxx
|Andrew Ducharme
|No
|No
|style="text-align:center;"|TBD
|{{TM|1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG}}
|10 ↑↑ 93
|[https://drive.google.com/drive/folders/16uDjgOahkhAMWv3v-YWmxJG7xxsBvj4h?usp=sharing Google Drive folder]
|-
|500xxx
|@prurq
|Yes
|No
|style="text-align:center;"|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/145H4sT4F9KJYGSrlIETZdBOIMR7krLQm Google Drive folder]
|-
|700xxx
701xxx
|@hipparcos
|Yes
|Yes
|style="text-align:right;"|160,792
|{{TM|1RB0LF_1LC1LE_1RE0LD_0LC0LA_1LB1RA_0LG0RC_1RZ0LA}}
|10 ↑↑ 26
|[https://discord.com/channels/960643023006490684/1369339127652159509/1372088267364634704 Posted to Discord]
|-
|90xxxx
|Terry Ligocki
|Yes
|No
|style="text-align:right;"|1,025,733
|TBD
|TBD
| rowspan="10" |[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|91xxxx
|Terry Ligocki
|Yes
|No
|style="text-align:right;"|1,437,031
|TBD
|TBD
|-
|92xxxx
|Terry Ligocki
|Yes
|Yes
|style="text-align:right;"|806,127
|{{TM|1RB1RZ_1RC1RA_1RD0RB_1LE0RF_1LG0LD_1RD1RB_0LB0LG}}
|10 ↑↑ 48
|-
|93xxxx
|Terry Ligocki
|Yes
|Yes
|style="text-align:right;"|1,101,660
|{{TM|1RB1RA_1LC1RF_1LD1LB_1RE1LG_1LF0LE_0RA0RB_1LE1RZ}}
|10 ↑↑ 41
|-
|94xxxx
|Terry Ligocki
|Yes
|No
|style="text-align:right;"|1,040,565
|TBD
|TBD
|-
|95xxxx-99xxxx
|Terry Ligocki
|Yes
|Yes
|style="text-align:right;"|6,381,012
|
{{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|1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ}} 
{{TM|1RB0RF_1LC0LD_1RC0LB_1LE1RG_1RA1RE_1RD0RD_0RA1RZ}}
|
10 ↑↑ 286 
10 ↑↑ 193 
10 ↑↑ 188 
10 ↑↑ 113 
10 ↑↑ 94
|}
[[Category:BB Domain]]

BB(7)

2025-05-20T01:08:03Z

Axolotldailyweek:

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 some of the top known halting machines are:
{| class="wikitable"
!TM
!Approximate sigma score
|-
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|-
|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}}
|10 ↑↑ 286
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188
|-
|{{TM|1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ}}
|10 ↑↑ 113
|-
|{{TM|1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG}}
|10 ↑↑ 93.81
|-
|{{TM|1RB0RF_1LC0LD_1RC0LB_1LE1RG_1RA1RE_1RD0RD_0RA1RZ}}
|10 ↑↑ 93.78
|-
|{{TM|1RB1RF_1LC1LB_0RE0LD_0LC0LB_0RA1RE_1RG1RZ_0LG0RA}}
{{TM|1RB1RF_1LC1LB_0RE0LD_0LC0LB_0RA1RE_1RG1RZ_0LG0LE}}
|10 ↑↑ 63
|-
|{{TM|1RB0RG_0RC0RF_1LD0RA_0LE0LA_1RA0LC_0LG1LC_1RE1RZ}}
|10 ↑↑ 51
|-
|{{TM|1RB1RZ_1RC0RG_0RD1RB_0LE0RB_0LF0RA_1LB1RF_1RE1LD}}
|10 ↑↑ 50
|-
|{{TM|1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC}}
|10 ↑↑ 35
|}

== 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"
!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
|728495
|{{TM|1RB0RF_1RC1LF_0RD0RD_1LE0LB_1RA1RZ_1LG1RA_1LD0RC}}
|10 ↑↑ 46
| rowspan="5" |[https://drive.google.com/drive/folders/1wniwrAuvsHfkvro8Tg65WAMNZEuIekzD Google Drive folder]
|-
|01xxxx
|@Iijil
|Yes
|No
|1056253
|TBD
|TBD
|-
|02xxxx
|@Iijil
|Yes
|No
|963486
|TBD
|TBD
|-
|03xxxx
|@Iijil
|Yes
|No
|1052504
|TBD
|TBD
|-
|04xxxx
|@Iijil
|Yes
|No
|955711
|TBD
|TBD
|-
|13xxxx
|Shawn Ligocki
|No
|No
|TBD
|TBD
|TBD
| rowspan="3" |TBE
|-
|138xxx
|Shawn Ligocki
|Yes
|Yes
|129930
|{{TM|1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC}}
|10 ↑↑ 35
|-
|139xxx
|Shawn Ligocki
|Yes
|No
|155407
|TBD
|TBD
|-
|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
|No
|No
|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|43xxxx
|Andrew Ducharme
|No
|No
|TBD
|{{TM|1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG}}
|10 ↑↑ 93
|TBE
|-
|500xxx
|@prurq
|Yes
|No
|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/145H4sT4F9KJYGSrlIETZdBOIMR7krLQm Google Drive folder]
|-
|700000-701999
|@hipparcos
|Yes
|Yes
|160792
|{{TM|1RB0LF_1LC1LE_1RE0LD_0LC0LA_1LB1RA_0LG0RC_1RZ0LA}}
|10 ↑↑ 26
|[https://discord.com/channels/960643023006490684/1369339127652159509/1372088267364634704 Posted to Discord]
|-
|90xxxx
|Terry Ligocki
|Yes
|No
|1025733
|TBD
|TBD
| rowspan="10" |[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|91xxxx
|Terry Ligocki
|Yes
|No
|1437031
|TBD
|TBD
|-
|92xxxx
|Terry Ligocki
|Yes
|No
|1037736
|TBD
|TBD
|-
|93xxxx
|Terry Ligocki
|Yes
|No
|1436093
|TBD
|TBD
|-
|94xxxx
|Terry Ligocki
|Yes
|No
|1040565
|TBD
|TBD
|-
|95xxxx
|Terry Ligocki
|Yes
|No
|1434203
|TBD
|TBD
|-
|96xxxx
|Terry Ligocki
|Yes
|No
|1036863
|TBD
|TBD
|-
|97xxxx
|Terry Ligocki
|Yes
|Yes
|1436051
|{{TM|1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ}}
|10 ↑↑ 113
|-
|98xxxx
|Terry Ligocki
|Yes
|Yes
|797084
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188
|-
|99xxxx
|Terry Ligocki
|Yes
|Yes
|1105427
|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}}
|10 ↑↑ 286
|}
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