BB(7)

2025-05-29T20:42:42Z

Tobias B.: mark tasks I am in the process of running

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|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
|No
|No
|TBD
|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]
|-
|
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
|No
|style="text-align:right;"|951,627
|TBD
|TBD
|[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]]

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BB(7)