BB(7): Difference between revisions

Revision as of 23:41, 17 July 2025

The 7-state, 2-symbol Busy Beaver problem, BB(7), refers to the unsolved 7^th 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 1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch) was discovered by Pavel Kropitz in May 2025, proving the lower bound:

S(7)>\Sigma (7)>2\uparrow ^{11}2\uparrow ^{11}3

History

Before 2025, the only known BB(7) champions were produced by hand, not by search. In 1964, Milton Green designed a machine that had sigma score 22,961. In 2014, Wythagoras modified a BB(6) champion to produce a machine that had sigma score $>10\uparrow \uparrow 5$ .

In May 2025, mxdys shared 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, 1RB0RF_1LC0RE_1RD1LB_1LA1LD_0RA0LE_1RG0LB_1RZ1RB (bbch) and 1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC (bbch), with sigma scores of approximately 10 ↑↑ 22 and 10 ↑↑ 35. That evening, Terry Ligocki found 1RB0LG_1RC0RF_1LD1RZ_1LF0LE_1RA1LD_1LG1RE_0LB0LB (bbch), with sigma score ~10 ↑↑ 46. A few days later, Pavel found a TM that outpaces all of them.

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:

TM	Approximate sigma score	Discoverer
`1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF` (bbch)	$2\uparrow ^{11}2\uparrow ^{11}3$	Pavel Kropitz
`1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE` (bbch)	10 ↑↑ 519.20	Andrew Ducharme
`1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD1LF_1LB0LE` (bbch)	10 ↑↑ 519.20	Andrew Ducharme
`1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD0LG_1LB0LE` (bbch)	10 ↑↑ 519.20	@gerbil5709, Terry Ligocki
`1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ` (bbch)	10 ↑↑ 286.17	Terry Ligocki
`1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD` (bbch)	10 ↑↑ 246.32	@Iijil
`1RB1RZ_1RC0LE_0RD1RB_1LE1RA_1LF0LG_0LG0RG_1LB1RG` (bbch)	10 ↑↑ 243.88	@Iijil, Andrew Ducharme
`1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ` (bbch)	10 ↑↑ 228.78	Terry Ligocki
`1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RG0LD` (bbch)	10 ↑↑ 192.67	Terry Ligocki
`1RB1LA_1LC0RE_0LD1LB_1RD0LA_1RF0RA_0RG0LA_1RB1RZ` (bbch)	10 ↑↑ 192.67	Terry Ligocki
`1RB1LA_1LC0RE_0LD1LB_1RD0LA_1RF0RA_1RG0LA_0LE1RZ` (bbch)	10 ↑↑ 192.67	Terry Ligocki
`1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG` (bbch)	10 ↑↑ 192.67	Terry Ligocki
`1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RG0LG_1RB1LG` (bbch)	10 ↑↑ 192.67	Terry Ligocki
`1RB1RZ_1LC0RE_0LD1LB_1RE0LG_1RF0RG_0RA0LG_1RB1LG` (bbch)	10 ↑↑ 192.67	Terry Ligocki
`1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RC0LD` (bbch)	10 ↑↑ 192.67	Andrew Ducharme
`1RB1LA_1LC0RE_0LD1LB_1RE1LG_1RF0LG_0RA0LA_0RF1RZ` (bbch)	10 ↑↑ 192.67	Andrew Ducharme
`1RB1LA_1LC0RF_0LD0RD_1RF1LE_1LB1RZ_1RG0RA_0RA0LA` (bbch)	10 ↑↑ 192.67	@C7X
`1RB1LA_1LC0RE_0LD1LB_1RE0LA_1RF0RA_0RG0LA_1RB1RZ` (bbch)	10 ↑↑ 192.67	@Iijil, Terry Ligocki
`1RB1LA_1LC0RE_0LD1LB_1RE0LA_1RF0RA_1RG0LA_0LE1RZ` (bbch)	10 ↑↑ 192.67	@Iijil, Terry Ligocki
`1RB1LA_1LC0RE_0LD1LB_1RE0LG_1RF0RA_0RA0LA_1RB1RZ` (bbch)	10 ↑↑ 192.67	@Iijil, Terry Ligocki

The top 20 known halters with unique scores are:

TM	Approximate sigma score	Discoverer
`1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF` (bbch)	$2\uparrow ^{11}2\uparrow ^{11}3$	Pavel Kropitz
`1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE` (bbch)	10 ↑↑ 519.20	Andrew Ducharme
`1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ` (bbch)	10 ↑↑ 286.17	Terry Ligocki
`1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD` (bbch)	10 ↑↑ 246.32	@Iijil
`1RB1RZ_1RC0LE_0RD1RB_1LE1RA_1LF0LG_0LG0RG_1LB1RG` (bbch)	10 ↑↑ 243.88	@Iijil, Andrew Ducharme
`1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ` (bbch)	10 ↑↑ 228.78	Terry Ligocki
`1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG` (bbch)	10 ↑↑ 192.67	Terry Ligocki
`1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA` (bbch)	10 ↑↑ 188.28	Terry Ligocki
`1RB0LC_1LC0LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LC` (bbch)	10 ↑↑ 140.28	@stokastic
`1RB0RF_1RC1RZ_0LD1RF_0RA1LE_0LC1LF_1LE0RG_0LE1RA` (bbch)	10 ↑↑ 136.64	Katelyn Doucette, Andrew Ducharme
`1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG` (bbch)	10 ↑↑ 133.85	@poppuncher
`1RB1RZ_1RC0RF_1LD1RB_1RG0LE_1LD0RA_1RE0LD_0RC1LF` (bbch)	10 ↑↑ 129.24	@Iijil
`1RB0LC_1RC0RG_1RD0LF_1RE0RF_1LA1RG_1LE1LF_1RZ1RD` (bbch)	10 ↑↑ 126.20	@stokastic
`1RB0LD_1RC1RA_0RD1RG_1LE1LF_0LF1LE_0RA0LD_0RA1RZ` (bbch)	10 ↑↑ 124.86	Terry Ligocki
`1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ` (bbch)	10 ↑↑ 116.98	Terry Ligocki
`1RB0RD_1RC0LA_0LA0LE_1RE1RZ_1RF0RA_1LG0LE_1LC0LG` (bbch)	10 ↑↑ 116.05
`1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ` (bbch)	10 ↑↑ 115.52	@prurq
`1RB0RG_1LC0LE_1LD0LB_0LE1RE_0RA1RF_0RD1RC_1RD1RZ` (bbch)	10 ↑↑ 114.83	Andrew Ducharme
`1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ` (bbch)	10 ↑↑ 114.60	Shawn Ligocki
`1RB0RE_0RC1LC_0LD1LF_1LE0LG_1RA0RC_0LB1LA_1LB1RZ` (bbch)	10 ↑↑ 114.57	Andrew Ducharme

Current Progress

This is a summary of the 1 million subtasks from mxdys's code that have been executed and their output processed by Shawn Ligocki's linear rule code.

Task range	Done by	Completed		# holdouts	Maximum Score TM	~Sigma	Source
Task range	Done by	enumeration	linear rule	# holdouts	Maximum Score TM	~Sigma	Source
00-01xxxx	@Iijil	Yes	Yes	1,545,673	`1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD` (bbch)	10 ↑↑ 246.32	Google Drive folder
02-04xxxx	@Iijil Terry Ligocki	Yes	Yes	2,279,734	`1RB0LF_1RC1RA_1RD0RG_1LE1RZ_1LA0LF_1RA1LE_0RE1RG` (bbch)	10 ↑↑ 93.81	@Iijil Terry Ligocki
05-09xxxx	@Iijil Andrew Ducharme	Yes	Yes	3,889,955	`1RB1RZ_1RC0LE_0RD1RB_1LE1RA_1LF0LG_0LG0RG_1LB1RG` (bbch)	10 ↑↑ 243.88	@Iijil Andrew
10-12xxxx	Andrew Ducharme	Yes	Yes	2,708,888	`1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD1LF_1LB0LE` (bbch)	10 ↑↑ 519.20	Google Drive folder
13xxxx	Shawn Ligocki	Yes	Yes	1,192,442	`1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ` (bbch)	10 ↑↑ 114.60	Google Drive folder
14-16xxxx	Andrew Ducharme	Yes	Yes	2,701,637	`1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0LD_0RA1RE_1RZ1LA` (bbch)	10 ↑↑ 188.28	Google Drive folder
17-18xxxx	@gerbil5709 Terry Ligocki	Yes	Yes	1,898,156	`1RB1LA_1LC0RE_0LD1LB_1RE0LA_1RF0RA_0RG0LA_1RB1RZ` (bbch)	10 ↑↑ 192.67	@gerbil5709 Terry Ligocki
19xxxx	Katelyn Doucette Andrew Ducharme	Yes	Yes	1,601,356	`1RB0RF_1RC1RZ_0LD1RF_0RA1LE_0LC1LF_1LE0RG_0LE1RA` (bbch)	10 ↑↑ 136.64	Google Drive folder
20-23xxxx	@C7X	Yes	Yes	4,528,827	`1RB1LA_1LC0RF_0LD0RD_1RF1LE_1LB1RZ_1RG0RA_0RA0LA` (bbch)	10 ↑↑ 192.67	Google Drive folder
24xxxx	Andrew Ducharme	Yes	Yes	712,356	`1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF` (bbch)*	$2\uparrow ^{11}2\uparrow ^{11}3^{*}$	Google Drive folder
25-34xxxx	@stokastic	Yes	Yes	10,339,816	`1RB0LC_1LC0LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LC` (bbch)	10 ↑↑ 140.28	Google Drive folder
35-39xxxx	Terry Ligocki	Yes	Yes	4,894,047	`1RB1RZ_1LC0RF_0LD1LB_1RD0LE_1RB1LE_1RG0RE_0RA0LE` (bbch)	10 ↑↑ 192.67 Google Drive folder
40-47xxxx	Andrew Ducharme	Yes	Yes	6,181,327	`1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE` (bbch)	10 ↑↑ 519.20	Google Drive folder
48xxxx	@star	No	No	TBD	TBD	TBD
49xxxx	Tobiáš Brichta Terry Ligocki	Yes	Yes	804,722	`1RB0LG_1RC0RG_0LD1RE_1RD0RE_1LF1RB_0LA1RZ_1LC1LG` (bbch)	10 ↑↑ 126.20	Tobiáš Brichta Terry Ligocki
50xxxx	@prurq Andrew Ducharme	Yes	Yes	797,224	`1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ` (bbch)	10 ↑↑ 115.52	Google Drive folder
51-53xxxx	@gerbil5709 Terry Ligocki	Yes	Yes	3,016,175	`1RB0LC_1LC0LD_1LA1LB_0LG1RE_0RF0RF_0RA1RE_1RZ1LC` (bbch)	10 ↑↑ 140.28	@gerbil5709 Terry Ligocki
54-59xxxx	Terry Ligocki	Yes	Yes	5,689,850	`1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0RF_0RA1RE_1RZ1LA` (bbch)	10 ↑↑ 188.28 Google Drive folder
60-64xxxx	@gerbil5709 Terry Ligocki	Yes	Yes	3,817,876	`1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD0LG_1LB0LE` (bbch)	10 ↑↑ 519.20	@gerbil5709 Terry Ligocki
65-68xxxx	Terry Ligocki	Yes	Yes	3,076,778	`1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RG0LD` (bbch)	10 ↑↑ 192.67 Google Drive folder
69xxxx	@poppuncher	Yes	Yes	1,053,119	`1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG` (bbch)	10 ↑↑ 133.85	Google Drive folder
70-71xxxx	@hipparcos	Yes	Yes	1,899,094	`1RB1RZ_1LC1RD_0LD0LC_1LE1RA_1LF0LE_1RF0RG_1RG0RD` (bbch)	10 ↑↑ 77.50	Github release
72-79xxxx	Terry Ligocki	Yes	Yes	7,627,514	`1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ` (bbch)	10 ↑↑ 228.78 Google Drive folder
80-81xxxx	@xnoobspeakable	Yes	Yes	1,537,533	`1RB0LA_0RC1RZ_0RD0RG_1LE1RA_1LF1LD_1RG0RG_1RD1RC` (bbch)	10 ↑↑ 74.85	Google Drive folder
82-99xxxx	Terry Ligocki	Yes	Yes	15,673,786	`1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ` (bbch)	10 ↑↑ 286.17 Google Drive folder

*The current BB(7) champion TM 1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch)* 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.

@@ Line 222: / Line 222: @@
 |
 [https://drive.google.com/drive/folders/1wniwrAuvsHfkvro8Tg65WAMNZEuIekzD @Iijil]<br/>
-[https://drive.google.com/drive/folders/1uaSs-CfT6yX2UIboCaNi2U651bEYa_y0?usp=drive_link Terry Ligocki]
+[https://drive.google.com/drive/folders/1yQFLcznvNzEF9uWXL1xkJhhfxPDtbC7x?usp=drive_link Terry Ligocki]
 |-
 |05-09xxxx
@@ Line 253: / Line 253: @@
 |{{TM|1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ}}
 |10 ↑↑ 114.60
-|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
+|[https://drive.google.com/drive/folders/1yQFLcznvNzEF9uWXL1xkJhhfxPDtbC7x?usp=drive_link Google Drive folder]
 |-
 |14-16xxxx
@@ Line 275: / Line 275: @@
 |
 [https://drive.google.com/drive/folders/1kAvBebeF09CEVocCk5bGKlDJfRN8co_i?usp=sharing @gerbil5709]<br/>
-[https://drive.google.com/drive/folders/1uaSs-CfT6yX2UIboCaNi2U651bEYa_y0?usp=drive_link Terry Ligocki]
+[https://drive.google.com/drive/folders/1yQFLcznvNzEF9uWXL1xkJhhfxPDtbC7x?usp=drive_link Terry Ligocki]
 |-
 |19xxxx
@@ Line 322: / Line 322: @@
 |{{TM|1RB1RZ_1LC0RF_0LD1LB_1RD0LE_1RB1LE_1RG0RE_0RA0LE}}
 |10 ↑↑ 192.67
-|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
+[https://drive.google.com/drive/folders/1yQFLcznvNzEF9uWXL1xkJhhfxPDtbC7x?usp=drive_link Google Drive folder]
 |-
 |40-47xxxx
@@ Line 353: / Line 353: @@
 |
 [https://drive.google.com/drive/folders/1-csgJ5uSIX3SKlqTkSnhkUuEYLKgCw81 Tobiáš Brichta]<br/>
-[https://drive.google.com/drive/folders/1uaSs-CfT6yX2UIboCaNi2U651bEYa_y0?usp=drive_link Terry Ligocki]
+[https://drive.google.com/drive/folders/1yQFLcznvNzEF9uWXL1xkJhhfxPDtbC7x?usp=drive_link Terry Ligocki]
 |-
 |50xxxx
@@ Line 377: / Line 377: @@
 |
 [https://drive.google.com/drive/folders/1kAvBebeF09CEVocCk5bGKlDJfRN8co_i?usp=sharing @gerbil5709]<br/>
-[https://drive.google.com/drive/folders/1uaSs-CfT6yX2UIboCaNi2U651bEYa_y0?usp=drive_link Terry Ligocki]
+[https://drive.google.com/drive/folders/1yQFLcznvNzEF9uWXL1xkJhhfxPDtbC7x?usp=drive_link Terry Ligocki]
 |-
 |54-59xxxx
@@ Line 386: / Line 386: @@
 |{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0RF_0RA1RE_1RZ1LA}}
 |10 ↑↑ 188.28
-|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
+[https://drive.google.com/drive/folders/1yQFLcznvNzEF9uWXL1xkJhhfxPDtbC7x?usp=drive_link Google Drive folder]
 |-
 |60-64xxxx
@@ Line 399: / Line 399: @@
 |
 [https://drive.google.com/drive/folders/1kAvBebeF09CEVocCk5bGKlDJfRN8co_i?usp=sharing @gerbil5709]<br/>
-[https://drive.google.com/drive/folders/1uaSs-CfT6yX2UIboCaNi2U651bEYa_y0?usp=drive_link Terry Ligocki]
+[https://drive.google.com/drive/folders/1yQFLcznvNzEF9uWXL1xkJhhfxPDtbC7x?usp=drive_link Terry Ligocki]
 |-
 |65-68xxxx
@@ Line 408: / Line 408: @@
 |{{TM|1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RG0LD}}
 |10 ↑↑ 192.67
-|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
+[https://drive.google.com/drive/folders/1yQFLcznvNzEF9uWXL1xkJhhfxPDtbC7x?usp=drive_link Google Drive folder]
 |-
 |69xxxx
@@ Line 435: / Line 435: @@
 |{{TM|1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ}}
 |10 ↑↑ 228.78
-|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
+[https://drive.google.com/drive/folders/1yQFLcznvNzEF9uWXL1xkJhhfxPDtbC7x?usp=drive_link Google Drive folder]
 |-
 |80-81xxxx
@@ Line 453: / Line 453: @@
 |{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}}
 |10 ↑↑ 286.17
-|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
+[https://drive.google.com/drive/folders/1yQFLcznvNzEF9uWXL1xkJhhfxPDtbC7x?usp=drive_link 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]]

BB(7): Difference between revisions

Revision as of 23:41, 17 July 2025

History

Top Halters

Current Progress

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