BB(6) - Revision history

XnoobSpeakable: fix archive

2026-10-17T14:19:28Z

fix archive

← Older revision		Revision as of 14:19, 17 October 2026
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	\|{{TM\|1RB0LF_1RC1RB_1LD0RA_1LB0LE_1RZ0LC_1LA1LF\|halt}}		\|{{TM\|1RB0LF_1RC1RB_1LD0RA_1LB0LE_1RZ0LC_1LA1LF\|halt}}
	\| rowspan="3" \|10 ↑↑ 7.52390		\| rowspan="3" \|10 ↑↑ 7.52390
	\| rowspan="3" \|Katelyn Doucette<ref>{{DiscordArchive}}</ref>		\| rowspan="3" \|Katelyn Doucette<ref>{{DiscordArchive\|1375512968569028648\|1378916236104171562}}</ref>
	\|-		\|-
	\|{{TM\|1RB0LF_1RC1RB_1LD0RA_1RF0LE_1RZ0LC_1LA1LF\|halt}}		\|{{TM\|1RB0LF_1RC1RB_1LD0RA_1RF0LE_1RZ0LC_1LA1LF\|halt}}

XnoobSpeakable: archiving one discord message

2026-10-17T14:17:29Z

archiving one discord message

← Older revision		Revision as of 14:17, 17 October 2026
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	\| rowspan="3" \|10 ↑↑ 7.52390		\| rowspan="3" \|10 ↑↑ 7.52390
	\| rowspan="3" \|Katelyn Doucette<ref>~~https://discord.com/channels/960643023006490684/1375512968569028648/1378916236104171562~~</ref>		\| rowspan="3" \|Katelyn Doucette<ref>{{DiscordArchive}}</ref>
	\|-		\|-
	\|{{TM\|1RB0LF_1RC1RB_1LD0RA_1RF0LE_1RZ0LC_1LA1LF\|halt}}		\|{{TM\|1RB0LF_1RC1RB_1LD0RA_1RF0LE_1RZ0LC_1LA1LF\|halt}}

HelpMe: linked the arrow stuff. yeah

2026-10-17T13:01:01Z

linked the arrow stuff. yeah

← Older revision		Revision as of 13:01, 17 October 2026
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	== Top Halters ==		== Top Halters ==
	Below is a table of the machines in TNF-1RB format with the 20 highest known runtimes.<ref>Shawn Ligocki's list of 6-state, 2-symbol machines with large runtimes ([https://github.com/sligocki/busy-beaver/blob/main/Machines/bb/6x2.txt Link])</ref> Their runtimes are expressed using an extension of [[wikipedia:Knuth's_up-arrow_notation\|Knuth's up-arrow notation]].<ref>Shawn Ligocki. 2022. [https://www.sligocki.com/2022/06/25/ext-up-notation.html "Extending Up-arrow Notation"]</ref>		Below is a table of the machines in TNF-1RB format with the 20 highest known runtimes.<ref>Shawn Ligocki's list of 6-state, 2-symbol machines with large runtimes ([https://github.com/sligocki/busy-beaver/blob/main/Machines/bb/6x2.txt Link])</ref> Their runtimes are expressed using an [[Measuring large numbers#Knuth's up-arrow notation\|extension]] of [[wikipedia:Knuth's_up-arrow_notation\|Knuth's up-arrow notation]].<ref>Shawn Ligocki. 2022. [https://www.sligocki.com/2022/06/25/ext-up-notation.html "Extending Up-arrow Notation"]</ref>
	{\| class="wikitable"		{\| class="wikitable"
	\|+Top Known BB(6) Halters		\|+Top Known BB(6) Halters

Polygon: /* History */ Updated holdout counts

2026-10-16T17:25:13Z

History: Updated holdout counts

← Older revision		Revision as of 17:25, 16 October 2026
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	In June 2024, the machine {{TM\|1RB1RA_0LC1LE_1LD1LC_1LA0LB_1LF1RE_---0RA}} (now known as [[Antihydra]]) was isolated from the BB(6) holdouts, and recognised as a [[Cryptids\|Cryptid]], implying that determining the exact value of S(6) would be, in a certain mathematical sense, hard.		In June 2024, the machine {{TM\|1RB1RA_0LC1LE_1LD1LC_1LA0LB_1LF1RE_---0RA}} (now known as [[Antihydra]]) was isolated from the BB(6) holdouts, and recognised as a [[Cryptids\|Cryptid]], implying that determining the exact value of S(6) would be, in a certain mathematical sense, hard.

	@mxdys's [[Holdouts lists\|holdouts list]] has ~~698~~ machines up to equivalence and ~~1501~~ machines not considering equivalence as of 15 October 2026. Partial Rocq proof is [https://github.com/ccz181078/busycoq/tree/BB6 available on Github].		@mxdys's [[Holdouts lists\|holdouts list]] has 663 machines up to equivalence and 1417 machines not considering equivalence as of 16 October 2026. Partial Rocq proof is [https://github.com/ccz181078/busycoq/tree/BB6 available on Github].

	Often up-to-date annotated spreadsheet, with links to Discord discussions: [https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=1330361301#gid=1330361301 Spreadsheet]. The informal holdout count is 998.		Often up-to-date annotated spreadsheet, with links to Discord discussions: [https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=1330361301#gid=1330361301 Spreadsheet]. The informal holdout count is 998.

Qwertyasdf: AI

2026-10-16T00:12:07Z

← Older revision		Revision as of 00:12, 16 October 2026
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	All machines have been simulated out to 1e13 steps. ~140 machines remain to be simulated to 1e14, and ~190 to 1e15. See [https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=806905077#gid=806905077 Spreadsheet]		All machines have been simulated out to 1e13 steps. ~140 machines remain to be simulated to 1e14, and ~190 to 1e15. See [https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=806905077#gid=806905077 Spreadsheet]

			In contrast to BB(5), a substantial portion of BB(6) holdouts (and especially the last thousand holdouts) have seen greater degree of AI assistance, autosolutions, and autoformalizations.

	== Cryptids ==		== Cryptids ==

Yves30.: update nb of holdouts to 698

2026-10-15T11:25:12Z

update nb of holdouts to 698

← Older revision		Revision as of 11:25, 15 October 2026
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	In June 2024, the machine {{TM\|1RB1RA_0LC1LE_1LD1LC_1LA0LB_1LF1RE_---0RA}} (now known as [[Antihydra]]) was isolated from the BB(6) holdouts, and recognised as a [[Cryptids\|Cryptid]], implying that determining the exact value of S(6) would be, in a certain mathematical sense, hard.		In June 2024, the machine {{TM\|1RB1RA_0LC1LE_1LD1LC_1LA0LB_1LF1RE_---0RA}} (now known as [[Antihydra]]) was isolated from the BB(6) holdouts, and recognised as a [[Cryptids\|Cryptid]], implying that determining the exact value of S(6) would be, in a certain mathematical sense, hard.

	@mxdys's [[Holdouts lists\|holdouts list]] has ~~740~~ machines up to equivalence and ~~1581~~ machines not considering equivalence as of 10 October 2026. Partial Rocq proof is [https://github.com/ccz181078/busycoq/tree/BB6 available on Github].		@mxdys's [[Holdouts lists\|holdouts list]] has 698 machines up to equivalence and 1501 machines not considering equivalence as of 15 October 2026. Partial Rocq proof is [https://github.com/ccz181078/busycoq/tree/BB6 available on Github].

	Often up-to-date annotated spreadsheet, with links to Discord discussions: [https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=1330361301#gid=1330361301 Spreadsheet]. The informal holdout count is 998.		Often up-to-date annotated spreadsheet, with links to Discord discussions: [https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=1330361301#gid=1330361301 Spreadsheet]. The informal holdout count is 998.

HelpMe: missing bb5 champs which were also bb6 champs

2026-10-13T06:46:42Z

missing bb5 champs which were also bb6 champs

@@ Line 59: / Line 59: @@
 |≥ 4,208,824
 |≥ 2,075
 |-
 | rowspan="2" |January 1990

C1: /* History */ Updated holdouts count for BB(6).

2026-10-12T06:52:27Z

History: Updated holdouts count for BB(6).

← Older revision		Revision as of 06:52, 12 October 2026
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	In June 2024, the machine {{TM\|1RB1RA_0LC1LE_1LD1LC_1LA0LB_1LF1RE_---0RA}} (now known as [[Antihydra]]) was isolated from the BB(6) holdouts, and recognised as a [[Cryptids\|Cryptid]], implying that determining the exact value of S(6) would be, in a certain mathematical sense, hard.		In June 2024, the machine {{TM\|1RB1RA_0LC1LE_1LD1LC_1LA0LB_1LF1RE_---0RA}} (now known as [[Antihydra]]) was isolated from the BB(6) holdouts, and recognised as a [[Cryptids\|Cryptid]], implying that determining the exact value of S(6) would be, in a certain mathematical sense, hard.

	@mxdys's [[Holdouts lists\|holdouts list]] has ~~778~~ machines up to equivalence and ~~1590~~ machines not considering equivalence as of 7 October 2026. Partial Rocq proof is [https://github.com/ccz181078/busycoq/tree/BB6 available on Github].		@mxdys's [[Holdouts lists\|holdouts list]] has 740 machines up to equivalence and 1581 machines not considering equivalence as of 10 October 2026. Partial Rocq proof is [https://github.com/ccz181078/busycoq/tree/BB6 available on Github].

	Often up-to-date annotated spreadsheet, with links to Discord discussions: [https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=1330361301#gid=1330361301 Spreadsheet]. The informal holdout count is 998.		Often up-to-date annotated spreadsheet, with links to Discord discussions: [https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=1330361301#gid=1330361301 Spreadsheet]. The informal holdout count is 998.

Yves30.: Update bb6 holdout count in the BB(6) page

2026-10-08T13:28:54Z

Update bb6 holdout count in the BB(6) page

← Older revision		Revision as of 13:28, 8 October 2026
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	In June 2024, the machine {{TM\|1RB1RA_0LC1LE_1LD1LC_1LA0LB_1LF1RE_---0RA}} (now known as [[Antihydra]]) was isolated from the BB(6) holdouts, and recognised as a [[Cryptids\|Cryptid]], implying that determining the exact value of S(6) would be, in a certain mathematical sense, hard.		In June 2024, the machine {{TM\|1RB1RA_0LC1LE_1LD1LC_1LA0LB_1LF1RE_---0RA}} (now known as [[Antihydra]]) was isolated from the BB(6) holdouts, and recognised as a [[Cryptids\|Cryptid]], implying that determining the exact value of S(6) would be, in a certain mathematical sense, hard.

	@mxdys's [[Holdouts lists\|holdouts list]] has ~~797~~ machines up to equivalence and ~~1630~~ machines not considering equivalence as of ~~30 September~~ 2026. Partial Rocq proof is [https://github.com/ccz181078/busycoq/tree/BB6 available on Github].		@mxdys's [[Holdouts lists\|holdouts list]] has 778 machines up to equivalence and 1590 machines not considering equivalence as of 7 October 2026. Partial Rocq proof is [https://github.com/ccz181078/busycoq/tree/BB6 available on Github].

	Often up-to-date annotated spreadsheet, with links to Discord discussions: [https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=1330361301#gid=1330361301 Spreadsheet]. The informal holdout count is 998.		Often up-to-date annotated spreadsheet, with links to Discord discussions: [https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=1330361301#gid=1330361301 Spreadsheet]. The informal holdout count is 998.

HelpMe: oh yeah and that

2026-10-07T16:34:01Z

oh yeah and that

← Older revision		Revision as of 16:34, 7 October 2026
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	{\| class="wikitable mw-collapsible"		{\| class="wikitable mw-collapsible"
	\|+		\|+
	! colspan="6" \|Timeline of ~~lower~~ bounds established for Σ(6) and S(6)<ref name=":PMH">Pascal Michel. (last updated 2026). The Busy Beaver Competition: a historical survey. https://bbchallenge.org/~pascal.michel/ha#tm62 </ref>		! colspan="6" \|Timeline of bounds established for Σ(6) and S(6)<ref name=":PMH">Pascal Michel. (last updated 2026). The Busy Beaver Competition: a historical survey. https://bbchallenge.org/~pascal.michel/ha#tm62 </ref>
	\|-		\|-
	!Month of discovery		!Month of discovery
	!Machine		!Machine
	!S(6) ~~lower bound~~		!S(6)
	!Σ(6) ~~lower bound~~		!Σ(6)
	!Discoverer		!Discoverer
	!Notes		!Notes

← Older revision		Revision as of 14:19, 17 October 2026
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	\| rowspan="3" \|10 ↑↑ 7.52390		\| rowspan="3" \|10 ↑↑ 7.52390
	\| rowspan="3" \|Katelyn Doucette<ref>{{DiscordArchive}}</ref>		\| rowspan="3" \|Katelyn Doucette<ref>{{DiscordArchive\|1375512968569028648\|1378916236104171562}}</ref>
	\|-		\|-
	\|{{TM\|1RB0LF_1RC1RB_1LD0RA_1RF0LE_1RZ0LC_1LA1LF\|halt}}		\|{{TM\|1RB0LF_1RC1RB_1LD0RA_1RF0LE_1RZ0LC_1LA1LF\|halt}}

← Older revision		Revision as of 14:17, 17 October 2026
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	\|{{TM\|1RB0LF_1RC1RB_1LD0RA_1LB0LE_1RZ0LC_1LA1LF\|halt}}		\|{{TM\|1RB0LF_1RC1RB_1LD0RA_1LB0LE_1RZ0LC_1LA1LF\|halt}}
	\| rowspan="3" \|10 ↑↑ 7.52390		\| rowspan="3" \|10 ↑↑ 7.52390
	\| rowspan="3" \|Katelyn Doucette<ref>~~https://discord.com/channels/960643023006490684/1375512968569028648/1378916236104171562~~</ref>		\| rowspan="3" \|Katelyn Doucette<ref>{{DiscordArchive}}</ref>
	\|-		\|-
	\|{{TM\|1RB0LF_1RC1RB_1LD0RA_1RF0LE_1RZ0LC_1LA1LF\|halt}}		\|{{TM\|1RB0LF_1RC1RB_1LD0RA_1RF0LE_1RZ0LC_1LA1LF\|halt}}