TMBR: December 2025 - Revision history

Sligocki: Reverted edit by RobinCodes (talk) to last revision by ADucharme

2026-03-10T16:55:07Z

Reverted edit by RobinCodes (talk) to last revision by ADucharme

← Older revision		Revision as of 16:55, 10 March 2026
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	~~For a summary of our research in 2025, see [[TYBR: 2025]].~~{{TMBRnav\|November 2025\|January 2026}}		{{TMBRnav\|November 2025\|January 2026}}

	[[:Category:This Month in Beaver Research\|This Month in Beaver Research]] for December 2025.		[[:Category:This Month in Beaver Research\|This Month in Beaver Research]] for December 2025.

RobinCodes: Added TYBR reference

2026-03-10T06:16:17Z

Added TYBR reference

← Older revision		Revision as of 06:16, 10 March 2026
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	{{TMBRnav\|November 2025\|January 2026}}		For a summary of our research in 2025, see [[TYBR: 2025]].{{TMBRnav\|November 2025\|January 2026}}

	[[:Category:This Month in Beaver Research\|This Month in Beaver Research]] for December 2025.		[[:Category:This Month in Beaver Research\|This Month in Beaver Research]] for December 2025.

ADucharme: Changed first sentence formatting for consistency. Edited the first two bullet points under the BB(6) entry in Holdouts.

2026-02-08T20:14:55Z

Changed first sentence formatting for consistency. Edited the first two bullet points under the BB(6) entry in Holdouts.

Sligocki at 16:41, 8 February 2026

2026-02-08T16:41:28Z

← Older revision		Revision as of 16:41, 8 February 2026
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	[[:Category:This Month in Beaver Research\|This Month in Beaver Research]] for December 2025. In commemoration of the end of the year, we've summarized some of the major accomplishments into This Year in Beaver Research: [[TYBR: 2025]]. This month saw a lot of exploration into BB-adjacent models with the introduction of BB for [[General Recursive Function\|General Recursive Functions]] and [[Register machine\|Register machines]] and new champions for many previously introduced variants.		[[:Category:This Month in Beaver Research\|This Month in Beaver Research]] for December 2025. In commemoration of the end of the year, we've summarized some of the major accomplishments into This Year in Beaver Research: [[TYBR: 2025]]. This month saw a lot of exploration into BB-adjacent models with the introduction of BB for [[General Recursive Function\|General Recursive Functions]] and [[Register machine\|Register machines]] and new champions for many previously introduced variants.

	~~== Misc ==~~

	* TODO: kalikimaka sonified [[Antihydra]] https://discord.com/channels/960643023006490684/960643023530762341/1455164551678005369

	== In the News ==		== In the News ==
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	== Champions ==		== Champions ==
	* Patcail and [https://github.com/tromp/AIT/blob/master/fast_growing_and_conjectures/melo.lam Gustavo Melo] discovered a new [[Busy Beaver for lambda calculus\|BBλ(63)]] champion, running for more than <math>f_{\omega^3}\left(2\right)</math> steps and <code>50_ft_lock</code> discovered a new [[Busy Beaver for lambda calculus\|BBλ(91)]] champion, running for over <math>f_{\varepsilon_0 + 1}\left(3\right)</math> steps. f represents the [[Fast-Growing Hierarchy]].		* Patcail and [https://github.com/tromp/AIT/blob/master/fast_growing_and_conjectures/melo.lam Gustavo Melo] discovered a new [[Busy Beaver for lambda calculus\|BBλ]](63) champion, running for more than <math>f_{\omega^3}\left(2\right)</math> steps and <code>50_ft_lock</code> discovered a new [[Busy Beaver for lambda calculus\|BBλ(91)]] champion, running for over <math>f_{\varepsilon_0 + 1}\left(3\right)</math> steps. f represents the [[Fast-Growing Hierarchy]].
	* On 11 Dec, a BB [[Fractran]] champion demonstrating <math>BBf(22) > 10^{62}</math> was found by Shawn Ligocki<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1448912286713384961]</sup> and verified by Jason Yuen.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1448953682237460480]</sup> This was the first champion which required accelerated simulation. On 12 Dec, Shawn modified that program to create [[Frankenstein's Monster]], a BBf(23) Cryptid.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1449138938215141478]</sup>		* On 11 Dec, a BB [[Fractran]] champion demonstrating <math>BBf(22) > 10^{62}</math> was found by Shawn Ligocki<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1448912286713384961]</sup> and verified by Jason Yuen.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1448953682237460480]</sup> This was the first Fractran champion which required accelerated simulation. On 12 Dec, Shawn modified that program to create [[Frankenstein's Monster]], a BBf(23) Cryptid.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1449138938215141478]</sup>
	* A new [[Non-halting Turing machine#Translated cycler preperiod\|BBS(4,3)]] champion ({{TM\|1RB1RD1LC_2LB1RB1LC_1LB1LA1LD_0RB2RA2RD}}) was discovered by changing the C0 transition of the [[BB(4,3)]] champion {{TM\|1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD\|halt}} from <code>C0 --> 1RZ</code> to <code>C0 --> 1LB</code>.		* A new [[Non-halting Turing machine#Translated cycler preperiod\|BBS(4,3)]] champion ({{TM\|1RB1RD1LC_2LB1RB1LC_1LB1LA1LD_0RB2RA2RD}}) was discovered by changing the C0 transition of the [[BB(4,3)]] champion {{TM\|1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD\|halt}} from <code>C0 --> 1RZ</code> to <code>C0 --> 1LB</code>.
	* [[User:Azerty\|Azerty]] discovered a series of [[Blanking Busy Beaver]] 3x3 champions, culminating in {{TM\|1RB2LC2LA_1LC---2RA_2RC2LB0LC}} which blanks the tape after 329 steps on 31 Dec 2025.		* [[User:Azerty\|Azerty]] discovered a series of [[Blanking Busy Beaver]] 3x3 champions, culminating in {{TM\|1RB2LC2LA_1LC---2RA_2RC2LB0LC}} which blanks the tape after 329 steps on 31 Dec 2025.
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	* [[BB(2,7)\|BB(2,7):]]		* [[BB(2,7)\|BB(2,7):]]
	** Terry Ligocki enumerated 60K more subtasks, increasing the number of holdouts to 309,868,865. A total of 100K subtasks out of the 1 million subtasks (or '''10%''') have been enumerated.		** Terry Ligocki enumerated 60K more subtasks, increasing the number of holdouts to 309,868,865. A total of 100K subtasks out of the 1 million subtasks (or '''10%''') have been enumerated.
			== Misc ==

			* <code>kalikimaka</code> sonified [[Antihydra]].<sup>[https://discord.com/channels/960643023006490684/960643023530762341/1455164551678005369]</sup>

	[[Category:This Month in Beaver Research\|2025-12]]		[[Category:This Month in Beaver Research\|2025-12]]

Sligocki: Cleanup

2026-02-08T16:38:31Z

Cleanup

← Older revision		Revision as of 16:38, 8 February 2026
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	{{TMBRnav\|November 2025\|January 2026}}		{{TMBRnav\|November 2025\|January 2026}}

	''This edition of TMBR is in progress and has not yet been released. Please add any notes you think may be relevant (including in the form a of a TODO with a link to any relevant Discord discussion).''

	[[:Category:This Month in Beaver Research\|This Month in Beaver Research]] for December 2025. In commemoration of the end of the year, we've summarized some of the major accomplishments into This Year in Beaver Research: [[TYBR: 2025]]. This month saw a lot of exploration into BB-adjacent models with the introduction of BB for [[General Recursive Function\|General Recursive Functions]] and [[Register machine\|Register machines]] and new champions for many previously introduced variants.		[[:Category:This Month in Beaver Research\|This Month in Beaver Research]] for December 2025. In commemoration of the end of the year, we've summarized some of the major accomplishments into This Year in Beaver Research: [[TYBR: 2025]]. This month saw a lot of exploration into BB-adjacent models with the introduction of BB for [[General Recursive Function\|General Recursive Functions]] and [[Register machine\|Register machines]] and new champions for many previously introduced variants.
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	* [[Register machine\|Busy Beaver for Register machines]] (MBB(n)) was introduced and computed up to n = 5 and a lower bound for n = 6 was discovered.		* [[Register machine\|Busy Beaver for Register machines]] (MBB(n)) was introduced and computed up to n = 5 and a lower bound for n = 6 was discovered.
	* [[Busy Beaver for lambda calculus#De Bruijn\|Busy Beaver for lambda calculus using De Bruijn indexes]] was introduced with lower bounds having been calculated up to n = 26.		* [[Busy Beaver for lambda calculus#De Bruijn\|Busy Beaver for lambda calculus using De Bruijn indexes]] was introduced with lower bounds having been calculated up to n = 26.
	~~TODO. [[Fractran]] progress, [https://discord.com/channels/960643023006490684/1450894930422530161/1450894930422530161 Semi-infinite tape Busy Beaver]~~

	== [[Holdouts]] ==		== [[Holdouts]] ==
	{\| class="wikitable"		{\| class="wikitable"

Sligocki: Add some more Fractran results

2026-02-08T16:37:21Z

Add some more Fractran results

← Older revision		Revision as of 16:37, 8 February 2026
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	[[:Category:This Month in Beaver Research\|This Month in Beaver Research]] for December 2025. In commemoration of the end of the year, we've summarized some of the major accomplishments into This Year in Beaver Research: [[TYBR: 2025]]. This month saw a lot of exploration into BB-adjacent models with the introduction of BB for [[General Recursive Function\|General Recursive Functions]] and [[Register machine\|Register machines]] and new champions for many previously introduced variants.		[[:Category:This Month in Beaver Research\|This Month in Beaver Research]] for December 2025. In commemoration of the end of the year, we've summarized some of the major accomplishments into This Year in Beaver Research: [[TYBR: 2025]]. This month saw a lot of exploration into BB-adjacent models with the introduction of BB for [[General Recursive Function\|General Recursive Functions]] and [[Register machine\|Register machines]] and new champions for many previously introduced variants.

			== Misc ==

			* TODO: kalikimaka sonified [[Antihydra]] https://discord.com/channels/960643023006490684/960643023530762341/1455164551678005369

	== In the News ==		== In the News ==
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	== Champions ==		== Champions ==
			* Patcail and [https://github.com/tromp/AIT/blob/master/fast_growing_and_conjectures/melo.lam Gustavo Melo] discovered a new [[Busy Beaver for lambda calculus\|BBλ(63)]] champion, running for more than <math>f_{\omega^3}\left(2\right)</math> steps and <code>50_ft_lock</code> discovered a new [[Busy Beaver for lambda calculus\|BBλ(91)]] champion, running for over <math>f_{\varepsilon_0 + 1}\left(3\right)</math> steps. f represents the [[Fast-Growing Hierarchy]].
			* On 11 Dec, a BB [[Fractran]] champion demonstrating <math>BBf(22) > 10^{62}</math> was found by Shawn Ligocki<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1448912286713384961]</sup> and verified by Jason Yuen.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1448953682237460480]</sup> This was the first champion which required accelerated simulation. On 12 Dec, Shawn modified that program to create [[Frankenstein's Monster]], a BBf(23) Cryptid.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1449138938215141478]</sup>
	* A new [[Non-halting Turing machine#Translated cycler preperiod\|BBS(4,3)]] champion ({{TM\|1RB1RD1LC_2LB1RB1LC_1LB1LA1LD_0RB2RA2RD}}) was discovered by changing the C0 transition of the [[BB(4,3)]] champion {{TM\|1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD\|halt}} from <code>C0 --> 1RZ</code> to <code>C0 --> 1LB</code>.		* A new [[Non-halting Turing machine#Translated cycler preperiod\|BBS(4,3)]] champion ({{TM\|1RB1RD1LC_2LB1RB1LC_1LB1LA1LD_0RB2RA2RD}}) was discovered by changing the C0 transition of the [[BB(4,3)]] champion {{TM\|1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD\|halt}} from <code>C0 --> 1RZ</code> to <code>C0 --> 1LB</code>.
	* [[User:Azerty\|Azerty]] discovered a series of [[Blanking Busy Beaver]] 3x3 champions, culminating in {{TM\|1RB2LC2LA_1LC---2RA_2RC2LB0LC}} which blanks the tape after 329 steps on 31 Dec 2025.		* [[User:Azerty\|Azerty]] discovered a series of [[Blanking Busy Beaver]] 3x3 champions, culminating in {{TM\|1RB2LC2LA_1LC---2RA_2RC2LB0LC}} which blanks the tape after 329 steps on 31 Dec 2025.
	* On 25 Dec 2025, [[User:Azerty\|Azerty]] discovered {{TM\|1RB2RC1LC_0RC0RB1LA_2LA2RC1LB}} which is a [[Translated cycler]] and new [[Non-halting Turing machine#Translated cycler period\|BBP(3,3)]] champion with a new record period length of 1195 steps.		* On 25 Dec 2025, [[User:Azerty\|Azerty]] discovered {{TM\|1RB2RC1LC_0RC0RB1LA_2LA2RC1LB}} which is a [[Translated cycler]] and new [[Non-halting Turing machine#Translated cycler period\|BBP(3,3)]] champion with a new record period length of 1195 steps.
	* Patcail and [https://github.com/tromp/AIT/blob/master/fast_growing_and_conjectures/melo.lam Gustavo Melo] discovered a new [[Busy Beaver for lambda calculus\|BBλ(63)]] champion, running for more than <math>f_{\omega^3}\left(2\right)</math> steps and <code>50_ft_lock</code> discovered a new [[Busy Beaver for lambda calculus\|BBλ(91)]] champion, running for over <math>f_{\varepsilon_0 + 1}\left(3\right)</math> steps. f represents the [[Fast-Growing Hierarchy]].
	* On 18 Dec, Azerty discovered the new [[TT]](2) champion <code>1TB---_1PA0PB</code> with a runtime of 13 steps. This was followed by new champions a day later: <code>1PB0PA_1TA0PC_1PA---</code> for TT(3) with a runtime of 82 steps, <code>1TB---_0PD1PB_1PA1TA_0PC0PD</code> for TT(4) with a runtime of 758 steps, <code>1TB0PA2PA_2PA---1PA</code> for TT(2,3) with a runtime of 223 steps and <code>1TB3TB2PB---_2TB1PA0PA2TB</code> for TT(2,4) with a runtime of 1,068 steps. On 21 Dec Azerty also discovered the new TT(3,3) champion with a runtime of 427 steps <code>1TB2TA2PA_1TA0TC1PC_---2PA0PA</code>, this champion was surpassed on 22 Dec by <code>1TB2PB1PB_2TA0TA2PC_2TA---2PA</code> with a runtime of 1,072 steps, on 23 Dec by <code>1PB2PC1PB_2TC0TA---_1PA1PC0PC</code> with a runtime of 3,786 steps and again on 28 Dec by <code>1PB1PA1TA_2TB2PB2PC_---2PA1TC</code> with a runtime of 45,153 steps.		* On 18 Dec, Azerty discovered the new [[TT]](2) champion <code>1TB---_1PA0PB</code> with a runtime of 13 steps. This was followed by new champions a day later: <code>1PB0PA_1TA0PC_1PA---</code> for TT(3) with a runtime of 82 steps, <code>1TB---_0PD1PB_1PA1TA_0PC0PD</code> for TT(4) with a runtime of 758 steps, <code>1TB0PA2PA_2PA---1PA</code> for TT(2,3) with a runtime of 223 steps and <code>1TB3TB2PB---_2TB1PA0PA2TB</code> for TT(2,4) with a runtime of 1,068 steps. On 21 Dec Azerty also discovered the new TT(3,3) champion with a runtime of 427 steps <code>1TB2TA2PA_1TA0TC1PC_---2PA0PA</code>, this champion was surpassed on 22 Dec by <code>1TB2PB1PB_2TA0TA2PC_2TA---2PA</code> with a runtime of 1,072 steps, on 23 Dec by <code>1PB2PC1PB_2TC0TA---_1PA1PC0PC</code> with a runtime of 3,786 steps and again on 28 Dec by <code>1PB1PA1TA_2TB2PB2PC_---2PA1TC</code> with a runtime of 45,153 steps.
	* Azerty [https://azertywastaken.github.io/Website/Champions/index.html shared a website] with champions for many BB-Adjacent functions and original BB.		* Azerty [https://azertywastaken.github.io/Website/Champions/index.html shared a website] with champions for many BB-Adjacent functions and original BB.

	== BB Adjacent ==		== BB Adjacent ==
			* Many new deciders were introduced for [[Fractran]]. BBf(20) = 746 was solved. BBf(21) holdouts were reduced from 9427 to 345. BBf(22) was enumerated and reduced to 5682 holdouts. A Cryptid was constructed in BBf(23).
	* Busy Beaver for [[General Recursive Function\|General Recursive Functions]] (BBµ) was introduced by [[User:Sligocki\|Shawn Ligocki]], computed up to BBµ(3) = 1 and general lower bound <math>BB\mu(6k+19) \ge 2 \uparrow^k 5</math> was established.		* Busy Beaver for [[General Recursive Function\|General Recursive Functions]] (BBµ) was introduced by [[User:Sligocki\|Shawn Ligocki]], computed up to BBµ(3) = 1 and general lower bound <math>BB\mu(6k+19) \ge 2 \uparrow^k 5</math> was established.
	* [[Register machine\|Busy Beaver for Register machines]] (MBB(n)) was introduced and computed up to n = 5 and a lower bound for n = 6 was discovered.		* [[Register machine\|Busy Beaver for Register machines]] (MBB(n)) was introduced and computed up to n = 5 and a lower bound for n = 6 was discovered.

Sligocki: Fixed link. Add lede.

2026-02-08T16:07:23Z

Fixed link. Add lede.

← Older revision		Revision as of 16:07, 8 February 2026
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	''This edition of TMBR is in progress and has not yet been released. Please add any notes you think may be relevant (including in the form a of a TODO with a link to any relevant Discord discussion).''		''This edition of TMBR is in progress and has not yet been released. Please add any notes you think may be relevant (including in the form a of a TODO with a link to any relevant Discord discussion).''

	~~This is the last edition of TMBR this year. 2025 was a very productive year for~~ [[~~Busy~~ Beaver ~~Challenge~~\|~~BBChallenge~~]]~~: about 60%~~ of the ~~next domain, [[BB(6)]], was solved. Furthermore, new champions were discovered for BB(6), [[BB(7)]] and [[BB(4,3)]]. Many models~~ of ~~computation other than Turing Machines were also explored - most notably [[Fractran]] and [[Instruction-Limited Busy Beaver]]. Some new methods were developed~~, ~~such as [https://discord.com/channels/960643023006490684/1028746861395316776/1442964185599447152 mxdys~~'~~s new version~~ of ~~FAR.]~~		[[:Category:This Month in Beaver Research\|This Month in Beaver Research]] for December 2025. In commemoration of the end of the year, we've summarized some of the major accomplishments into This Year in Beaver Research: [[TYBR: 2025]]. This month saw a lot of exploration into BB-adjacent models with the introduction of BB for [[General Recursive Function\|General Recursive Functions]] and [[Register machine\|Register machines]] and new champions for many previously introduced variants.

	This ~~year,~~ [[~~TMBR~~: ~~November~~ 2025~~#Themed Months\|Themed Months~~]] ~~were introduced - first, for [[BB(3,3)]], then for [[~~BB~~(2,5)]]~~ - ~~and~~ the ~~result is the clarification and verification~~ of ~~some of the results and techniques on the [https://discord.com/channels/960643023006490684/1259770474897080380 Discord] and [https://wiki.bbchallenge.org/wiki/~~BB~~(3,3) wiki]. See [[TMBR: November 2025#Themed Months]]~~ for ~~more information.~~

	~~An annotated spreadsheet of~~ [[~~BB(6)~~]] ~~holdouts was also shared by~~ [[~~User:RobinCodes~~\|~~Robin Rovenszky~~]]~~, which includes links to Discord discussions, classification of machines~~ and ~~is almost always up-to-date. See [https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=1330361301#gid=1330361301 Google Sheets]~~

	~~== Misc ==~~

	* Azerty [https://azertywastaken.github.io/TuringMachinesSimulator/bb_champions.html shared a website] with champions for many ~~BB-Adjacent functions and original BB~~.

	== In the News ==		== In the News ==
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	* Patcail and [https://github.com/tromp/AIT/blob/master/fast_growing_and_conjectures/melo.lam Gustavo Melo] discovered a new [[Busy Beaver for lambda calculus\|BBλ(63)]] champion, running for more than <math>f_{\omega^3}\left(2\right)</math> steps and <code>50_ft_lock</code> discovered a new [[Busy Beaver for lambda calculus\|BBλ(91)]] champion, running for over <math>f_{\varepsilon_0 + 1}\left(3\right)</math> steps. f represents the [[Fast-Growing Hierarchy]].		* Patcail and [https://github.com/tromp/AIT/blob/master/fast_growing_and_conjectures/melo.lam Gustavo Melo] discovered a new [[Busy Beaver for lambda calculus\|BBλ(63)]] champion, running for more than <math>f_{\omega^3}\left(2\right)</math> steps and <code>50_ft_lock</code> discovered a new [[Busy Beaver for lambda calculus\|BBλ(91)]] champion, running for over <math>f_{\varepsilon_0 + 1}\left(3\right)</math> steps. f represents the [[Fast-Growing Hierarchy]].
	* On 18 Dec, Azerty discovered the new [[TT]](2) champion <code>1TB---_1PA0PB</code> with a runtime of 13 steps. This was followed by new champions a day later: <code>1PB0PA_1TA0PC_1PA---</code> for TT(3) with a runtime of 82 steps, <code>1TB---_0PD1PB_1PA1TA_0PC0PD</code> for TT(4) with a runtime of 758 steps, <code>1TB0PA2PA_2PA---1PA</code> for TT(2,3) with a runtime of 223 steps and <code>1TB3TB2PB---_2TB1PA0PA2TB</code> for TT(2,4) with a runtime of 1,068 steps. On 21 Dec Azerty also discovered the new TT(3,3) champion with a runtime of 427 steps <code>1TB2TA2PA_1TA0TC1PC_---2PA0PA</code>, this champion was surpassed on 22 Dec by <code>1TB2PB1PB_2TA0TA2PC_2TA---2PA</code> with a runtime of 1,072 steps, on 23 Dec by <code>1PB2PC1PB_2TC0TA---_1PA1PC0PC</code> with a runtime of 3,786 steps and again on 28 Dec by <code>1PB1PA1TA_2TB2PB2PC_---2PA1TC</code> with a runtime of 45,153 steps.		* On 18 Dec, Azerty discovered the new [[TT]](2) champion <code>1TB---_1PA0PB</code> with a runtime of 13 steps. This was followed by new champions a day later: <code>1PB0PA_1TA0PC_1PA---</code> for TT(3) with a runtime of 82 steps, <code>1TB---_0PD1PB_1PA1TA_0PC0PD</code> for TT(4) with a runtime of 758 steps, <code>1TB0PA2PA_2PA---1PA</code> for TT(2,3) with a runtime of 223 steps and <code>1TB3TB2PB---_2TB1PA0PA2TB</code> for TT(2,4) with a runtime of 1,068 steps. On 21 Dec Azerty also discovered the new TT(3,3) champion with a runtime of 427 steps <code>1TB2TA2PA_1TA0TC1PC_---2PA0PA</code>, this champion was surpassed on 22 Dec by <code>1TB2PB1PB_2TA0TA2PC_2TA---2PA</code> with a runtime of 1,072 steps, on 23 Dec by <code>1PB2PC1PB_2TC0TA---_1PA1PC0PC</code> with a runtime of 3,786 steps and again on 28 Dec by <code>1PB1PA1TA_2TB2PB2PC_---2PA1TC</code> with a runtime of 45,153 steps.
			* Azerty [https://azertywastaken.github.io/Website/Champions/index.html shared a website] with champions for many BB-Adjacent functions and original BB.

	== BB Adjacent ==		== BB Adjacent ==

Sligocki: Move TYBR to it's own article

2026-02-08T16:00:00Z

Move TYBR to it's own article

Show changes

Sligocki: Trim some from Champions and add BBµ()

2026-02-08T15:56:37Z

Trim some from Champions and add BBµ()

← Older revision		Revision as of 15:56, 8 February 2026
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	== Champions ==		== Champions ==
	* A new [[Non-halting Turing machine#Translated cycler preperiod\|BBS(4,3)]] champion ({{TM\|1RB1RD1LC_2LB1RB1LC_1LB1LA1LD_0RB2RA2RD}}) was discovered by changing the C0 transition of the [[BB(4,3)]] champion {{TM\|1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD\|halt}} from <code>C0 --> 1RZ</code> to <code>C0 --> 1LB</code>.		* A new [[Non-halting Turing machine#Translated cycler preperiod\|BBS(4,3)]] champion ({{TM\|1RB1RD1LC_2LB1RB1LC_1LB1LA1LD_0RB2RA2RD}}) was discovered by changing the C0 transition of the [[BB(4,3)]] champion {{TM\|1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD\|halt}} from <code>C0 --> 1RZ</code> to <code>C0 --> 1LB</code>.
	* ~~On 27 Dec 2025,~~ [[User:Azerty\|Azerty]] discovered ~~{{TM\|1RB1LA---_2RC2LB1RB_2LC2LA0RC}} which blanks the tape after 225 steps. A day later he found {{TM\|1RB1RC---_1LB1RA2RB_0RB2LC0RC}}~~, ~~which blanks the tape after 308 steps. That record was surpassed again on 31 Dec by the discovery of~~ {{TM\|1RB2LC2LA_1LC---2RA_2RC2LB0LC}} which blanks the tape after 329 steps.		* [[User:Azerty\|Azerty]] discovered a series of [[Blanking Busy Beaver]] 3x3 champions, culminating in {{TM\|1RB2LC2LA_1LC---2RA_2RC2LB0LC}} which blanks the tape after 329 steps on 31 Dec 2025.
	* On 25 Dec 2025, [[User:Azerty\|Azerty]] discovered {{TM\|1RB2RC1LC_0RC0RB1LA_2LA2RC1LB}} which is a [[Translated cycler]] and new [[Non-halting Turing machine#Translated cycler period\|BBP(3,3)]] champion with a new record period length of 1195 steps.		* On 25 Dec 2025, [[User:Azerty\|Azerty]] discovered {{TM\|1RB2RC1LC_0RC0RB1LA_2LA2RC1LB}} which is a [[Translated cycler]] and new [[Non-halting Turing machine#Translated cycler period\|BBP(3,3)]] champion with a new record period length of 1195 steps.
	* Patcail and [https://github.com/tromp/AIT/blob/master/fast_growing_and_conjectures/melo.lam Gustavo Melo] discovered a new [[Busy Beaver for lambda calculus\|BBλ(63)]] champion, running for more than <math>f_{\omega^3}\left(2\right)</math> steps and 50_ft_lock discovered a new [[Busy Beaver for lambda calculus\|BBλ(91)]] champion, running for over <math>f_{\varepsilon_0 + 1}\left(3\right)</math> steps. f represents the [[Fast-Growing Hierarchy]].		* Patcail and [https://github.com/tromp/AIT/blob/master/fast_growing_and_conjectures/melo.lam Gustavo Melo] discovered a new [[Busy Beaver for lambda calculus\|BBλ(63)]] champion, running for more than <math>f_{\omega^3}\left(2\right)</math> steps and <code>50_ft_lock</code> discovered a new [[Busy Beaver for lambda calculus\|BBλ(91)]] champion, running for over <math>f_{\varepsilon_0 + 1}\left(3\right)</math> steps. f represents the [[Fast-Growing Hierarchy]].
	* On 18 Dec Azerty discovered the new [[TT]](2) champion <code>1TB---_1PA0PB</code> with a runtime of 13 steps. This was followed by new champions a day later: <code>1PB0PA_1TA0PC_1PA---</code> for TT(3) with a runtime of 82 steps, <code>1TB---_0PD1PB_1PA1TA_0PC0PD</code> for TT(4) with a runtime of 758 steps, <code>1TB0PA2PA_2PA---1PA</code> for TT(2,3) with a runtime of 223 steps and <code>1TB3TB2PB---_2TB1PA0PA2TB</code> for TT(2,4) with a runtime of 1,068 steps. On 21 Dec Azerty also discovered the new TT(3,3) champion with a runtime of 427 steps <code>1TB2TA2PA_1TA0TC1PC_---2PA0PA</code>, this champion was surpassed on 22 Dec by <code>1TB2PB1PB_2TA0TA2PC_2TA---2PA</code> with a runtime of 1,072 steps, on 23 Dec by <code>1PB2PC1PB_2TC0TA---_1PA1PC0PC</code> with a runtime of 3,786 steps and again on 28 Dec by <code>1PB1PA1TA_2TB2PB2PC_---2PA1TC</code> with a runtime of 45,153 steps.		* On 18 Dec, Azerty discovered the new [[TT]](2) champion <code>1TB---_1PA0PB</code> with a runtime of 13 steps. This was followed by new champions a day later: <code>1PB0PA_1TA0PC_1PA---</code> for TT(3) with a runtime of 82 steps, <code>1TB---_0PD1PB_1PA1TA_0PC0PD</code> for TT(4) with a runtime of 758 steps, <code>1TB0PA2PA_2PA---1PA</code> for TT(2,3) with a runtime of 223 steps and <code>1TB3TB2PB---_2TB1PA0PA2TB</code> for TT(2,4) with a runtime of 1,068 steps. On 21 Dec Azerty also discovered the new TT(3,3) champion with a runtime of 427 steps <code>1TB2TA2PA_1TA0TC1PC_---2PA0PA</code>, this champion was surpassed on 22 Dec by <code>1TB2PB1PB_2TA0TA2PC_2TA---2PA</code> with a runtime of 1,072 steps, on 23 Dec by <code>1PB2PC1PB_2TC0TA---_1PA1PC0PC</code> with a runtime of 3,786 steps and again on 28 Dec by <code>1PB1PA1TA_2TB2PB2PC_---2PA1TC</code> with a runtime of 45,153 steps.
	* [[Maximum Consecutive Ones Function\|num]] TODO

	== BB Adjacent ==		== BB Adjacent ==
			* Busy Beaver for [[General Recursive Function\|General Recursive Functions]] (BBµ) was introduced by [[User:Sligocki\|Shawn Ligocki]], computed up to BBµ(3) = 1 and general lower bound <math>BB\mu(6k+19) \ge 2 \uparrow^k 5</math> was established.
			* [[Register machine\|Busy Beaver for Register machines]] (MBB(n)) was introduced and computed up to n = 5 and a lower bound for n = 6 was discovered.
	* [[Busy Beaver for lambda calculus#De Bruijn\|Busy Beaver for lambda calculus using De Bruijn indexes]] was introduced with lower bounds having been calculated up to n = 26.		* [[Busy Beaver for lambda calculus#De Bruijn\|Busy Beaver for lambda calculus using De Bruijn indexes]] was introduced with lower bounds having been calculated up to n = 26.
	* [[Register machine\|Busy Beaver for Register machines]] (MBB(n)) was introduced and computed up to n = 5 and a lower bound for n = 6 was discovered.		TODO. [[Fractran]] progress, [https://discord.com/channels/960643023006490684/1450894930422530161/1450894930422530161 Semi-infinite tape Busy Beaver]
	TODO. ~~[[General Recursive Function\|General Recursive Functions]],~~ [[Fractran]] progress, [https://discord.com/channels/960643023006490684/1450894930422530161/1450894930422530161 Semi-infinite tape Busy Beaver]

	== [[Holdouts]] ==		== [[Holdouts]] ==

RobinCodes: /* Holdouts */ Added clarification

2026-02-02T18:14:46Z

Holdouts: Added clarification

← Older revision		Revision as of 18:14, 2 February 2026
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	**There are 14 holdouts left to simulate up to 1e12 steps, and 288 to simulate up to 1e13 steps<sup>[https://discord.com/channels/960643023006490684/1239205785913790465/1447303829400846482 <nowiki>[1]</nowiki>]</sup>. Later, at the end of the year, all 14 machines were simulated up to 1e12 machines, which means that now, all holdouts TMs must have a score >1e12. 278 machines are left to simulate up to 1e13. A dynamic list can be found [https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=806905077#gid=806905077 here]. (See results on [https://discord.com/channels/960643023006490684/1026577255754903572/1455316822415900762 Discord], plus [https://discord.com/channels/960643023006490684/1456015962573766829/1456015962573766829 <nowiki>[2]</nowiki>], [https://discord.com/channels/960643023006490684/1456016713928671273/1456016713928671273 <nowiki>[3]</nowiki>] and [https://discord.com/channels/960643023006490684/1456214290955767963/1456214290955767963 <nowiki>[4]</nowiki>])		**There are 14 holdouts left to simulate up to 1e12 steps, and 288 to simulate up to 1e13 steps<sup>[https://discord.com/channels/960643023006490684/1239205785913790465/1447303829400846482 <nowiki>[1]</nowiki>]</sup>. Later, at the end of the year, all 14 machines were simulated up to 1e12 machines, which means that now, all holdouts TMs must have a score >1e12. 278 machines are left to simulate up to 1e13. A dynamic list can be found [https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=806905077#gid=806905077 here]. (See results on [https://discord.com/channels/960643023006490684/1026577255754903572/1455316822415900762 Discord], plus [https://discord.com/channels/960643023006490684/1456015962573766829/1456015962573766829 <nowiki>[2]</nowiki>], [https://discord.com/channels/960643023006490684/1456016713928671273/1456016713928671273 <nowiki>[3]</nowiki>] and [https://discord.com/channels/960643023006490684/1456214290955767963/1456214290955767963 <nowiki>[4]</nowiki>])
	**The possibility of simulating computationally tractable machines which nonetheless has large time and memory requirements [https://discord.com/channels/960643023006490684/1448725136340422717 was discussed]. [[User:RobinCodes/Machines at the Edge#1RB0RE 1LC1LD 0RA0LD 1LB0LA 1RF1RA ---1LB (bbch) CRYPTID\|List]]		**The possibility of simulating computationally tractable machines which nonetheless has large time and memory requirements [https://discord.com/channels/960643023006490684/1448725136340422717 was discussed]. [[User:RobinCodes/Machines at the Edge#1RB0RE 1LC1LD 0RA0LD 1LB0LA 1RF1RA ---1LB (bbch) CRYPTID\|List]]
	** mxdys [https://discord.com/channels/960643023006490684/1239205785913790465/1450455364179857410 shared a new holdouts list,] consisting of '''1343''' machines, which means 73 solved TMs. This is a 5.4% reduction. There is one extra machine that is solved formally, but unverified.		** mxdys [https://discord.com/channels/960643023006490684/1239205785913790465/1450455364179857410 shared a new holdouts list,] consisting of '''1343''' machines, which means 73 solved TMs. This is a 5.4% reduction. There is one extra machine that is solved formally, but unverified. (That is, not verified in Rocq.)
	** The old spreadsheet was replaced with a newer one, see [https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=1330361301#gid=1330361301 Google Sheets]		** The old spreadsheet was replaced with a newer one, see [https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=1330361301#gid=1330361301 Google Sheets]
	** At the end of the year, mxdys [https://discord.com/channels/960643023006490684/1239205785913790465/1455369448264568904 shared the latest holdouts list,] which consisted of '''1326''' machines, that is, 17 TMs solved and a 1.27% reduction.		** At the end of the year, mxdys [https://discord.com/channels/960643023006490684/1239205785913790465/1455369448264568904 shared the latest holdouts list,] which consisted of '''1326''' machines, that is, 17 TMs solved and a 1.27% reduction.

← Older revision		Revision as of 15:56, 8 February 2026
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	== Champions ==		== Champions ==
	* A new [[Non-halting Turing machine#Translated cycler preperiod\|BBS(4,3)]] champion ({{TM\|1RB1RD1LC_2LB1RB1LC_1LB1LA1LD_0RB2RA2RD}}) was discovered by changing the C0 transition of the [[BB(4,3)]] champion {{TM\|1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD\|halt}} from <code>C0 --> 1RZ</code> to <code>C0 --> 1LB</code>.		* A new [[Non-halting Turing machine#Translated cycler preperiod\|BBS(4,3)]] champion ({{TM\|1RB1RD1LC_2LB1RB1LC_1LB1LA1LD_0RB2RA2RD}}) was discovered by changing the C0 transition of the [[BB(4,3)]] champion {{TM\|1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD\|halt}} from <code>C0 --> 1RZ</code> to <code>C0 --> 1LB</code>.
	* ~~On 27 Dec 2025,~~ [[User:Azerty\|Azerty]] discovered ~~{{TM\|1RB1LA---_2RC2LB1RB_2LC2LA0RC}} which blanks the tape after 225 steps. A day later he found {{TM\|1RB1RC---_1LB1RA2RB_0RB2LC0RC}}~~, ~~which blanks the tape after 308 steps. That record was surpassed again on 31 Dec by the discovery of~~ {{TM\|1RB2LC2LA_1LC---2RA_2RC2LB0LC}} which blanks the tape after 329 steps.		* [[User:Azerty\|Azerty]] discovered a series of [[Blanking Busy Beaver]] 3x3 champions, culminating in {{TM\|1RB2LC2LA_1LC---2RA_2RC2LB0LC}} which blanks the tape after 329 steps on 31 Dec 2025.
	* On 25 Dec 2025, [[User:Azerty\|Azerty]] discovered {{TM\|1RB2RC1LC_0RC0RB1LA_2LA2RC1LB}} which is a [[Translated cycler]] and new [[Non-halting Turing machine#Translated cycler period\|BBP(3,3)]] champion with a new record period length of 1195 steps.		* On 25 Dec 2025, [[User:Azerty\|Azerty]] discovered {{TM\|1RB2RC1LC_0RC0RB1LA_2LA2RC1LB}} which is a [[Translated cycler]] and new [[Non-halting Turing machine#Translated cycler period\|BBP(3,3)]] champion with a new record period length of 1195 steps.
	* Patcail and [https://github.com/tromp/AIT/blob/master/fast_growing_and_conjectures/melo.lam Gustavo Melo] discovered a new [[Busy Beaver for lambda calculus\|BBλ(63)]] champion, running for more than <math>f_{\omega^3}\left(2\right)</math> steps and 50_ft_lock discovered a new [[Busy Beaver for lambda calculus\|BBλ(91)]] champion, running for over <math>f_{\varepsilon_0 + 1}\left(3\right)</math> steps. f represents the [[Fast-Growing Hierarchy]].		* Patcail and [https://github.com/tromp/AIT/blob/master/fast_growing_and_conjectures/melo.lam Gustavo Melo] discovered a new [[Busy Beaver for lambda calculus\|BBλ(63)]] champion, running for more than <math>f_{\omega^3}\left(2\right)</math> steps and <code>50_ft_lock</code> discovered a new [[Busy Beaver for lambda calculus\|BBλ(91)]] champion, running for over <math>f_{\varepsilon_0 + 1}\left(3\right)</math> steps. f represents the [[Fast-Growing Hierarchy]].
	* On 18 Dec Azerty discovered the new [[TT]](2) champion <code>1TB---_1PA0PB</code> with a runtime of 13 steps. This was followed by new champions a day later: <code>1PB0PA_1TA0PC_1PA---</code> for TT(3) with a runtime of 82 steps, <code>1TB---_0PD1PB_1PA1TA_0PC0PD</code> for TT(4) with a runtime of 758 steps, <code>1TB0PA2PA_2PA---1PA</code> for TT(2,3) with a runtime of 223 steps and <code>1TB3TB2PB---_2TB1PA0PA2TB</code> for TT(2,4) with a runtime of 1,068 steps. On 21 Dec Azerty also discovered the new TT(3,3) champion with a runtime of 427 steps <code>1TB2TA2PA_1TA0TC1PC_---2PA0PA</code>, this champion was surpassed on 22 Dec by <code>1TB2PB1PB_2TA0TA2PC_2TA---2PA</code> with a runtime of 1,072 steps, on 23 Dec by <code>1PB2PC1PB_2TC0TA---_1PA1PC0PC</code> with a runtime of 3,786 steps and again on 28 Dec by <code>1PB1PA1TA_2TB2PB2PC_---2PA1TC</code> with a runtime of 45,153 steps.		* On 18 Dec, Azerty discovered the new [[TT]](2) champion <code>1TB---_1PA0PB</code> with a runtime of 13 steps. This was followed by new champions a day later: <code>1PB0PA_1TA0PC_1PA---</code> for TT(3) with a runtime of 82 steps, <code>1TB---_0PD1PB_1PA1TA_0PC0PD</code> for TT(4) with a runtime of 758 steps, <code>1TB0PA2PA_2PA---1PA</code> for TT(2,3) with a runtime of 223 steps and <code>1TB3TB2PB---_2TB1PA0PA2TB</code> for TT(2,4) with a runtime of 1,068 steps. On 21 Dec Azerty also discovered the new TT(3,3) champion with a runtime of 427 steps <code>1TB2TA2PA_1TA0TC1PC_---2PA0PA</code>, this champion was surpassed on 22 Dec by <code>1TB2PB1PB_2TA0TA2PC_2TA---2PA</code> with a runtime of 1,072 steps, on 23 Dec by <code>1PB2PC1PB_2TC0TA---_1PA1PC0PC</code> with a runtime of 3,786 steps and again on 28 Dec by <code>1PB1PA1TA_2TB2PB2PC_---2PA1TC</code> with a runtime of 45,153 steps.
	* [[Maximum Consecutive Ones Function\|num]] TODO

	== BB Adjacent ==		== BB Adjacent ==
			* Busy Beaver for [[General Recursive Function\|General Recursive Functions]] (BBµ) was introduced by [[User:Sligocki\|Shawn Ligocki]], computed up to BBµ(3) = 1 and general lower bound <math>BB\mu(6k+19) \ge 2 \uparrow^k 5</math> was established.
			* [[Register machine\|Busy Beaver for Register machines]] (MBB(n)) was introduced and computed up to n = 5 and a lower bound for n = 6 was discovered.
	* [[Busy Beaver for lambda calculus#De Bruijn\|Busy Beaver for lambda calculus using De Bruijn indexes]] was introduced with lower bounds having been calculated up to n = 26.		* [[Busy Beaver for lambda calculus#De Bruijn\|Busy Beaver for lambda calculus using De Bruijn indexes]] was introduced with lower bounds having been calculated up to n = 26.
	* [[Register machine\|Busy Beaver for Register machines]] (MBB(n)) was introduced and computed up to n = 5 and a lower bound for n = 6 was discovered.		TODO. [[Fractran]] progress, [https://discord.com/channels/960643023006490684/1450894930422530161/1450894930422530161 Semi-infinite tape Busy Beaver]
	TODO. ~~[[General Recursive Function\|General Recursive Functions]],~~ [[Fractran]] progress, [https://discord.com/channels/960643023006490684/1450894930422530161/1450894930422530161 Semi-infinite tape Busy Beaver]

	== [[Holdouts]] ==		== [[Holdouts]] ==

← Older revision		Revision as of 20:14, 8 February 2026
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	{{TMBRnav\|November 2025\|January 2026}}		{{TMBRnav\|November 2025\|January 2026}}

	[[:Category:This Month in Beaver Research\|This Month in Beaver Research]] for December 2025. In commemoration of the end of the year, we've summarized some of the major accomplishments into This Year in Beaver Research: [[TYBR: 2025]]. This month saw a lot of exploration into BB-adjacent models with the introduction of BB for [[General Recursive Function\|General Recursive Functions]] and [[Register machine\|Register machines]] and new champions for many previously introduced variants.		[[:Category:This Month in Beaver Research\|This Month in Beaver Research]] for December 2025.

			In commemoration of the end of the year, we've summarized some of the major accomplishments into This Year in Beaver Research: [[TYBR: 2025]]. This month saw a lot of exploration into BB-adjacent models with the introduction of BB for [[General Recursive Function\|General Recursive Functions]] and [[Register machine\|Register machines]] and new champions for many previously introduced variants.

	== In the News ==		== In the News ==
Line 53:		Line 55:
	\|}		\|}
	* [[BB(6)\|BB(6):]] '''90''' machines solved, a '''6.36%''' reduction.		* [[BB(6)\|BB(6):]] '''90''' machines solved, a '''6.36%''' reduction.
	**~~There are~~ 14 holdouts ~~left to simulate up~~ to 1e12 steps, and 288 ~~to simulate up~~ to 1e13 steps~~<sup>[https://discord.com/channels/960643023006490684/1239205785913790465/1447303829400846482 <nowiki>[1]</nowiki>]</sup>~~. ~~Later~~, at the ~~end~~ of the ~~year, all 14 machines~~ were simulated ~~up to~~ 1e12 ~~machines, which~~ means ~~that now,~~ all ~~holdouts~~ TMs must ~~have a score >~~1e12. 278 machines are left to simulate up to 1e13. A dynamic list can be found [https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=806905077#gid=806905077 here]. (See results on [https://discord.com/channels/960643023006490684/1026577255754903572/1455316822415900762 Discord], plus [https://discord.com/channels/960643023006490684/1456015962573766829/1456015962573766829 <nowiki>[2]</nowiki>], [https://discord.com/channels/960643023006490684/1456016713928671273/1456016713928671273 <nowiki>[3]</nowiki>] and [https://discord.com/channels/960643023006490684/1456214290955767963/1456214290955767963 <nowiki>[4]</nowiki>])		**At the start of the month, 14 holdouts had not been simulated to 1e12 steps and 288 holdouts had not been simulated to 1e13 steps. This month, all 14 of the former holdouts and 10 of the latter holdouts were simulated past 1e12 steps and 1e13 steps respectively. This means all holdout TMs must continue for at least 1e12 steps. 278 machines are left to simulate up to 1e13 steps. A dynamic list can be found [https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=806905077#gid=806905077 here]. (See results on [https://discord.com/channels/960643023006490684/1026577255754903572/1455316822415900762 Discord], plus [https://discord.com/channels/960643023006490684/1239205785913790465/1447303829400846482 <nowiki>[1]</nowiki>], [https://discord.com/channels/960643023006490684/1456015962573766829/1456015962573766829 <nowiki>[2]</nowiki>], [https://discord.com/channels/960643023006490684/1456016713928671273/1456016713928671273 <nowiki>[3]</nowiki>] and [https://discord.com/channels/960643023006490684/1456214290955767963/1456214290955767963 <nowiki>[4]</nowiki>])
	**The possibility of simulating computationally tractable machines which nonetheless has large time and memory requirements [https://discord.com/channels/960643023006490684/1448725136340422717 was discussed]. [[User:RobinCodes/Machines at the Edge#1RB0RE 1LC1LD 0RA0LD 1LB0LA 1RF1RA ---1LB (bbch) CRYPTID\|~~List~~]]		**The possibility of simulating computationally tractable machines which nonetheless has large time and memory requirements [https://discord.com/channels/960643023006490684/1448725136340422717 was discussed]. See a list of such TMs [[User:RobinCodes/Machines at the Edge#1RB0RE 1LC1LD 0RA0LD 1LB0LA 1RF1RA ---1LB (bbch) CRYPTID\|here]].
	** mxdys [https://discord.com/channels/960643023006490684/1239205785913790465/1450455364179857410 shared a new holdouts list,] consisting of '''1343''' machines, which means 73 solved TMs. This is a 5.4% reduction. There is one extra machine that is solved formally, but unverified. (That is, not verified in Rocq.)		** mxdys [https://discord.com/channels/960643023006490684/1239205785913790465/1450455364179857410 shared a new holdouts list,] consisting of '''1343''' machines, which means 73 solved TMs. This is a 5.4% reduction. There is one extra machine that is solved formally, but unverified. (That is, not verified in Rocq.)
	** The old spreadsheet was replaced with a newer one, see [https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=1330361301#gid=1330361301 Google Sheets]		** The old spreadsheet was replaced with a newer one, see [https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=1330361301#gid=1330361301 Google Sheets]
	** At the end of the year, mxdys [https://discord.com/channels/960643023006490684/1239205785913790465/1455369448264568904 shared the latest holdouts list,] which consisted of '''1326''' machines, ~~that is,~~ 17 TMs ~~solved~~ and a 1.27% reduction.		** At the end of the year, mxdys [https://discord.com/channels/960643023006490684/1239205785913790465/1455369448264568904 shared the latest holdouts list,] which consisted of '''1326''' machines, meaning the solution of 17 TMs and a 1.27% reduction.
	* [[BB(7)\|BB(7):]]		* [[BB(7)\|BB(7):]]
	**Further enumeration by Andrew Ducharme has reduced the number of holdouts from 20,405,295 to 20,387,509, a 0.09% reduction.		**Further enumeration by Andrew Ducharme has reduced the number of holdouts from 20,405,295 to 20,387,509, a 0.09% reduction.