TMBR: November 2025 - Revision history

RobinCodes: Updated references for consistency, made sure BB6 spreadsheet was the current version

2026-04-11T18:31:05Z

Updated references for consistency, made sure BB6 spreadsheet was the current version

RobinCodes: /* Themed Months */ Added two machines analysed by hipparcos during BB(2,5) month, which was missed

2025-12-16T18:26:46Z

Themed Months: Added two machines analysed by hipparcos during BB(2,5) month, which was missed

← Older revision		Revision as of 18:26, 16 December 2025
Line 12:		Line 12:
	== Themed Months ==		== Themed Months ==

	There have been two specific BB domain themed months: BB(3,3) month (October) and BB(2,5) month (November). For BB(3,3), this resulted in the clarification 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]. LegionMammal wrote up [https://discord.com/channels/960643023006490684/1259770474897080380/1431274106736873685 a detailed explanation] of the probvious halter. No further progress on holdouts was made in October due to the limited number of holdouts and the work that's already been put into trying to solve them. For BB(2,5), it was verified that the [https://wiki.bbchallenge.org/wiki/BB(2,5) Wiki] was up to date. @mxdys shared some of [https://discord.com/channels/960643023006490684/1259770421046411285/1436149296004071615 his old notes] on the unanalyzed machines.		There have been two specific BB domain themed months: BB(3,3) month (October) and BB(2,5) month (November). For BB(3,3), this resulted in the clarification 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]. LegionMammal wrote up [https://discord.com/channels/960643023006490684/1259770474897080380/1431274106736873685 a detailed explanation] of the probvious halter. No further progress on holdouts was made in October due to the limited number of holdouts and the work that's already been put into trying to solve them. For BB(2,5), it was verified that the [https://wiki.bbchallenge.org/wiki/BB(2,5) Wiki] was up to date. @mxdys shared some of [https://discord.com/channels/960643023006490684/1259770421046411285/1436149296004071615 his old notes] on the unanalyzed machines, and hipparcos analysed two machines<sup>[https://discord.com/channels/960643023006490684/1436181033992327333/1436181033992327333 <nowiki>[1]</nowiki>][https://discord.com/channels/960643023006490684/1440877223744770259/1440877223744770259 <nowiki>[2]</nowiki>]</sup>, both of which turned out to be shift overflow mixed-digits counters, lowering the unanalysed holdout count to 15. (Two of which have notes by mxdys).

	== Optimization ==		== Optimization ==

Sligocki: Note Shen Lin

2025-12-05T17:45:34Z

Note Shen Lin

← Older revision		Revision as of 17:45, 5 December 2025
Line 3:		Line 3:
	[[:Category:This Month in Beaver Research\|This Month in Beaver Research]] for November 2025.		[[:Category:This Month in Beaver Research\|This Month in Beaver Research]] for November 2025.

	This month we continue to see progress in many different directions. @mxdys reduced the [[BB(6)]] holdout count by 12% to 1416 (very significant progress with a list this small and pored over). There was significant exploration into Busy Beaver functions for alternative models of computation including [[Fractran]] and [[Cyclic Tag]] systems. Furthermore, both Tristan and Carl gave talks about Busy Beaver.		This month we continue to see progress in many different directions. @mxdys reduced the [[BB(6)]] holdout count by 12% to 1416 (very significant progress with a list this small and pored over). There was significant exploration into Busy Beaver functions for alternative models of computation including [[Fractran]] and [[Cyclic Tag]] systems. Furthermore, both Tristan and Carl gave talks about Busy Beaver. This month we added [[Shen Lin]] to the wiki as our first article about a [[:Category:People\|person]].

	== Talks ==		== Talks ==

RobinCodes: Small grammar fix

2025-12-05T17:35:50Z

Small grammar fix

← Older revision		Revision as of 17:35, 5 December 2025
Line 3:		Line 3:
	[[:Category:This Month in Beaver Research\|This Month in Beaver Research]] for November 2025.		[[:Category:This Month in Beaver Research\|This Month in Beaver Research]] for November 2025.

	This month we continue to see progress in many different directions. @mxdys reduced the [[BB(6)]] holdout count by 12% to 1416 (very significant progress with a list this small and pored over). There was significant exploration into Busy Beaver functions for alternative models of computation including [[Fractran]] and [[Cyclic Tag]] systems. ~~And~~ both Tristan and Carl gave talks about Busy Beaver.		This month we continue to see progress in many different directions. @mxdys reduced the [[BB(6)]] holdout count by 12% to 1416 (very significant progress with a list this small and pored over). There was significant exploration into Busy Beaver functions for alternative models of computation including [[Fractran]] and [[Cyclic Tag]] systems. Furthermore, both Tristan and Carl gave talks about Busy Beaver.

	== Talks ==		== Talks ==

Sligocki: Add lede

2025-12-05T17:26:52Z

Add lede

← Older revision		Revision as of 17:26, 5 December 2025
Line 1:		Line 1:
	{{TMBRnav\|October 2025\|December 2025}}		{{TMBRnav\|October 2025\|December 2025}}

	''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 November 2025.

			This month we continue to see progress in many different directions. @mxdys reduced the [[BB(6)]] holdout count by 12% to 1416 (very significant progress with a list this small and pored over). There was significant exploration into Busy Beaver functions for alternative models of computation including [[Fractran]] and [[Cyclic Tag]] systems. And both Tristan and Carl gave talks about Busy Beaver.

	== Talks ==		== Talks ==
Line 15:		Line 17:
	[[File:Vonhust bb6 benchmark.png\|thumb\|Benchmark for vonhust's simulator run on [[BB(6)]] holdouts.]]		[[File:Vonhust bb6 benchmark.png\|thumb\|Benchmark for vonhust's simulator run on [[BB(6)]] holdouts.]]

	~~Discord user~~ vonhust created a fast TM simulator that averages 2 billion steps / s. It uses fixed-block [[Macro Machine\|Macro Machines]] with each block bit-packed into integers. It is about 10x faster than direct simulators across most TMs.<sup>[https://discord.com/channels/960643023006490684/1226543091264126976/1438890558499061821]</sup>		@vonhust created a fast TM simulator that averages 2 billion steps / s. It uses fixed-block [[Macro Machine\|Macro Machines]] with each block bit-packed into integers. It is about 10x faster than direct simulators across most TMs.<sup>[https://discord.com/channels/960643023006490684/1226543091264126976/1438890558499061821]</sup>

	==BB Adjacent==		==BB Adjacent==
Line 21:		Line 23:

	* [[Fractran\|Busy Beaver for Fractan]] (BBf) was introduced on 1 Nov by Jason Yuen.<sup>[https://discord.com/channels/960643023006490684/1362008236118511758/1433148101170040924]</sup> Exact values have been proven up to BBf(19) = 370 and exhaustive enumeration has been run up to size 21 (with BBf(21) ≥ 31,957,632 and 587 holdouts). No [[Cryptids]] have been found yet by enumeration, but [[Hydra]] has been encoded into a size 29 fractran program, so this provides a sort of upper bound on solvability.		* [[Fractran\|Busy Beaver for Fractan]] (BBf) was introduced on 1 Nov by Jason Yuen.<sup>[https://discord.com/channels/960643023006490684/1362008236118511758/1433148101170040924]</sup> Exact values have been proven up to BBf(19) = 370 and exhaustive enumeration has been run up to size 21 (with BBf(21) ≥ 31,957,632 and 587 holdouts). No [[Cryptids]] have been found yet by enumeration, but [[Hydra]] has been encoded into a size 29 fractran program, so this provides a sort of upper bound on solvability.
	* [[Cyclic Tree Busy Beaver]] (CTBB) was introduced by ~~Discord user~~ Jack on 14 Nov.<sup>[https://discord.com/channels/960643023006490684/1438694294042181742]</sup> The exact value is known for CTBB(2) = 5 and lower bounds have been found up to size 7 with CTBB(7) > 4↑↑↑↑(4↑↑↑3).		* [[Cyclic Tree Busy Beaver]] (CTBB) was introduced by @Jack on 14 Nov.<sup>[https://discord.com/channels/960643023006490684/1438694294042181742]</sup> The exact value is known for CTBB(2) = 5 and lower bounds have been found up to size 7 with CTBB(7) > 4↑↑↑↑(4↑↑↑3).
	* Quite a few other BB variants have been proposed this month, but don't seem to have been significantly explored yet: [https://discord.com/channels/960643023006490684/1440230138242662400 BB110] (for [[wikipedia:Rule_110\|Rule 110]]), [https://discord.com/channels/960643023006490684/1443176113353261200 BB_trw], [https://discord.com/channels/960643023006490684/1443330663288934702 BB_cgol] (for [[wikipedia:Conway's_Game_of_Life\|Conway's Game of Life]]), [[Tiny Tag]] and [[Busy Beaver for SKI calculus]].		* Quite a few other BB variants have been proposed this month, but don't seem to have been significantly explored yet: [https://discord.com/channels/960643023006490684/1440230138242662400 BB110] (for [[wikipedia:Rule_110\|Rule 110]]), [https://discord.com/channels/960643023006490684/1443176113353261200 BB_trw], [https://discord.com/channels/960643023006490684/1443330663288934702 BB_cgol] (for [[wikipedia:Conway's_Game_of_Life\|Conway's Game of Life]]), [[Tiny Tag]] and [[Busy Beaver for SKI calculus]].
	* The [https://googology.miraheze.org/wiki/Bashicu_matrix_system Bashicu Matrix System] milestone for [[BBλ]] has been reduced from 350 to 331.<sup>[https://discord.com/channels/960643023006490684/1355653587824283678/1436844104742076507]</sup>		* The [https://googology.miraheze.org/wiki/Bashicu_matrix_system Bashicu Matrix System] milestone for [[BBλ]] has been reduced from 350 to 331.<sup>[https://discord.com/channels/960643023006490684/1355653587824283678/1436844104742076507]</sup>

	= Holdouts =		== Holdouts ==

	* [[BB(6)\|BB(6):]] Total holdout reduction: 204 TMs, a 12% reduction!		* [[BB(6)\|BB(6):]] Total holdout reduction: 204 TMs, a 12% reduction!
	** @mxdys [https://discord.com/channels/960643023006490684/1239205785913790465/1438983076662477004 released a holdouts list] consisting of 1534 machines up to equivalence, which is a 6% reduction (84 machines)		** @mxdys [https://discord.com/channels/960643023006490684/1239205785913790465/1438983076662477004 released a holdouts list] consisting of 1534 machines up to equivalence, which is a 6% reduction (84 machines)

Polygon: /* BB Adjacent */ linked tiny tag to its wiki page

2025-12-04T18:01:57Z

BB Adjacent: linked tiny tag to its wiki page

← Older revision		Revision as of 18:01, 4 December 2025
Line 22:		Line 22:
	* [[Fractran\|Busy Beaver for Fractan]] (BBf) was introduced on 1 Nov by Jason Yuen.<sup>[https://discord.com/channels/960643023006490684/1362008236118511758/1433148101170040924]</sup> Exact values have been proven up to BBf(19) = 370 and exhaustive enumeration has been run up to size 21 (with BBf(21) ≥ 31,957,632 and 587 holdouts). No [[Cryptids]] have been found yet by enumeration, but [[Hydra]] has been encoded into a size 29 fractran program, so this provides a sort of upper bound on solvability.		* [[Fractran\|Busy Beaver for Fractan]] (BBf) was introduced on 1 Nov by Jason Yuen.<sup>[https://discord.com/channels/960643023006490684/1362008236118511758/1433148101170040924]</sup> Exact values have been proven up to BBf(19) = 370 and exhaustive enumeration has been run up to size 21 (with BBf(21) ≥ 31,957,632 and 587 holdouts). No [[Cryptids]] have been found yet by enumeration, but [[Hydra]] has been encoded into a size 29 fractran program, so this provides a sort of upper bound on solvability.
	* [[Cyclic Tree Busy Beaver]] (CTBB) was introduced by Discord user Jack on 14 Nov.<sup>[https://discord.com/channels/960643023006490684/1438694294042181742]</sup> The exact value is known for CTBB(2) = 5 and lower bounds have been found up to size 7 with CTBB(7) > 4↑↑↑↑(4↑↑↑3).		* [[Cyclic Tree Busy Beaver]] (CTBB) was introduced by Discord user Jack on 14 Nov.<sup>[https://discord.com/channels/960643023006490684/1438694294042181742]</sup> The exact value is known for CTBB(2) = 5 and lower bounds have been found up to size 7 with CTBB(7) > 4↑↑↑↑(4↑↑↑3).
	* Quite a few other BB variants have been proposed this month, but don't seem to have been significantly explored yet: [https://discord.com/channels/960643023006490684/1440230138242662400 BB110] (for [[wikipedia:Rule_110\|Rule 110]]), [https://discord.com/channels/960643023006490684/1443176113353261200 BB_trw], [https://discord.com/channels/960643023006490684/1443330663288934702 BB_cgol] (for [[wikipedia:Conway's_Game_of_Life\|Conway's Game of Life]]), [~~https://discord.com/channels/960643023006490684/1445557217905475666~~ Tiny Tag] and [[Busy Beaver for SKI calculus]].		* Quite a few other BB variants have been proposed this month, but don't seem to have been significantly explored yet: [https://discord.com/channels/960643023006490684/1440230138242662400 BB110] (for [[wikipedia:Rule_110\|Rule 110]]), [https://discord.com/channels/960643023006490684/1443176113353261200 BB_trw], [https://discord.com/channels/960643023006490684/1443330663288934702 BB_cgol] (for [[wikipedia:Conway's_Game_of_Life\|Conway's Game of Life]]), [[Tiny Tag]] and [[Busy Beaver for SKI calculus]].
	* The [https://googology.miraheze.org/wiki/Bashicu_matrix_system Bashicu Matrix System] milestone for [[BBλ]] has been reduced from 350 to 331.<sup>[https://discord.com/channels/960643023006490684/1355653587824283678/1436844104742076507]</sup>		* The [https://googology.miraheze.org/wiki/Bashicu_matrix_system Bashicu Matrix System] milestone for [[BBλ]] has been reduced from 350 to 331.<sup>[https://discord.com/channels/960643023006490684/1355653587824283678/1436844104742076507]</sup>

Polygon: /* BB Adjacent */ added link to Bashicu matrix system

2025-12-04T17:56:18Z

BB Adjacent: added link to Bashicu matrix system

← Older revision		Revision as of 17:56, 4 December 2025
Line 23:		Line 23:
	* [[Cyclic Tree Busy Beaver]] (CTBB) was introduced by Discord user Jack on 14 Nov.<sup>[https://discord.com/channels/960643023006490684/1438694294042181742]</sup> The exact value is known for CTBB(2) = 5 and lower bounds have been found up to size 7 with CTBB(7) > 4↑↑↑↑(4↑↑↑3).		* [[Cyclic Tree Busy Beaver]] (CTBB) was introduced by Discord user Jack on 14 Nov.<sup>[https://discord.com/channels/960643023006490684/1438694294042181742]</sup> The exact value is known for CTBB(2) = 5 and lower bounds have been found up to size 7 with CTBB(7) > 4↑↑↑↑(4↑↑↑3).
	* Quite a few other BB variants have been proposed this month, but don't seem to have been significantly explored yet: [https://discord.com/channels/960643023006490684/1440230138242662400 BB110] (for [[wikipedia:Rule_110\|Rule 110]]), [https://discord.com/channels/960643023006490684/1443176113353261200 BB_trw], [https://discord.com/channels/960643023006490684/1443330663288934702 BB_cgol] (for [[wikipedia:Conway's_Game_of_Life\|Conway's Game of Life]]), [https://discord.com/channels/960643023006490684/1445557217905475666 Tiny Tag] and [[Busy Beaver for SKI calculus]].		* Quite a few other BB variants have been proposed this month, but don't seem to have been significantly explored yet: [https://discord.com/channels/960643023006490684/1440230138242662400 BB110] (for [[wikipedia:Rule_110\|Rule 110]]), [https://discord.com/channels/960643023006490684/1443176113353261200 BB_trw], [https://discord.com/channels/960643023006490684/1443330663288934702 BB_cgol] (for [[wikipedia:Conway's_Game_of_Life\|Conway's Game of Life]]), [https://discord.com/channels/960643023006490684/1445557217905475666 Tiny Tag] and [[Busy Beaver for SKI calculus]].
	* The ~~BMS~~ milestone for [[BBλ]] has been reduced from 350 to 331.<sup>[https://discord.com/channels/960643023006490684/1355653587824283678/1436844104742076507]</sup>		* The [https://googology.miraheze.org/wiki/Bashicu_matrix_system Bashicu Matrix System] milestone for [[BBλ]] has been reduced from 350 to 331.<sup>[https://discord.com/channels/960643023006490684/1355653587824283678/1436844104742076507]</sup>

	= Holdouts =		= Holdouts =

Tjligocki: /* Holdouts */ Corrected number of completed subtasks to 40K - 4 "batches" of 10K subtasks each have been completed

2025-12-03T21:42:33Z

Holdouts: Corrected number of completed subtasks to 40K - 4 "batches" of 10K subtasks each have been completed

← Older revision		Revision as of 21:42, 3 December 2025
Line 36:		Line 36:
	* [[BB(2,7)\|BB(2,7):]] Enumeration started!		* [[BB(2,7)\|BB(2,7):]] Enumeration started!
	** The [https://github.com/ccz181078/TM code provided by mxdys] breaks up the BB(2,7) enumeration into 1 million subtasks which each run for ~10 minutes and leave ~2500 holdouts based on an average of the first 1K subtasks. These values are about 5 times longer than and 25 times larger than the ones for [[BB(7)]].		** The [https://github.com/ccz181078/TM code provided by mxdys] breaks up the BB(2,7) enumeration into 1 million subtasks which each run for ~10 minutes and leave ~2500 holdouts based on an average of the first 1K subtasks. These values are about 5 times longer than and 25 times larger than the ones for [[BB(7)]].
	** Terry Ligocki enumerated the first 4 subtasks, resulting in 124,025,546 holdouts, which can be found [https://drive.google.com/drive/folders/11AiZYiKJq7v0ns9o5nt-xUsSgSpcuNvZ?usp=drive_link here].		** Terry Ligocki enumerated the first 40K subtasks, resulting in 124,025,546 holdouts, which can be found [https://drive.google.com/drive/folders/11AiZYiKJq7v0ns9o5nt-xUsSgSpcuNvZ?usp=drive_link here].
	** The expected number of holdouts after the enumeration is ~3B TMs.		** The expected number of holdouts after the enumeration is ~3B TMs.

	[[Category:This Month in Beaver Research\|2025-11]]		[[Category:This Month in Beaver Research\|2025-11]]

Sligocki: /* BB Adjacent */ List a number of other proposed BB variants

2025-12-03T21:37:12Z

BB Adjacent: List a number of other proposed BB variants

← Older revision		Revision as of 21:37, 3 December 2025
Line 22:		Line 22:
	* [[Fractran\|Busy Beaver for Fractan]] (BBf) was introduced on 1 Nov by Jason Yuen.<sup>[https://discord.com/channels/960643023006490684/1362008236118511758/1433148101170040924]</sup> Exact values have been proven up to BBf(19) = 370 and exhaustive enumeration has been run up to size 21 (with BBf(21) ≥ 31,957,632 and 587 holdouts). No [[Cryptids]] have been found yet by enumeration, but [[Hydra]] has been encoded into a size 29 fractran program, so this provides a sort of upper bound on solvability.		* [[Fractran\|Busy Beaver for Fractan]] (BBf) was introduced on 1 Nov by Jason Yuen.<sup>[https://discord.com/channels/960643023006490684/1362008236118511758/1433148101170040924]</sup> Exact values have been proven up to BBf(19) = 370 and exhaustive enumeration has been run up to size 21 (with BBf(21) ≥ 31,957,632 and 587 holdouts). No [[Cryptids]] have been found yet by enumeration, but [[Hydra]] has been encoded into a size 29 fractran program, so this provides a sort of upper bound on solvability.
	* [[Cyclic Tree Busy Beaver]] (CTBB) was introduced by Discord user Jack on 14 Nov.<sup>[https://discord.com/channels/960643023006490684/1438694294042181742]</sup> The exact value is known for CTBB(2) = 5 and lower bounds have been found up to size 7 with CTBB(7) > 4↑↑↑↑(4↑↑↑3).		* [[Cyclic Tree Busy Beaver]] (CTBB) was introduced by Discord user Jack on 14 Nov.<sup>[https://discord.com/channels/960643023006490684/1438694294042181742]</sup> The exact value is known for CTBB(2) = 5 and lower bounds have been found up to size 7 with CTBB(7) > 4↑↑↑↑(4↑↑↑3).
			* Quite a few other BB variants have been proposed this month, but don't seem to have been significantly explored yet: [https://discord.com/channels/960643023006490684/1440230138242662400 BB110] (for [[wikipedia:Rule_110\|Rule 110]]), [https://discord.com/channels/960643023006490684/1443176113353261200 BB_trw], [https://discord.com/channels/960643023006490684/1443330663288934702 BB_cgol] (for [[wikipedia:Conway's_Game_of_Life\|Conway's Game of Life]]), [https://discord.com/channels/960643023006490684/1445557217905475666 Tiny Tag] and [[Busy Beaver for SKI calculus]].
	* The BMS milestone for [[BBλ]] has been reduced from 350 to 331.<sup>[https://discord.com/channels/960643023006490684/1355653587824283678/1436844104742076507]</sup>		* The BMS milestone for [[BBλ]] has been reduced from 350 to 331.<sup>[https://discord.com/channels/960643023006490684/1355653587824283678/1436844104742076507]</sup>

Sligocki: Move image out of list

2025-12-03T21:26:12Z

Move image out of list

← Older revision		Revision as of 21:26, 3 December 2025
Line 14:		Line 14:
	== Optimization ==		== Optimization ==
	[[File:Vonhust bb6 benchmark.png\|thumb\|Benchmark for vonhust's simulator run on [[BB(6)]] holdouts.]]		[[File:Vonhust bb6 benchmark.png\|thumb\|Benchmark for vonhust's simulator run on [[BB(6)]] holdouts.]]

	Discord user vonhust created a fast TM simulator that averages 2 billion steps / s. It uses fixed-block [[Macro Machine\|Macro Machines]] with each block bit-packed into integers. It is about 10x faster than direct simulators across most TMs.<sup>[https://discord.com/channels/960643023006490684/1226543091264126976/1438890558499061821]</sup>		Discord user vonhust created a fast TM simulator that averages 2 billion steps / s. It uses fixed-block [[Macro Machine\|Macro Machines]] with each block bit-packed into integers. It is about 10x faster than direct simulators across most TMs.<sup>[https://discord.com/channels/960643023006490684/1226543091264126976/1438890558499061821]</sup>

	==BB Adjacent==		==BB Adjacent==
			[[File:Fractran deciders.png\|alt=All Fractran deciders\|thumb\|All Fractran deciders summarized and their relations, shared by Daniel Yuan on [https://discord.com/channels/960643023006490684/1438019511155691521/1439001835904958655 14 Nov 2025]]]

	* [[File:Fractran deciders.png\|alt=All Fractran deciders\|thumb\|All Fractran deciders summarized and their relations, shared by Daniel Yuan on [https://discord.com/channels/960643023006490684/1438019511155691521/1439001835904958655 14 Nov 2025]]][[Fractran\|Busy Beaver for Fractan]] (BBf) was introduced on 1 Nov by Jason Yuen.<sup>[https://discord.com/channels/960643023006490684/1362008236118511758/1433148101170040924]</sup> Exact values have been proven up to BBf(19) = 370 and exhaustive enumeration has been run up to size 21 (with BBf(21) ≥ 31,957,632 and 587 holdouts). No [[Cryptids]] have been found yet by enumeration, but [[Hydra]] has been encoded into a size 29 fractran program, so this provides a sort of upper bound on solvability.		* [[Fractran\|Busy Beaver for Fractan]] (BBf) was introduced on 1 Nov by Jason Yuen.<sup>[https://discord.com/channels/960643023006490684/1362008236118511758/1433148101170040924]</sup> Exact values have been proven up to BBf(19) = 370 and exhaustive enumeration has been run up to size 21 (with BBf(21) ≥ 31,957,632 and 587 holdouts). No [[Cryptids]] have been found yet by enumeration, but [[Hydra]] has been encoded into a size 29 fractran program, so this provides a sort of upper bound on solvability.
	* [[Cyclic Tree Busy Beaver]] (CTBB) was introduced by Discord user Jack on 14 Nov.<sup>[https://discord.com/channels/960643023006490684/1438694294042181742]</sup> The exact value is known for CTBB(2) = 5 and lower bounds have been found up to size 7 with CTBB(7) > 4↑↑↑↑(4↑↑↑3).		* [[Cyclic Tree Busy Beaver]] (CTBB) was introduced by Discord user Jack on 14 Nov.<sup>[https://discord.com/channels/960643023006490684/1438694294042181742]</sup> The exact value is known for CTBB(2) = 5 and lower bounds have been found up to size 7 with CTBB(7) > 4↑↑↑↑(4↑↑↑3).
	* The BMS milestone for [[BBλ]] has been reduced from 350 to 331.<sup>[https://discord.com/channels/960643023006490684/1355653587824283678/1436844104742076507]</sup>		* The BMS milestone for [[BBλ]] has been reduced from 350 to 331.<sup>[https://discord.com/channels/960643023006490684/1355653587824283678/1436844104742076507]</sup>

← Older revision		Revision as of 18:31, 11 April 2026
Line 12:		Line 12:
	== Themed Months ==		== Themed Months ==

	There have been two specific BB domain themed months: BB(3,3) month (October) and BB(2,5) month (November). For BB(3,3), this resulted in the clarification 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]. LegionMammal wrote up [https://discord.com/channels/960643023006490684/1259770474897080380/1431274106736873685 a detailed explanation] of the probvious halter. No further progress on holdouts was made in October due to the limited number of holdouts and the work that's already been put into trying to solve them. For BB(2,5), it was verified that the [https://wiki.bbchallenge.org/wiki/BB(2,5) Wiki] was up to date. @mxdys shared some of [https://discord.com/channels/960643023006490684/1259770421046411285/1436149296004071615 his old notes] on the unanalyzed machines, and hipparcos analysed two machines<sup>[https://discord.com/channels/960643023006490684/1436181033992327333/1436181033992327333 <nowiki>[1]</nowiki>][https://discord.com/channels/960643023006490684/1440877223744770259/1440877223744770259 <nowiki>[2]</nowiki>]</sup>, both of which turned out to be shift overflow mixed-digits counters, lowering the unanalysed holdout count to 15. (Two of which have notes by mxdys).		There have been two specific BB domain themed months: BB(3,3) month (October) and BB(2,5) month (November). For BB(3,3), this resulted in the clarification 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]. LegionMammal wrote up [https://discord.com/channels/960643023006490684/1259770474897080380/1431274106736873685 a detailed explanation] of the probvious halter. No further progress on holdouts was made in October due to the limited number of holdouts and the work that's already been put into trying to solve them. For BB(2,5), it was verified that the [https://wiki.bbchallenge.org/wiki/BB(2,5) Wiki] was up to date. @mxdys shared some of [https://discord.com/channels/960643023006490684/1259770421046411285/1436149296004071615 his old notes] on the unanalyzed machines, and hipparcos analysed two machines<sup>[https://discord.com/channels/960643023006490684/1436181033992327333/1436181033992327333 <nowiki>[4]</nowiki>][https://discord.com/channels/960643023006490684/1440877223744770259/1440877223744770259 <nowiki>[5]</nowiki>]</sup>, both of which turned out to be shift overflow mixed-digits counters, lowering the unanalysed holdout count to 15. (Two of which have notes by mxdys).

	== Optimization ==		== Optimization ==
	[[File:Vonhust bb6 benchmark.png\|thumb\|Benchmark for vonhust's simulator run on [[BB(6)]] holdouts.]]		[[File:Vonhust bb6 benchmark.png\|thumb\|Benchmark for vonhust's simulator run on [[BB(6)]] holdouts.]]

	@vonhust created a fast TM simulator that averages 2 billion steps / s. It uses fixed-block [[~~Macro Machine\|~~Macro Machines]] with each block bit-packed into integers. It is about 10x faster than direct simulators across most TMs.<sup>[https://discord.com/channels/960643023006490684/1226543091264126976/1438890558499061821]</sup>		@vonhust created a fast TM simulator that averages 2 billion steps / s. It uses fixed-block [[Macro Machines]] with each block bit-packed into integers. It is about 10x faster than direct simulators across most TMs.<sup>[https://discord.com/channels/960643023006490684/1226543091264126976/1438890558499061821 <nowiki>[6]</nowiki>]</sup>

	==BB Adjacent==		==BB Adjacent==
	[[File:Fractran deciders.png\|alt=All Fractran deciders\|thumb\|All Fractran deciders summarized and their relations, shared by Daniel Yuan on [https://discord.com/channels/960643023006490684/1438019511155691521/1439001835904958655 14 Nov 2025]]]		[[File:Fractran deciders.png\|alt=All Fractran deciders\|thumb\|All Fractran deciders summarized and their relations, shared by Daniel Yuan on [https://discord.com/channels/960643023006490684/1438019511155691521/1439001835904958655 14 Nov 2025]]]

	* [[Fractran\|Busy Beaver for Fractan]] (BBf) was introduced on 1 Nov by Jason Yuen.<sup>[https://discord.com/channels/960643023006490684/1362008236118511758/1433148101170040924]</sup> Exact values have been proven up to BBf(19) = 370 and exhaustive enumeration has been run up to size 21 (with BBf(21) ≥ 31,957,632 and 587 holdouts). No [[Cryptids]] have been found yet by enumeration, but [[Hydra]] has been encoded into a size 29 fractran program, so this provides a sort of upper bound on solvability.		* [[Fractran\|Busy Beaver for Fractan]] (BBf) was introduced on 1 Nov by Jason Yuen.<sup>[https://discord.com/channels/960643023006490684/1362008236118511758/1433148101170040924 <nowiki>[7]</nowiki>]</sup> Exact values have been proven up to BBf(19) = 370 and exhaustive enumeration has been run up to size 21 (with BBf(21) ≥ 31,957,632 and 587 holdouts). No [[Cryptids]] have been found yet by enumeration, but [[Hydra]] has been encoded into a size 29 fractran program, so this provides a sort of upper bound on solvability.
	* [[Cyclic Tree Busy Beaver]] (CTBB) was introduced by @Jack on 14 Nov.<sup>[https://discord.com/channels/960643023006490684/1438694294042181742]</sup> The exact value is known for CTBB(2) = 5 and lower bounds have been found up to size 7 with CTBB(7) > 4↑↑↑↑(4↑↑↑3).		* [[Cyclic Tree Busy Beaver]] (CTBB) was introduced by @Jack on 14 Nov.<sup>[https://discord.com/channels/960643023006490684/1438694294042181742 <nowiki>[8]</nowiki>]</sup> The exact value is known for CTBB(2) = 5 and lower bounds have been found up to size 7 with CTBB(7) > 4↑↑↑↑(4↑↑↑3).
	* Quite a few other BB variants have been proposed this month, but don't seem to have been significantly explored yet: [https://discord.com/channels/960643023006490684/1440230138242662400 BB110] (for [[wikipedia:Rule_110\|Rule 110]]), [https://discord.com/channels/960643023006490684/1443176113353261200 BB_trw], [https://discord.com/channels/960643023006490684/1443330663288934702 BB_cgol] (for [[wikipedia:Conway's_Game_of_Life\|Conway's Game of Life]]), [[Tiny Tag]] and [[Busy Beaver for SKI calculus]].		* Quite a few other BB variants have been proposed this month, but don't seem to have been significantly explored yet: [https://discord.com/channels/960643023006490684/1440230138242662400 BB110] (for [[wikipedia:Rule_110\|Rule 110]]), [https://discord.com/channels/960643023006490684/1443176113353261200 BB_trw], [https://discord.com/channels/960643023006490684/1443330663288934702 BB_cgol] (for [[wikipedia:Conway's_Game_of_Life\|Conway's Game of Life]]), [[Tiny Tag]] and [[Busy Beaver for SKI calculus]].
	* The [https://googology.miraheze.org/wiki/Bashicu_matrix_system Bashicu Matrix System] milestone for [[BBλ]] has been reduced from 350 to 331.<sup>[https://discord.com/channels/960643023006490684/1355653587824283678/1436844104742076507]</sup>		* The [https://googology.miraheze.org/wiki/Bashicu_matrix_system Bashicu Matrix System] milestone for [[BBλ]] has been reduced from 350 to 331.<sup>[https://discord.com/channels/960643023006490684/1355653587824283678/1436844104742076507 <nowiki>[9]</nowiki>]</sup>

	== Holdouts ==		== Holdouts ==
Line 32:		Line 32:
	** @mxdys [https://discord.com/channels/960643023006490684/1400456788955893840/1438559730640355378 decided a holdout] from [https://discord.com/channels/960643023006490684/1400456788955893840 50 Random Holdouts] by hand, making 11/50 solved. He also [https://discord.com/channels/960643023006490684/1239205785913790465/1440413375950487693 decided 5 more machines] with a single strategy. (This machine was solved before the holdouts list, and as such, is not in it).		** @mxdys [https://discord.com/channels/960643023006490684/1400456788955893840/1438559730640355378 decided a holdout] from [https://discord.com/channels/960643023006490684/1400456788955893840 50 Random Holdouts] by hand, making 11/50 solved. He also [https://discord.com/channels/960643023006490684/1239205785913790465/1440413375950487693 decided 5 more machines] with a single strategy. (This machine was solved before the holdouts list, and as such, is not in it).
	** At the end of the month, @mxdys [https://discord.com/channels/960643023006490684/1239205785913790465/1443989662019354647 released a holdouts list] consisting of only 1416 holdout TMs. A total of 118 holdouts were solved. 88 [https://discord.com/channels/960643023006490684/1028746861395316776/1442964185599447152 by a new FAR method], created by mxdys. 30 more by 14 new individual proofs by mxdys and 16 informal proofs verified.		** At the end of the month, @mxdys [https://discord.com/channels/960643023006490684/1239205785913790465/1443989662019354647 released a holdouts list] consisting of only 1416 holdout TMs. A total of 118 holdouts were solved. 88 [https://discord.com/channels/960643023006490684/1028746861395316776/1442964185599447152 by a new FAR method], created by mxdys. 30 more by 14 new individual proofs by mxdys and 16 informal proofs verified.
	** [https://docs.google.com/spreadsheets/d/~~10y2aMp9yZVLyN-nXAxgA25rw4EA_lJqn3Vxy2kB-m-U~~/edit?gid=1330361301#gid=1330361301 A new holdouts list] was created by Robin Rovenszky via searching the Discord server for any results on TMs. This spreadsheet thus includes every informal result alongside verified results.		** [https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=1330361301#gid=1330361301 A new holdouts list] was created by Robin Rovenszky via searching the Discord server for any results on TMs. This spreadsheet thus includes every informal result alongside verified results.
	** Right after, [https://discord.com/channels/960643023006490684/1239205785913790465/1443997231970648206 Peacemaker decided a TM by hand.] @mxdys verified this result using an [[Inductive Proof System\|Inductive]] decider.		** Right after, [https://discord.com/channels/960643023006490684/1239205785913790465/1443997231970648206 Peacemaker decided a TM by hand.] @mxdys verified this result using an [[Inductive Proof System\|Inductive]] decider.
	** With substantial work, [https://discord.com/channels/960643023006490684/1443295684878143579/1443295684878143579 a machine was formally proven nonhalting] by Pomme, Autumn Pan, vyx and mxdys. However, this result is yet to be verified.		** With substantial work, [https://discord.com/channels/960643023006490684/1443295684878143579/1443295684878143579 a machine was formally proven nonhalting] by Pomme, Autumn Pan, vyx and mxdys. However, this result is yet to be verified.