TMBR: September 2026 - Revision history

ADucharme: intro standardization

2026-11-09T09:34:02Z

intro standardization

← Older revision		Revision as of 09:34, 9 November 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 ~~month~~ in Beaver Research: This month saw a clear up-tick in solved BB(6) machines. A large factor in this was the increasing use of AI solvers.		[[:Category:This Month in Beaver Research\|This Month in Beaver Research]] for September 2026. This month saw a clear up-tick in solved BB(6) machines. A large factor in this was the increasing use of AI solvers.

	== Media ==		== Media ==

Sligocki: Add Gasarch column #2

2026-11-08T18:56:17Z

Add Gasarch column #2

← Older revision		Revision as of 18:56, 8 November 2026
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	This month in Beaver Research: This month saw a clear up-tick in solved BB(6) machines. A large factor in this was the increasing use of AI solvers.		This month in Beaver Research: This month saw a clear up-tick in solved BB(6) machines. A large factor in this was the increasing use of AI solvers.

	== ~~Blog Posts~~ ==		== Media ==

	* September 1, 2026. Nick Drozd. [https://nickdrozd.github.io/2026/09/01/tetrational-self-cleaning-turing-machine.html A Tetrational Self-Cleaning Turing Machine].		* September 1, 2026. Nick Drozd. [https://nickdrozd.github.io/2026/09/01/tetrational-self-cleaning-turing-machine.html A Tetrational Self-Cleaning Turing Machine].
			* William Gasarch. 2026. ''Relationships Between the Busy Beaver Function and Mathematics II:Small Turing Machines and Open Problems''. SIGACT News 57, 3 (September 2026), 25–50. https://doi.org/10.1145/3848065.3848068

	== Champions ==		== Champions ==

Polygon: /* Champions */ spacing

2026-11-03T13:23:35Z

Champions: spacing

← Older revision		Revision as of 13:23, 3 November 2026
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	== Champions ==		== Champions ==

	* On September 1, nickdrozd discovered a new [[BLB\|BLB(3,3)]] champion which runs for over ~~10↑↑6~~.54 steps before blanking the tape.<sup>[https://discord.com/channels/960643023006490684/1259770474897080380/1544448259437895680]</sup> Note that this is not a new [[BBB\|BBB(3,3)]] champion.		* On September 1, nickdrozd discovered a new [[BLB\|BLB(3,3)]] champion which runs for over 10 ↑↑ 6.54 steps before blanking the tape.<sup>[https://discord.com/channels/960643023006490684/1259770474897080380/1544448259437895680]</sup> Note that this is not a new [[BBB\|BBB(3,3)]] champion.
	* On September 9, @-d discovered a new [[BBf\|BBf(24)]] champion which runs for over 9.000 × 10<sup>14,448</sup> steps.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1547182811713380383]</sup>		* On September 9, @-d discovered a new [[BBf\|BBf(24)]] champion which runs for over 9.000 × 10<sup>14,448</sup> steps.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1547182811713380383]</sup>

HelpMe: reworded

2026-10-29T10:01:23Z

reworded

← Older revision		Revision as of 10:01, 29 October 2026
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	** On September 9, @mathmasterzach discovered champion PLUSMINUS strings for sizes 9,<sup>[https://discord.com/channels/960643023006490684/1243312334907375676/1547051560972845178]</sup> 11,<sup>[https://discord.com/channels/960643023006490684/1243312334907375676/1547050522425561209]</sup> 12,<sup>[https://discord.com/channels/960643023006490684/1243312334907375676/1547054625134477342]</sup>, 15, and 16.<sup>[https://discord.com/channels/960643023006490684/1547296154105159722/1547336527334613092]</sup>		** On September 9, @mathmasterzach discovered champion PLUSMINUS strings for sizes 9,<sup>[https://discord.com/channels/960643023006490684/1243312334907375676/1547051560972845178]</sup> 11,<sup>[https://discord.com/channels/960643023006490684/1243312334907375676/1547050522425561209]</sup> 12,<sup>[https://discord.com/channels/960643023006490684/1243312334907375676/1547054625134477342]</sup>, 15, and 16.<sup>[https://discord.com/channels/960643023006490684/1547296154105159722/1547336527334613092]</sup>
	** On the same day, @Furious discovered champion PLUSMINUS strings for sizes 1 to 8<sup>[https://discord.com/channels/960643023006490684/1243312334907375676/1547258179589775523]</sup> and size 10-14.<sup>[https://discord.com/channels/960643023006490684/1547296154105159722/1547300240019816589]</sup>		** On the same day, @Furious discovered champion PLUSMINUS strings for sizes 1 to 8<sup>[https://discord.com/channels/960643023006490684/1243312334907375676/1547258179589775523]</sup> and size 10-14.<sup>[https://discord.com/channels/960643023006490684/1547296154105159722/1547300240019816589]</sup>
	** On the same day, racheline provided an estimate for the halting times of PLUSMINUS ~~programs~~.<sup>[https://discord.com/channels/960643023006490684/1243312334907375676/1547306730487283832]</sup> This suggests that PLUSMINUS ~~is not~~ Turing-~~complete~~.		** On the same day, racheline provided an estimate for the halting times of programs under a simplified model of PLUSMINUS.<sup>[https://discord.com/channels/960643023006490684/1243312334907375676/1547306730487283832]</sup> This suggests that PLUSMINUS may be near the edge of Turing-completeness.
	** On September 10, @Furious converted the rules of PLUSMINUS into a piecewise mathematical function.<sup>[https://discord.com/channels/960643023006490684/1547296154105159722/1547678473429065831]</sup>		** On September 10, @Furious converted the rules of PLUSMINUS into a piecewise mathematical function.<sup>[https://discord.com/channels/960643023006490684/1547296154105159722/1547678473429065831]</sup>
	** On September 11, @Jack discovered champion PLUSMINUS strings for sizes 20, 23, 32, 36, and 40.<sup>[https://discord.com/channels/960643023006490684/1547296154105159722/1548057628503179335]</sup>		** On September 11, @Jack discovered champion PLUSMINUS strings for sizes 20, 23, 32, 36, and 40.<sup>[https://discord.com/channels/960643023006490684/1547296154105159722/1548057628503179335]</sup>

Tlonuqbar: i hope this isn't controversial, but the solving speedup is highly linked with AI

2026-10-19T21:39:48Z

i hope this isn't controversial, but the solving speedup is highly linked with AI

← Older revision		Revision as of 21:39, 19 October 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 month in Beaver Research: This month saw a clear up-tick in solved BB(6) machines. A large factor in this was the increasing use of AI solvers.

	== Blog Posts ==		== Blog Posts ==

Polygon: /* Holdouts */ fixed typo

2026-10-18T13:16:23Z

Holdouts: fixed typo

← Older revision		Revision as of 13:16, 18 October 2026
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	**On September 25 and 26, prurq claimed to have used Aristotle AI and GPT6 to solve 21 of the 60 remaining holdouts.<sup>[https://discord.com/channels/960643023006490684/1259770421046411285/1552990521650319453][https://discord.com/channels/960643023006490684/1259770421046411285/1553433274762919997 <nowiki>[67]</nowiki>]</sup>		**On September 25 and 26, prurq claimed to have used Aristotle AI and GPT6 to solve 21 of the 60 remaining holdouts.<sup>[https://discord.com/channels/960643023006490684/1259770421046411285/1552990521650319453][https://discord.com/channels/960643023006490684/1259770421046411285/1553433274762919997 <nowiki>[67]</nowiki>]</sup>
	* [[BB(2,7)]]		* [[BB(2,7)]]
	** Terry Ligocki enumerated ~~31K~~ more subtasks, increasing the number of holdouts to '''3,062,427,379'''. A total of 980K subtasks out of the 1 million subtasks (or '''98%''') have been enumerated.		** Terry Ligocki enumerated 30K more subtasks, increasing the number of holdouts to '''3,062,427,379'''. A total of 980K subtasks out of the 1 million subtasks (or '''98%''') have been enumerated.

	== Misc ==		== Misc ==

HelpMe: pebble AUTOMATON not eating i got tired when reading the message

2026-10-13T12:41:35Z

pebble AUTOMATON not eating i got tired when reading the message

← Older revision		Revision as of 12:41, 13 October 2026
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	** On the same day, sheep discovered a 7-register, 28-state machine beating [[Graham's number]].<sup>[https://discord.com/channels/960643023006490684/1552294888740098139/1554558141964886190]</sup>		** On the same day, sheep discovered a 7-register, 28-state machine beating [[Graham's number]].<sup>[https://discord.com/channels/960643023006490684/1552294888740098139/1554558141964886190]</sup>
	** On September 30, @mineralli discovered a new MBB(11,2) champion,<sup>[https://discord.com/channels/960643023006490684/1552294888740098139/1554893821857501236]</sup> improved upon by sheep.<sup>[https://discord.com/channels/960643023006490684/1552294888740098139/1554913439695249570]</sup>		** On September 30, @mineralli discovered a new MBB(11,2) champion,<sup>[https://discord.com/channels/960643023006490684/1552294888740098139/1554893821857501236]</sup> improved upon by sheep.<sup>[https://discord.com/channels/960643023006490684/1552294888740098139/1554913439695249570]</sup>
	* [[Pebble Eating]]		* [[Pebble Automaton\|Pebble Eating]]
	** On September 30, sheep discovered an 86 pebble Cryptid, showing peBBle(86) is hard.<sup>[https://discord.com/channels/960643023006490684/1535695107448381591/1554751849742082102]</sup>		** On September 30, sheep discovered an 86 pebble Cryptid, showing peBBle(86) is hard.<sup>[https://discord.com/channels/960643023006490684/1535695107448381591/1554751849742082102]</sup>

Δ⁵: /* Misc */ minor grammar issue

2026-10-12T14:12:00Z

Misc: minor grammar issue

← Older revision		Revision as of 14:12, 12 October 2026
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	* On September 5, [[User:XnoobSpeakable\|XnoobSpeakable]] began an opt-in archival project of the bbchallenge Discord server.<sup>[https://discord.com/channels/960643023006490684/960643023530762341/1545742987710038088]</sup>		* On September 5, [[User:XnoobSpeakable\|XnoobSpeakable]] began an opt-in archival project of the bbchallenge Discord server.<sup>[https://discord.com/channels/960643023006490684/960643023530762341/1545742987710038088]</sup>
	* On September 23, Joseph M. Shunia published a preprint presenting a 120-state, 2-symbol TM that halts iff Riemann hypothesis is false.<sup>[https://arxiv.org/abs/2609.30306]</sup>		* On September 23, Joseph M. Shunia published a preprint presenting a 120-state, 2-symbol TM that halts iff Riemann hypothesis is false.<sup>[https://arxiv.org/abs/2609.30306]</sup>
	* On September 22, Twitter user @_Mira___Mira_, ~~using~~ GPT-6 Astra~~, claimed~~ to ~~have discovered~~ a 387-state, 2-symbol TM whose halting status is [[Independence from ZFC\|independent of ZFC]].<sup>[https://twitter.com/_Mira___Mira_/status/2102108613028560993]</sup>		* On September 22, Twitter user @_Mira___Mira_, claimed to have used GPT-6 Astra to discover a 387-state, 2-symbol TM whose halting status is [[Independence from ZFC\|independent of ZFC]].<sup>[https://twitter.com/_Mira___Mira_/status/2102108613028560993]</sup>
	** On September 24, they claimed to have reduced this to a 314-state ZFC-independent TM, and claimed to have found a 289-state, 2-symbol PA-independent TM.<sup>[https://twitter.com/_Mira___Mira_/status/2102796188265439626]</sup>		** On September 24, they claimed to have reduced this to a 314-state ZFC-independent TM, and claimed to have found a 289-state, 2-symbol PA-independent TM.<sup>[https://twitter.com/_Mira___Mira_/status/2102796188265439626]</sup>
	** On September 30~~, after a series of improvements~~, they claimed to have reduced these to a 256-state ZFC-independent TM, and a 238-state PA-independent TM. A Metamath formalization is in progress.<sup>[https://twitter.com/_Mira___Mira_/status/2105184649098268774]</sup>		** On September 30, they claimed to have reduced these to a 256-state ZFC-independent TM , and a 238-state PA-independent TM, after a series of improvements. A Metamath formalization is in progress.<sup>[https://twitter.com/_Mira___Mira_/status/2105184649098268774]</sup>
	* On September 28, Twitter user @_Mira___Mira_ discovered a fractal related to the Antihydra conjecture.<sup>[https://twitter.com/_Mira___Mira_/status/2104539527117513127]</sup>		* On September 28, Twitter user @_Mira___Mira_ discovered a fractal related to the Antihydra conjecture.<sup>[https://twitter.com/_Mira___Mira_/status/2104539527117513127]</sup>

	[[Category:This Month in Beaver Research\|2026-09]]		[[Category:This Month in Beaver Research\|2026-09]]

Δ⁵: minor grammar issue

2026-10-12T14:07:59Z

minor grammar issue

← Older revision		Revision as of 14:07, 12 October 2026
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	*[[BB(2,5)]]		*[[BB(2,5)]]
	**On September 8, mxdys released a new holdouts list of '''60''' machines.<sup>[https://discord.com/channels/960643023006490684/1259770421046411285/1546880921318326282]</sup>		**On September 8, mxdys released a new holdouts list of '''60''' machines.<sup>[https://discord.com/channels/960643023006490684/1259770421046411285/1546880921318326282]</sup>
	**On September 25 and 26, prurq~~, using~~ Aristotle AI and GPT6~~, solved~~ 21 of the 60 remaining holdouts.<sup>[https://discord.com/channels/960643023006490684/1259770421046411285/1552990521650319453][https://discord.com/channels/960643023006490684/1259770421046411285/1553433274762919997 <nowiki>[67]</nowiki>]</sup>		**On September 25 and 26, prurq claimed to have used Aristotle AI and GPT6 to solve 21 of the 60 remaining holdouts.<sup>[https://discord.com/channels/960643023006490684/1259770421046411285/1552990521650319453][https://discord.com/channels/960643023006490684/1259770421046411285/1553433274762919997 <nowiki>[67]</nowiki>]</sup>
	* [[BB(2,7)]]		* [[BB(2,7)]]
	** Terry Ligocki enumerated 31K more subtasks, increasing the number of holdouts to '''3,062,427,379'''. A total of 980K subtasks out of the 1 million subtasks (or '''98%''') have been enumerated.		** Terry Ligocki enumerated 31K more subtasks, increasing the number of holdouts to '''3,062,427,379'''. A total of 980K subtasks out of the 1 million subtasks (or '''98%''') have been enumerated.

HelpMe: ohhh yeah thats what i was here for to add symbols

2026-10-12T13:32:00Z

ohhh yeah thats what i was here for to add symbols

← Older revision		Revision as of 13:32, 12 October 2026
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	*[[BB(2,5)]]		*[[BB(2,5)]]
	**On September 8, mxdys released a new holdouts list of '''60''' machines.<sup>[https://discord.com/channels/960643023006490684/1259770421046411285/1546880921318326282]</sup>		**On September 8, mxdys released a new holdouts list of '''60''' machines.<sup>[https://discord.com/channels/960643023006490684/1259770421046411285/1546880921318326282]</sup>
	**On September 25 and 26, prurq ~~used~~ Aristotle AI and GPT6 ~~to solve~~ 21 of the 60 remaining holdouts.<sup>[https://discord.com/channels/960643023006490684/1259770421046411285/1552990521650319453][https://discord.com/channels/960643023006490684/1259770421046411285/1553433274762919997 <nowiki>[67]</nowiki>]</sup>		**On September 25 and 26, prurq, using Aristotle AI and GPT6, solved 21 of the 60 remaining holdouts.<sup>[https://discord.com/channels/960643023006490684/1259770421046411285/1552990521650319453][https://discord.com/channels/960643023006490684/1259770421046411285/1553433274762919997 <nowiki>[67]</nowiki>]</sup>
	* [[BB(2,7)]]		* [[BB(2,7)]]
	** Terry Ligocki enumerated 31K more subtasks, increasing the number of holdouts to '''3,062,427,379'''. A total of 980K subtasks out of the 1 million subtasks (or '''98%''') have been enumerated.		** Terry Ligocki enumerated 31K more subtasks, increasing the number of holdouts to '''3,062,427,379'''. A total of 980K subtasks out of the 1 million subtasks (or '''98%''') have been enumerated.
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	* On September 2, RobinCodes began work on updating the BB(6) holdout [https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?pli=1&gid=1330361301#gid=1330361301 spreadsheet].<sup>[https://discord.com/channels/960643023006490684/1239205785913790465/1544742905850236978]</sup>		* On September 2, RobinCodes began work on updating the BB(6) holdout [https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?pli=1&gid=1330361301#gid=1330361301 spreadsheet].<sup>[https://discord.com/channels/960643023006490684/1239205785913790465/1544742905850236978]</sup>
	* On September 5, [[User:XnoobSpeakable\|XnoobSpeakable]] began an opt-in archival project of the bbchallenge Discord server.<sup>[https://discord.com/channels/960643023006490684/960643023530762341/1545742987710038088]</sup>		* On September 5, [[User:XnoobSpeakable\|XnoobSpeakable]] began an opt-in archival project of the bbchallenge Discord server.<sup>[https://discord.com/channels/960643023006490684/960643023530762341/1545742987710038088]</sup>
	* On September 23, Joseph M. Shunia published a preprint presenting a 120-state TM that halts iff Riemann hypothesis is false.<sup>[https://arxiv.org/abs/2609.30306]</sup>		* On September 23, Joseph M. Shunia published a preprint presenting a 120-state, 2-symbol TM that halts iff Riemann hypothesis is false.<sup>[https://arxiv.org/abs/2609.30306]</sup>
	* On September 22, Twitter user @_Mira___Mira_, using GPT-6 Astra, claimed to have discovered a 387-state TM whose halting status is [[Independence from ZFC\|independent of ZFC]].<sup>[https://twitter.com/_Mira___Mira_/status/2102108613028560993]</sup>		* On September 22, Twitter user @_Mira___Mira_, using GPT-6 Astra, claimed to have discovered a 387-state, 2-symbol TM whose halting status is [[Independence from ZFC\|independent of ZFC]].<sup>[https://twitter.com/_Mira___Mira_/status/2102108613028560993]</sup>
	** On September 24, they claimed to have reduced this to a 314-state ZFC-independent TM, and claimed to have found a 289-state PA-independent TM.<sup>[https://twitter.com/_Mira___Mira_/status/2102796188265439626]</sup>		** On September 24, they claimed to have reduced this to a 314-state ZFC-independent TM, and claimed to have found a 289-state, 2-symbol PA-independent TM.<sup>[https://twitter.com/_Mira___Mira_/status/2102796188265439626]</sup>
	** On September 30, after a series of improvements, they claimed to have reduced these to a 256-state ZFC-independent TM, and a 238-state PA-independent TM. A Metamath formalization is in progress.<sup>[https://twitter.com/_Mira___Mira_/status/2105184649098268774]</sup>		** On September 30, after a series of improvements, they claimed to have reduced these to a 256-state ZFC-independent TM, and a 238-state PA-independent TM. A Metamath formalization is in progress.<sup>[https://twitter.com/_Mira___Mira_/status/2105184649098268774]</sup>
	* On September 28, Twitter user @_Mira___Mira_ discovered a fractal related to the Antihydra conjecture.<sup>[https://twitter.com/_Mira___Mira_/status/2104539527117513127]</sup>		* On September 28, Twitter user @_Mira___Mira_ discovered a fractal related to the Antihydra conjecture.<sup>[https://twitter.com/_Mira___Mira_/status/2104539527117513127]</sup>

	[[Category:This Month in Beaver Research\|2026-09]]		[[Category:This Month in Beaver Research\|2026-09]]