TMBR: August 2026 - Revision history

ADucharme: intro standardization

2026-11-09T09:32:37Z

intro standardization

← Older revision		Revision as of 09:32, 9 November 2026
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	{{TMBRnav\|July 2026\|September 2026}}		{{TMBRnav\|July 2026\|September 2026}}
	[[File:Sligocki BBB 4 equals 32779478.png\|thumb\|757x757px\|BBB(4) = 32,779,478 was proven this month by @carrino using Claude AI. The first 71 steps of the champion, {{TM\|1RB1LD_1RC1RB_1LC1LA_0RC0RD\|halt}}, are depicted in this spacetime diagram, using Shawn Ligocki's [https://github.com/sligocki/busy-beaver/blob/main/Code/Visual_Simulator Visual Simulator]. (Credit: [https://www.sligocki.com/2021/07/17/bb-collatz.html Shawn Ligocki])]][[:Category:This Month in Beaver Research\|This Month in Beaver Research]] for August 2026.		[[File:Sligocki BBB 4 equals 32779478.png\|thumb\|757x757px\|BBB(4) = 32,779,478 was proven this month by @carrino using Claude AI. The first 71 steps of the champion, {{TM\|1RB1LD_1RC1RB_1LC1LA_0RC0RD\|halt}}, are depicted in this spacetime diagram, using Shawn Ligocki's [https://github.com/sligocki/busy-beaver/blob/main/Code/Visual_Simulator Visual Simulator]. (Credit: [https://www.sligocki.com/2021/07/17/bb-collatz.html Shawn Ligocki])]][[:Category:This Month in Beaver Research\|This Month in Beaver Research]] for August 2026. This month saw us finally cross the long-awaited milestone of less than '''1,000 holdouts''' in [[BB(6)]], after a flurry of simulations, as well as proofs from users both new and old, resulting in ''65'' holdouts being solved this month. mxdys has also added the 9th and 10th problems to the [[Beaver Math Olympiad]]. [[BB(4,3)]] recorded small but substantial reductions in holdouts, while Terry Ligocki's enumeration of [[BB(2,7)]] slowly but surely reaches the 85% mark.

	This month saw us finally cross the long-awaited milestone of less than '''1,000 holdouts''' in [[BB(6)]], after a flurry of simulations, as well as proofs from users both new and old, resulting in ''65'' holdouts being solved this month. mxdys has also added the 9th and 10th problems to the [[Beaver Math Olympiad]]. [[BB(4,3)]] recorded small but substantial reductions in holdouts, while Terry Ligocki's enumeration of [[BB(2,7)]] slowly but surely reaches the 85% mark.

	This month was also quite a busy one for BB-adjacent functions. Most notably, for [[Beeping Busy Beaver]] functions, '''BBB(4) = 32,779,478''', proven by @carrino! '''BBλ(41) = 5 × 3<sup>3<sup>3</sup></sup> + 6''' has also been proven this month, and BBf(23) has been almost completely solved, save for 12 Cryptids and 1 oddball machine. creeperman7002 has been working in the field of [[Terminating Turmite\|Terminating Turmites]], finding a machine that demonstrates TT(3,3) > 2.27 × 10<sup>248</sup>, while reducing the domain to under 20,000 holdouts. Δ⁵ has also been incrementally finding new large champions for the [[SKI Calculus#Champions\|SKI]] and [[SKI Calculus#SK calculus\|SK]] calculi, and the [[SKI Calculus#BCKW system\|BCKW system]], notably finding 6 new ''hexational''-level champions in the calculi!		This month was also quite a busy one for BB-adjacent functions. Most notably, for [[Beeping Busy Beaver]] functions, '''BBB(4) = 32,779,478''', proven by @carrino! '''BBλ(41) = 5 × 3<sup>3<sup>3</sup></sup> + 6''' has also been proven this month, and BBf(23) has been almost completely solved, save for 12 Cryptids and 1 oddball machine. creeperman7002 has been working in the field of [[Terminating Turmite\|Terminating Turmites]], finding a machine that demonstrates TT(3,3) > 2.27 × 10<sup>248</sup>, while reducing the domain to under 20,000 holdouts. Δ⁵ has also been incrementally finding new large champions for the [[SKI Calculus#Champions\|SKI]] and [[SKI Calculus#SK calculus\|SK]] calculi, and the [[SKI Calculus#BCKW system\|BCKW system]], notably finding 6 new ''hexational''-level champions in the calculi!

Elgan65536: fix error in lambda section according to spreadhseet

2026-11-09T06:30:53Z

fix error in lambda section according to spreadhseet

← Older revision		Revision as of 06:30, 9 November 2026
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	** On the same day, Δ⁵ discovered another new champion for Ξ₀<sub>SK</sub>(25).<sup>[https://wiki.bbchallenge.org/w/index.php?title=SKI_Calculus&diff=next&oldid=8347]</sup>		** On the same day, Δ⁵ discovered another new champion for Ξ₀<sub>SK</sub>(25).<sup>[https://wiki.bbchallenge.org/w/index.php?title=SKI_Calculus&diff=next&oldid=8347]</sup>
	* [[Lambda Calculus]]		* [[Lambda Calculus]]
	** On August 7, '''BBλ(41) was solved!'''<sup>[https://discord.com/channels/960643023006490684/1355653587824283678/1535401128164982865]</sup> We now know that '''BBλ(41) = 5 × 3<sup>3<sup>3</sup></sup> + 6''' after solving 237 holdouts, thanks to the help of 2014MELO03, cppdecksucker, mxdys, and others.<sup>[https://docs.google.com/spreadsheets/d/1jZ6TK9m3xmXUlC69727T-8WwvhALcsp8FrK6DzgThtw/edit?gid=1605140783#gid=1605140783]</sup>		** On August 7, '''BBλ(41) was solved!'''<sup>[https://discord.com/channels/960643023006490684/1355653587824283678/1535401128164982865]</sup> We now know that '''BBλ(41) = 5 × 3<sup>3<sup>85</sup></sup> + 6''' after solving 237 holdouts, thanks to the help of 2014MELO03, cppdecksucker, mxdys, and others.<sup>[https://docs.google.com/spreadsheets/d/1jZ6TK9m3xmXUlC69727T-8WwvhALcsp8FrK6DzgThtw/edit?gid=1605140783#gid=1605140783]</sup>
	*** As a result, the bet between Sam and cppdecksucker (which began in April<sup>[https://discord.com/channels/960643023006490684/1355653587824283678/1492986885302390834]</sup>) has also concluded; cppdecksucker, who lost the bet on whether there would be any Cryptids shorter than 42 bits, has donated 50 NZD to the Mermaids charity.<sup>[https://discord.com/channels/960643023006490684/1355653587824283678/1535811720742834256]</sup>		*** As a result, the bet between Sam and cppdecksucker (which began in April<sup>[https://discord.com/channels/960643023006490684/1355653587824283678/1492986885302390834]</sup>) has also concluded; cppdecksucker, who lost the bet on whether there would be any Cryptids shorter than 42 bits, has donated 50 NZD to the Mermaids charity.<sup>[https://discord.com/channels/960643023006490684/1355653587824283678/1535811720742834256]</sup>
	[[File:AlephSquirrel PE 9 Bounded By 63,577.png\|thumb\|AlephSquirrel has found a new champion for peBBle(9), which runs for 63,577 steps, by modifying mathmasterzach's 323 step 9-pebble automaton. The first 200 steps of this champion are displayed here using AlephSquirrel's [https://www.uiua.org/pad?src=0_20_0-dev_1__eJxNkTFrAkEQhfv9FUtsFJHsHQZSihapkohXSKph8AY9srmTdS_BdLlCcEFMlUKuSCAhTcCUgqSx9V_MLwmnmDjdfPAeb940EzRhNwrtQPLkWXpKicCise1kJOUO1cVVYGlYrHvgKyVaiU7MP2pq7N1Ch0K4Nhj3CW5I6-QBLgxRDK0xxtDUKUE7NUNNcIl9ii1CdxBZEp1UU2DNwetEKVA-KA_qCrw6eD4oBWc-nHsnQrDLFLu8XGuoCrsVT18bcGSwm5JsoxmRxDiUOBxSHMoojmyEWippkgfBs5xn0zK7uQcKfHbZNq9tvtnN2a1Oq5U_J1mSLdS9VKMlGVgcy3vUKY0ET9ab5aEo_looniybf1XWOHsqwn2uCwNDhfqQYGTRkuDZR_m0ytM3nqyLDJulx7Mpvy8KmZtXjiovySC62yUQ_PLDWVbf5uzm8ugFR1Pa8-hxfz7FGk2fxC_nlrju simulator], with colors corresponding to the numbers of pebbles in a single cell. (Credit: [https://discord.com/channels/960643023006490684/1535695107448381591/1540746719711592468 AlephSquirrel])\|506x506px]]		[[File:AlephSquirrel PE 9 Bounded By 63,577.png\|thumb\|AlephSquirrel has found a new champion for peBBle(9), which runs for 63,577 steps, by modifying mathmasterzach's 323 step 9-pebble automaton. The first 200 steps of this champion are displayed here using AlephSquirrel's [https://www.uiua.org/pad?src=0_20_0-dev_1__eJxNkTFrAkEQhfv9FUtsFJHsHQZSihapkohXSKph8AY9srmTdS_BdLlCcEFMlUKuSCAhTcCUgqSx9V_MLwmnmDjdfPAeb940EzRhNwrtQPLkWXpKicCise1kJOUO1cVVYGlYrHvgKyVaiU7MP2pq7N1Ch0K4Nhj3CW5I6-QBLgxRDK0xxtDUKUE7NUNNcIl9ii1CdxBZEp1UU2DNwetEKVA-KA_qCrw6eD4oBWc-nHsnQrDLFLu8XGuoCrsVT18bcGSwm5JsoxmRxDiUOBxSHMoojmyEWippkgfBs5xn0zK7uQcKfHbZNq9tvtnN2a1Oq5U_J1mSLdS9VKMlGVgcy3vUKY0ET9ab5aEo_looniybf1XWOHsqwn2uCwNDhfqQYGTRkuDZR_m0ytM3nqyLDJulx7Mpvy8KmZtXjiovySC62yUQ_PLDWVbf5uzm8ugFR1Pa8-hxfz7FGk2fxC_nlrju simulator], with colors corresponding to the numbers of pebbles in a single cell. (Credit: [https://discord.com/channels/960643023006490684/1535695107448381591/1540746719711592468 AlephSquirrel])\|506x506px]]

Sligocki: Edit down several sections that I think went into a bit too much detail. Especially the Fractran section which I think can be summarized a bit more suscinctly

2026-11-08T18:37:11Z

Edit down several sections that I think went into a bit too much detail. Especially the Fractran section which I think can be summarized a bit more suscinctly

← Older revision		Revision as of 18:37, 8 November 2026
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	{{TMBRnav\|July 2026\|September 2026}}		{{TMBRnav\|July 2026\|September 2026}}
	[[File:Sligocki BBB 4 equals 32779478.png\|thumb\|757x757px\|BBB(4) = 32,779,478 was proven this month by @carrino using Claude AI. The first 71 steps of the champion, {{TM\|1RB1LD_1RC1RB_1LC1LA_0RC0RD\|halt}}, are depicted in this spacetime diagram, using Shawn Ligocki's [https://github.com/sligocki/busy-beaver/blob/main/Code/Visual_Simulator Visual Simulator]. (Credit: [https://www.sligocki.com/2021/07/17/bb-collatz.html Shawn Ligocki])]]		[[File:Sligocki BBB 4 equals 32779478.png\|thumb\|757x757px\|BBB(4) = 32,779,478 was proven this month by @carrino using Claude AI. The first 71 steps of the champion, {{TM\|1RB1LD_1RC1RB_1LC1LA_0RC0RD\|halt}}, are depicted in this spacetime diagram, using Shawn Ligocki's [https://github.com/sligocki/busy-beaver/blob/main/Code/Visual_Simulator Visual Simulator]. (Credit: [https://www.sligocki.com/2021/07/17/bb-collatz.html Shawn Ligocki])]][[:Category:This Month in Beaver Research\|This Month in Beaver Research]] for August 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 August 2026.

	This month saw us finally cross the long-awaited milestone of less than '''1,000 holdouts''' in [[BB(6)]], after a flurry of simulations, as well as proofs from users both new and old, resulting in ''65'' holdouts being solved this month. mxdys has also added the 9th and 10th problems to the [[Beaver Math Olympiad]]. [[BB(4,3)]] recorded small but substantial reductions in holdouts, while Terry Ligocki's enumeration of [[BB(2,7)]] slowly but surely reaches the 85% mark.		This month saw us finally cross the long-awaited milestone of less than '''1,000 holdouts''' in [[BB(6)]], after a flurry of simulations, as well as proofs from users both new and old, resulting in ''65'' holdouts being solved this month. mxdys has also added the 9th and 10th problems to the [[Beaver Math Olympiad]]. [[BB(4,3)]] recorded small but substantial reductions in holdouts, while Terry Ligocki's enumeration of [[BB(2,7)]] slowly but surely reaches the 85% mark.

	This month was also quite a busy one for BB-adjacent functions. Most notably, for [[Beeping Busy Beaver]] functions, '''BBB(4) = 32,779,478''', proven by @carrino! '''BBλ(41) = 5 × 3<sup>3<sup>3</sup></sup> + 6''' has also been proven this month, and BBf(23) has been almost completely solved, save for 12 Cryptids and 1 oddball machine~~. Speaking of [[Fractran]], @-d has begun the enumeration BBf(24), with Shawn Ligocki finding a machine that demonstrates BBf(24) > 9.263 × 10<sup>9,595</sup>~~. creeperman7002 has been working in the field of [[Terminating Turmite\|Terminating Turmites]], finding a machine that demonstrates TT(3,3) > 2.27 × 10<sup>248</sup>, while reducing the domain to under 20,000 holdouts. Δ⁵ has also been incrementally finding new large champions for the [[SKI Calculus#Champions\|SKI]] and [[SKI Calculus#SK calculus\|SK]] calculi, and the [[SKI Calculus#BCKW system\|BCKW system]], notably finding 6 new ''hexational''-level champions in the calculi!		This month was also quite a busy one for BB-adjacent functions. Most notably, for [[Beeping Busy Beaver]] functions, '''BBB(4) = 32,779,478''', proven by @carrino! '''BBλ(41) = 5 × 3<sup>3<sup>3</sup></sup> + 6''' has also been proven this month, and BBf(23) has been almost completely solved, save for 12 Cryptids and 1 oddball machine. creeperman7002 has been working in the field of [[Terminating Turmite\|Terminating Turmites]], finding a machine that demonstrates TT(3,3) > 2.27 × 10<sup>248</sup>, while reducing the domain to under 20,000 holdouts. Δ⁵ has also been incrementally finding new large champions for the [[SKI Calculus#Champions\|SKI]] and [[SKI Calculus#SK calculus\|SK]] calculi, and the [[SKI Calculus#BCKW system\|BCKW system]], notably finding 6 new ''hexational''-level champions in the calculi!

	The Busy Beaver functions for [[Pebble Automaton\|Pebble Automata]] and [[Cyclic Tag]] have been introduced; [[Collatz-like]] behavior has already been detected amongst small pebble automata, but no Cryptids have been found as of yet, unlike in cyclic tag, where a size 36 Cryptid has been found. [[Diophantine Equation\|Diophantine Equations]] have also received some research this month through attempts to find Cryptids and new champions, many of which are related to the [[wikipedia:Sums_of_three_cubes\|sums of three cubes]] problem. A new family of champions has also been found for the Busy Beaver function for [[Wang Tiles]], and Shawn Ligocki has recently revived discussion about a small but chaotic and possible Cryptid [[General Recursive Function]]. A primality test and a program that computes the Fibonacci numbers have also been created in [[CounterScript]].		The Busy Beaver functions for [[Pebble Automaton\|Pebble Automata]] and [[Cyclic Tag]] have been introduced; [[Collatz-like]] behavior has already been detected amongst small pebble automata, but no Cryptids have been found as of yet, unlike in cyclic tag, where a size 36 Cryptid has been found. [[Diophantine Equation\|Diophantine Equations]] have also received some research this month through attempts to find Cryptids and new champions, many of which are related to the [[wikipedia:Sums_of_three_cubes\|sums of three cubes]] problem. A new family of champions has also been found for the Busy Beaver function for [[Wang Tiles]], and Shawn Ligocki has recently revived discussion about a small but chaotic and possible Cryptid [[General Recursive Function]]. A primality test and a program that computes the Fibonacci numbers have also been created in [[CounterScript]].

	There has also been extensive discussion on what should classify a machine or a program as a [[Cryptid]], due to the wide range of ''potential'' Cryptids in BB(6) (most notably [[BMO1]]) and how virtually all of the known machines or programs classified as Cryptids rely, at least in part, on [[Collatz-like#Why is Collatz randomness mysterious?\|Collatz-like randomness]]; a new ~~defintion~~ of Cryptid may even include solved machines with behaviors reminiscent of diabolically hard but solved problems, such as Fermat's Last Theorem.		There has also been extensive discussion on what should classify a machine or a program as a [[Cryptid]], due to the wide range of ''potential'' Cryptids in BB(6) (most notably [[BMO1]]) and how virtually all of the known machines or programs classified as Cryptids rely, at least in part, on [[Collatz-like#Why is Collatz randomness mysterious?\|Collatz-like randomness]]; a new definition of Cryptid may even include solved machines with behaviors reminiscent of diabolically hard but solved problems, such as Fermat's Last Theorem.

	An archive of the Discord server is also being considered, for accessibility purposes and to prevent sources from being lost; however, they may be some ethical concerns and problems with the suggestion as it stands currently.

	== General ==		== General ==

	* On August 2, @carrino, using Claude AI solved the last 290 holdouts remaining in the Coq proof, meaning '''BBB(4) is solved!'''<sup>[https://discord.com/channels/960643023006490684/1385498968011575366/1533342110005334046]</sup> Specifically, @carrino [https://github.com/carrino/Coq-BBB4 proved] that '''BBB(4) = 32,779,478''', the champion being {{TM\|1RB1LC_1RD1RB_0RD0RC_1LD1LA\|halt}}, discovered by Nick Drozd in July 2021, which [[Quasihalt\|quasihalts]] by turning into a period 1 [[translated cycler]] after 32,779,478 steps.<sup>[https://nickdrozd.github.io/2021/07/11/self-cleaning-turing-machine.html]</sup>		* On August 2, @carrino, using Claude AI solved the last [[BBB]](4) 290 holdouts remaining in the Coq proof, meaning '''BBB(4) is solved!'''<sup>[https://discord.com/channels/960643023006490684/1385498968011575366/1533342110005334046]</sup> Specifically, @carrino [https://github.com/carrino/Coq-BBB4 proved] that '''BBB(4) = 32,779,478''', the champion being {{TM\|1RB1LC_1RD1RB_0RD0RC_1LD1LA\|halt}}, discovered by Nick Drozd in July 2021, which [[Quasihalt\|quasihalts]] by turning into a period 1 [[translated cycler]] after 32,779,478 steps.<sup>[https://nickdrozd.github.io/2021/07/11/self-cleaning-turing-machine.html]</sup>

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

	* [[Fractran]]		* [[Fractran]]
	** On August 1, @-d used Opus 4.8 to write two deciders, potentially reducing the number of BBf(23) holdouts from 21,233 to 694.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1532980960281366548]</sup> ~~(Note that the new holdout lists are unofficial, as the correctness of the deciders has not yet been verified).~~		** On August 1, @-d used Opus 4.8 to write two deciders, potentially reducing the number of BBf(23) holdouts from 21,233 to 694<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1532980960281366548]</sup> and then decide 602 of those individually. As a result of additional equivalences and implications proven, the unofficial holdouts list for BBf(23) was reduced to 21.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1532984416434126848]</sup>
	** On the same day, @-d used Opus 4.8 to decide 602 of ~~the 694 remaining holdouts~~ individually~~, and to create equivalences and implications between the remaining holdouts~~. As a result, ~~21 holdouts remain in~~ the unofficial ~~holdout~~ list for BBf(23).<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1532984416434126848]</sup>		** On August 4, @-d and Opus had further reduced the holdout list to 13 of which 12 follow Hydra-like biased pseudorandom walks and are thus [[Cryptids]].<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1534417541265363087]</sup> The remaining holdout (#601) was analyzed by Shawn Ligocki and had a sort of mixture of Collatz-like and [[BMO1]]-like behavior.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1533155623137710270]</sup>
	** On ~~the same day~~, ~~Shawn Ligocki isolated one of the 21 remaining holdouts (#601 in~~ the ~~original 694~~ holdout list~~) as non-[[~~Hydra~~]]-like. They say that its behavior is a mix of Collatz~~-like and ~~BMO1.<sup>~~[~~https://discord.com/channels/960643023006490684/1438019511155691521/1533155623137710270~~]~~</sup>~~		** On August 22, @-d enumerated 20% of BBf(24) (the complete enumeration is expected to take 6 times longer than that of BBf(23).<sup>[https://discord.com/channels/960643023006490684/960643023530762341/1538703088263761992]</sup>), discovering a new champion which runs for over 4.804 × 10<sup>1,184</sup> steps.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1540831684071530637]</sup> Shawn Ligocki discovered another champion among that set which runs for over 9.263 × 10<sup>9,595</sup> steps.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1540835303202492467]</sup>
	** On August 2, @-d noticed that holdout #601 iterates a chaotic map, likely meaning it has no stable orbits that would otherwise allow for an easy proof.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/~~1533270850961412107~~]</sup>
	** On August 3, @-d identified 19 of the 21 remaining ~~size 23 holdouts as Hydra-like; the two remaining holdouts~~ (#601 ~~and #163~~) ~~were described as "ugly"~~ and ~~"messy" respectively.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1533686184092631050]</sup>~~
	** On August 4, @-d used Opus 4.8 to prove holdout #163 non-halting, as it fell into a ~~stable orbit; 4 holdouts have been removed due to equivalence, and another 3 have been removed due to implications regarding other holdouts. 12~~ of ~~the remaining 13 holdouts follow different Hydra~~-like ~~mechanisms~~ and ~~are Cryptids (a total of 90 size 23 machines are equivalent to one of these 12 holdouts), with the remaining holdout (#601) having been previously described as an ugly version of~~ BMO1.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/~~1534417541265363087~~]</sup>
	** On August 22, @-d enumerated 20% of BBf(24) (the complete ~~ennumeration~~ is expected to take 6 times longer than that of BBf(23).<sup>[https://discord.com/channels/960643023006490684/960643023530762341/1538703088263761992]</sup>), discovering a new champion which runs for over 4.804 × 10<sup>1,184</sup> steps.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1540831684071530637]</sup>
	** On the same day, Shawn Ligocki discovered another ~~new BBf(24)~~ champion which runs for over 9.263 × 10<sup>9,595</sup> steps.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1540835303202492467~~]</sup>~~
	** On August 26, Shawn Ligocki discovered two new size 24 halters (non-champions) which have [[Collatz-like]] and [[BMO1]]-like behaviors.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1542271972946485430]</sup>
	* [[Terminating Turmite\|Terminating Turmites]]		* [[Terminating Turmite\|Terminating Turmites]]
	** On August 2, Discord user creeperman7002 discovered a new step and score champion for TT(3,3), <code>1PB2PA0PC_2TB1PC2PB_2PB1PZ0PA</code>, running for 715,764,479 steps.<sup>[https://discord.com/channels/960643023006490684/1243312334907375676/1533503518906912778]</sup>		** On August 2, Discord user creeperman7002 discovered a new step and score champion for TT(3,3), <code>1PB2PA0PC_2TB1PC2PB_2PB1PZ0PA</code>, running for 715,764,479 steps.<sup>[https://discord.com/channels/960643023006490684/1243312334907375676/1533503518906912778]</sup>

HelpMe: clean up some stuff

2026-10-05T17:50:48Z

clean up some stuff

HelpMe: cryptid and archive are definitely important for this month imo.

2026-10-05T17:42:59Z

cryptid and archive are definitely important for this month imo.

Show changes

HelpMe: small tweaks to the page. also added one more point in counterscript

2026-10-05T15:49:16Z

small tweaks to the page. also added one more point in counterscript

Show changes

HelpMe: it is very in progress

2026-10-05T15:18:18Z

it is very in progress

Show changes

HelpMe: not messy but ugly

2026-10-05T13:29:27Z

not messy but ugly

← Older revision		Revision as of 13:29, 5 October 2026
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	** On August 2, @-d noticed that holdout #601 iterates a chaotic map, possibly meaning it has no stable orbits that would allow for an easy proof.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1533270850961412107]</sup>		** On August 2, @-d noticed that holdout #601 iterates a chaotic map, possibly meaning it has no stable orbits that would allow for an easy proof.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1533270850961412107]</sup>
	** On August 3, @-d identified 19 of the 21 remaining size 23 holdouts as hydra-like; the two remaining holdouts (#601 and #163) were described as "ugly" and "messy" respectively.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1533686184092631050]</sup>		** On August 3, @-d identified 19 of the 21 remaining size 23 holdouts as hydra-like; the two remaining holdouts (#601 and #163) were described as "ugly" and "messy" respectively.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1533686184092631050]</sup>
	** On August 4, @-d used Opus 4.8 to prove holdout #163 non-halting, as it fell into a stable orbit; another 4 holdouts have been removed due to equivalence, and another 3 holdouts have been removed due to implications. 12 of the remaining 13 holdouts follow different Hydra-like mechanisms and are Cryptids (a total of 90 size 23 machines are equivalent to one of these 12 holdouts), with the remaining holdout (#601) being previously described as ~~a messy~~ version of BMO1.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1534417541265363087]</sup>		** On August 4, @-d used Opus 4.8 to prove holdout #163 non-halting, as it fell into a stable orbit; another 4 holdouts have been removed due to equivalence, and another 3 holdouts have been removed due to implications. 12 of the remaining 13 holdouts follow different Hydra-like mechanisms and are Cryptids (a total of 90 size 23 machines are equivalent to one of these 12 holdouts), with the remaining holdout (#601) being previously described as an ugly version of BMO1.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1534417541265363087]</sup>
	** On August 22, @-d enumerated 20% of BBf(24), discovering a new champion, which runs for over 4.804 × 10<sup>1,184</sup> steps.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1540831684071530637]</sup>		** On August 22, @-d enumerated 20% of BBf(24), discovering a new champion, which runs for over 4.804 × 10<sup>1,184</sup> steps.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1540831684071530637]</sup>
	** On the same day, Shawn Ligocki discovered a new BBf(24) champion which runs for over 9.263 × 10<sup>9,595</sup> steps.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1540835303202492467]</sup>		** On the same day, Shawn Ligocki discovered a new BBf(24) champion which runs for over 9.263 × 10<sup>9,595</sup> steps.<sup>[https://discord.com/channels/960643023006490684/1438019511155691521/1540835303202492467]</sup>

HelpMe: added wow

2026-10-05T13:22:27Z

added wow

Show changes

Jacobzheng at 13:17, 5 October 2026

2026-10-05T13:17:51Z

← Older revision		Revision as of 13:17, 5 October 2026
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	[[File:TMBR August prurq 2.63e304 step halter 1RB0LB 0RC1RF 1LD1RE 0LA0RB 0RD0LD 0LE---.png\|thumb\|prurq simulated an impressive 4 holdouts to halting this month; one of the machines simulated, {{TM\|~~1RB0LB_0RC1RF 1LD1RE_0LA0RB_0RD0LD_0LE~~---\|halt}}, is shown here in mxdys's Turing Machine simulator using [[Longitudinal Analysis\|longitudinal analysis]], which was used to confirm prurq's result. (Image source: [https://discord.com/channels/960643023006490684/1239205785913790465/1533889409332674763 prurq])]]		[[File:TMBR August prurq 2.63e304 step halter 1RB0LB 0RC1RF 1LD1RE 0LA0RB 0RD0LD 0LE---.png\|thumb\|prurq simulated an impressive 4 holdouts to halting this month; one of the machines simulated, {{TM\|1RB0LB_0RC1RF_1LD1RE_0LA0RB_0RD0LD_0LE---\|halt}}, is shown here in mxdys's Turing Machine simulator using [[Longitudinal Analysis\|longitudinal analysis]], which was used to confirm prurq's result. (Image source: [https://discord.com/channels/960643023006490684/1239205785913790465/1533889409332674763 prurq])]]
	* [[BB(6)]]		* [[BB(6)]]
	** On August 1, mxdys added BMO 9 and BMO 10 to the [[Beaver Math Olympiad]].<sup>[https://discord.com/channels/960643023006490684/1239205785913790465/1533036863118508215][https://discord.com/channels/960643023006490684/1239205785913790465/1533044040403124336]</sup>		** On August 1, mxdys added BMO 9 and BMO 10 to the [[Beaver Math Olympiad]].<sup>[https://discord.com/channels/960643023006490684/1239205785913790465/1533036863118508215][https://discord.com/channels/960643023006490684/1239205785913790465/1533044040403124336]</sup>

← Older revision		Revision as of 09:32, 9 November 2026
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	{{TMBRnav\|July 2026\|September 2026}}		{{TMBRnav\|July 2026\|September 2026}}
	[[File:Sligocki BBB 4 equals 32779478.png\|thumb\|757x757px\|BBB(4) = 32,779,478 was proven this month by @carrino using Claude AI. The first 71 steps of the champion, {{TM\|1RB1LD_1RC1RB_1LC1LA_0RC0RD\|halt}}, are depicted in this spacetime diagram, using Shawn Ligocki's [https://github.com/sligocki/busy-beaver/blob/main/Code/Visual_Simulator Visual Simulator]. (Credit: [https://www.sligocki.com/2021/07/17/bb-collatz.html Shawn Ligocki])]][[:Category:This Month in Beaver Research\|This Month in Beaver Research]] for August 2026.		[[File:Sligocki BBB 4 equals 32779478.png\|thumb\|757x757px\|BBB(4) = 32,779,478 was proven this month by @carrino using Claude AI. The first 71 steps of the champion, {{TM\|1RB1LD_1RC1RB_1LC1LA_0RC0RD\|halt}}, are depicted in this spacetime diagram, using Shawn Ligocki's [https://github.com/sligocki/busy-beaver/blob/main/Code/Visual_Simulator Visual Simulator]. (Credit: [https://www.sligocki.com/2021/07/17/bb-collatz.html Shawn Ligocki])]][[:Category:This Month in Beaver Research\|This Month in Beaver Research]] for August 2026. This month saw us finally cross the long-awaited milestone of less than '''1,000 holdouts''' in [[BB(6)]], after a flurry of simulations, as well as proofs from users both new and old, resulting in ''65'' holdouts being solved this month. mxdys has also added the 9th and 10th problems to the [[Beaver Math Olympiad]]. [[BB(4,3)]] recorded small but substantial reductions in holdouts, while Terry Ligocki's enumeration of [[BB(2,7)]] slowly but surely reaches the 85% mark.

	This month saw us finally cross the long-awaited milestone of less than '''1,000 holdouts''' in [[BB(6)]], after a flurry of simulations, as well as proofs from users both new and old, resulting in ''65'' holdouts being solved this month. mxdys has also added the 9th and 10th problems to the [[Beaver Math Olympiad]]. [[BB(4,3)]] recorded small but substantial reductions in holdouts, while Terry Ligocki's enumeration of [[BB(2,7)]] slowly but surely reaches the 85% mark.

	This month was also quite a busy one for BB-adjacent functions. Most notably, for [[Beeping Busy Beaver]] functions, '''BBB(4) = 32,779,478''', proven by @carrino! '''BBλ(41) = 5 × 3<sup>3<sup>3</sup></sup> + 6''' has also been proven this month, and BBf(23) has been almost completely solved, save for 12 Cryptids and 1 oddball machine. creeperman7002 has been working in the field of [[Terminating Turmite\|Terminating Turmites]], finding a machine that demonstrates TT(3,3) > 2.27 × 10<sup>248</sup>, while reducing the domain to under 20,000 holdouts. Δ⁵ has also been incrementally finding new large champions for the [[SKI Calculus#Champions\|SKI]] and [[SKI Calculus#SK calculus\|SK]] calculi, and the [[SKI Calculus#BCKW system\|BCKW system]], notably finding 6 new ''hexational''-level champions in the calculi!		This month was also quite a busy one for BB-adjacent functions. Most notably, for [[Beeping Busy Beaver]] functions, '''BBB(4) = 32,779,478''', proven by @carrino! '''BBλ(41) = 5 × 3<sup>3<sup>3</sup></sup> + 6''' has also been proven this month, and BBf(23) has been almost completely solved, save for 12 Cryptids and 1 oddball machine. creeperman7002 has been working in the field of [[Terminating Turmite\|Terminating Turmites]], finding a machine that demonstrates TT(3,3) > 2.27 × 10<sup>248</sup>, while reducing the domain to under 20,000 holdouts. Δ⁵ has also been incrementally finding new large champions for the [[SKI Calculus#Champions\|SKI]] and [[SKI Calculus#SK calculus\|SK]] calculi, and the [[SKI Calculus#BCKW system\|BCKW system]], notably finding 6 new ''hexational''-level champions in the calculi!

← Older revision		Revision as of 17:50, 5 October 2026
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	The Busy Beaver functions for [[Pebble Automaton\|Pebble Automata]] and [[Cyclic Tag]] have been introduced; [[Collatz-like]] behavior has already been detected amongst small pebble automata, but no Cryptids have been found as of yet, unlike in cyclic tag, where a size 36 Cryptid has been found. [[Diophantine Equation\|Diophantine Equations]] have also received some research this month through attempts to find Cryptids and new champions, many of which are related to the [[wikipedia:Sums_of_three_cubes\|sums of three cubes]] problem. A new family of champions has also been found for the Busy Beaver function for [[Wang Tiles]], and Shawn Ligocki has recently revived discussion about a small but chaotic and possible Cryptid [[General Recursive Function]]. A primality test and a program that computes the Fibonacci numbers have also been created in [[CounterScript]].		The Busy Beaver functions for [[Pebble Automaton\|Pebble Automata]] and [[Cyclic Tag]] have been introduced; [[Collatz-like]] behavior has already been detected amongst small pebble automata, but no Cryptids have been found as of yet, unlike in cyclic tag, where a size 36 Cryptid has been found. [[Diophantine Equation\|Diophantine Equations]] have also received some research this month through attempts to find Cryptids and new champions, many of which are related to the [[wikipedia:Sums_of_three_cubes\|sums of three cubes]] problem. A new family of champions has also been found for the Busy Beaver function for [[Wang Tiles]], and Shawn Ligocki has recently revived discussion about a small but chaotic and possible Cryptid [[General Recursive Function]]. A primality test and a program that computes the Fibonacci numbers have also been created in [[CounterScript]].

	There has also been extensive discussion on what should classify a machine or a program as a Cryptid, due to the wide range of ''potential'' Cryptids in BB(6) (most notably BMO1) and how virtually all of the known machines or programs classified as Cryptids rely, at least in part, on Collatz-like randomness; a new defintion of Cryptid may even include solved machines with behaviors reminiscent of diabolically hard but solved problems, such as Fermat's Last Theorem.		There has also been extensive discussion on what should classify a machine or a program as a [[Cryptid]], due to the wide range of ''potential'' Cryptids in BB(6) (most notably [[BMO1]]) and how virtually all of the known machines or programs classified as Cryptids rely, at least in part, on [[Collatz-like#Why is Collatz randomness mysterious?\|Collatz-like randomness]]; a new defintion of Cryptid may even include solved machines with behaviors reminiscent of diabolically hard but solved problems, such as Fermat's Last Theorem.

	An archive of the Discord server is also being considered, for accessibility purposes and to prevent sources from being lost; however, they may be some ethical concerns and problems with the suggestion as it stands currently.		An archive of the Discord server is also being considered, for accessibility purposes and to prevent sources from being lost; however, they may be some ethical concerns and problems with the suggestion as it stands currently.
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	[[File:TMBR August prurq 2.63e304 step halter 1RB0LB 0RC1RF 1LD1RE 0LA0RB 0RD0LD 0LE---.png\|thumb\|466x466px\|prurq simulated an impressive 4 holdouts to halting this month; one of the machines simulated, {{TM\|1RB0LB_0RC1RF_1LD1RE_0LA0RB_0RD0LD_0LE---\|halt}}, is shown here in mxdys's general [https://ccz181078.github.io/TM/LongAcc/index.html accelerated simulator] using [[Longitudinal Analysis\|longitudinal analysis]], which prurq used to confirm the result. (Image source: [https://discord.com/channels/960643023006490684/1239205785913790465/1533889409332674763 prurq])]]		[[File:TMBR August prurq 2.63e304 step halter 1RB0LB 0RC1RF 1LD1RE 0LA0RB 0RD0LD 0LE---.png\|thumb\|466x466px\|prurq simulated an impressive 4 BB(6) holdouts to halting this month; one of the machines simulated, {{TM\|1RB0LB_0RC1RF_1LD1RE_0LA0RB_0RD0LD_0LE---\|halt}}, is shown here in mxdys's general [https://ccz181078.github.io/TM/LongAcc/index.html accelerated simulator] using [[Longitudinal Analysis\|longitudinal analysis]], which prurq used to confirm the result. (Image source: [https://discord.com/channels/960643023006490684/1239205785913790465/1533889409332674763 prurq])]]
	* [[BB(6)]]		* [[BB(6)]]
	** On August 1, mxdys added BMO9 ({{TM\|1RB1LA_1RC0RD_1LA---_1RE1RD_1LF0LA_---0LE\|halt}}) and BMO10 ({{TM\|1RB0LB_0RC0LD_1LD1RE_0LA0RF_0RD1RF_0RC---\|halt}}) to the [[Beaver Math Olympiad]].<sup>[https://discord.com/channels/960643023006490684/1239205785913790465/1533036863118508215][https://discord.com/channels/960643023006490684/1239205785913790465/1533044040403124336]</sup>		** On August 1, mxdys added BMO9 ({{TM\|1RB1LA_1RC0RD_1LA---_1RE1RD_1LF0LA_---0LE\|halt}}) and BMO10 ({{TM\|1RB0LB_0RC0LD_1LD1RE_0LA0RF_0RD1RF_0RC---\|halt}}) to the [[Beaver Math Olympiad]].<sup>[https://discord.com/channels/960643023006490684/1239205785913790465/1533036863118508215][https://discord.com/channels/960643023006490684/1239205785913790465/1533044040403124336]</sup>
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	** On the same day, mxdys released a new holdouts list of '''1,016''' machines up to equivalence,<sup>[https://discord.com/channels/960643023006490684/1239205785913790465/1538109685033607198]</sup> this is a '''4.51%''' reduction compared to the previous holdouts lists.		** On the same day, mxdys released a new holdouts list of '''1,016''' machines up to equivalence,<sup>[https://discord.com/channels/960643023006490684/1239205785913790465/1538109685033607198]</sup> this is a '''4.51%''' reduction compared to the previous holdouts lists.
	** On the same day, mxdys, using an LLM, produced proofs deciding 20 machines (the entirety of Counter Class 1, and 4 [[Dekaheptoid\|Dekaheptoids]]); 2 of these proofs (both belonging to Dekaheptoids) have been confirmed, whereas the other 18 proofs are under review.<sup>[https://discord.com/channels/960643023006490684/1239205785913790465/1538130536168693804]</sup>		** On the same day, mxdys, using an LLM, produced proofs deciding 20 machines (the entirety of Counter Class 1, and 4 [[Dekaheptoid\|Dekaheptoids]]); 2 of these proofs (both belonging to Dekaheptoids) have been confirmed, whereas the other 18 proofs are under review.<sup>[https://discord.com/channels/960643023006490684/1239205785913790465/1538130536168693804]</sup>
	*** mxdys also ~~notes~~ that the LLM has produced 32 other Rocq proofs, and has helped them find configurations in existing deciders that settle 10 other holdouts.<sup>[https://discord.com/channels/960643023006490684/1239205785913790465/1538130536168693804]</sup>		*** mxdys also says that the LLM has produced 32 other Rocq proofs, and has helped them find configurations in existing deciders that settle 10 other holdouts.<sup>[https://discord.com/channels/960643023006490684/1239205785913790465/1538130536168693804]</sup>
	** On August 24, Discord user flintt_6 informally [https://github.com/golirt1/bb6-shift-overflow-analysis proved] another machine halting.<sup>[https://discord.com/channels/960643023006490684/1239205785913790465/1541418968806334515]</sup>		** On August 24, Discord user flintt_6 informally [https://github.com/golirt1/bb6-shift-overflow-analysis proved] another machine halting.<sup>[https://discord.com/channels/960643023006490684/1239205785913790465/1541418968806334515]</sup>
	** On the same day, mxdys released a list of machines that are easy to accelerate using the UBRRBA decider, consisting of 86 machines.<sup>[https://discord.com/channels/960643023006490684/1239205785913790465/1541486462330085496]</sup>		** On the same day, mxdys released a list of machines that are easy to accelerate using the UBRRBA decider, consisting of 86 machines.<sup>[https://discord.com/channels/960643023006490684/1239205785913790465/1541486462330085496]</sup>
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	* On August 22, person89 began a discussion on what behaviors should be required to classify a machine, or another program, as a Cryptid.<sup>[https://discord.com/channels/960643023006490684/960643023530762341/1540652592340668427]</sup>		* On August 22, person89 began a discussion on what behaviors should be required to classify a machine, or another program, as a Cryptid.<sup>[https://discord.com/channels/960643023006490684/960643023530762341/1540652592340668427]</sup>
	** This may be relevant to the classification of BMO1, which is currently not considered a Cryptid,<sup>[https://discord.com/channels/960643023006490684/960643023530762341/1540837601458782368]</sup> despite it sharing many aspects with mathematically hard problems.		** This may be relevant to the classification of [[BMO1]], which is currently not considered a Cryptid,<sup>[https://discord.com/channels/960643023006490684/960643023530762341/1540837601458782368]</sup> despite it sharing many aspects with mathematically hard problems.
	** person89 has also suggested that machines or programs that would have relied on the validity of [[wikipedia:Fermat's_Last_Theorem\|Fermat's Last Theorem]] (prior to Andrew Wiles's proof in 1994<sup>[https://www.jstor.org/stable/2118559]</sup>) should be considered Cryptids in some sense, despite the problem being settled,<sup>[https://discord.com/channels/960643023006490684/960643023530762341/1541527287508377720]</sup> due to the length, complexity, and technicality of the proof.		** person89 has also suggested that machines or programs that would have relied on the validity of [[wikipedia:Fermat's_Last_Theorem\|Fermat's Last Theorem]] (prior to Andrew Wiles's proof in 1994<sup>[https://www.jstor.org/stable/2118559]</sup>) should be considered Cryptids in some sense, despite the problem being settled,<sup>[https://discord.com/channels/960643023006490684/960643023530762341/1541527287508377720]</sup> due to the length, complexity, and technicality of the proof.
	** Shawn Ligocki observed that the only programs that have been widely accepted as Cryptids are those that rely on Collatz-like randomness (e.g. [[Antihydra]], [[Lucy's Moonlight]]).<sup>[https://discord.com/channels/960643023006490684/960643023530762341/1542200200091664505]</sup> They also brought up recent discussion about [[Diophantine Equation\|Diophantine Equations]]<sup>[https://discord.com/channels/960643023006490684/960643023530762341/1542201592504131725]</sup> about whether the smallest holdout equations can be considered Cryptids by virtue of being simple, open problems in number theory;<sup>[https://discord.com/channels/960643023006490684/1461768250575687897/1538993715417194647]</sup> they believe otherwise, as not much effort has been put into deciding these holdouts.<sup>[https://discord.com/channels/960643023006490684/960643023530762341/1542201927205527553]</sup> (See also: discussion about whether <math>x^3 + y^3 + z^3 = 114</math> and other unsolved sums of three cubes problems are Cryptids). They also suggest that Cryptid-ness could instead considered as a spectrum, rather than a black-or-white category,<sup>[https://discord.com/channels/960643023006490684/960643023530762341/1542202781669265540]</sup> such as considering Fermat's Last Theorem as an easier type of Cryptid.<sup>[https://discord.com/channels/960643023006490684/960643023530762341/1542202330794168340]</sup>		** Shawn Ligocki observed that the only programs that have been widely accepted as Cryptids are those that rely on Collatz-like randomness (e.g. [[Antihydra]], [[Lucy's Moonlight]]).<sup>[https://discord.com/channels/960643023006490684/960643023530762341/1542200200091664505]</sup> They also brought up recent discussion about [[Diophantine Equation\|Diophantine Equations]]<sup>[https://discord.com/channels/960643023006490684/960643023530762341/1542201592504131725]</sup> about whether the smallest holdout equations can be considered Cryptids by virtue of being simple, open problems in number theory;<sup>[https://discord.com/channels/960643023006490684/1461768250575687897/1538993715417194647]</sup> they believe otherwise, as not much effort has been put into deciding these holdouts.<sup>[https://discord.com/channels/960643023006490684/960643023530762341/1542201927205527553]</sup> (See also: discussion about whether <math>x^3 + y^3 + z^3 = 114</math> and other unsolved sums of three cubes problems are Cryptids). They also suggest that Cryptid-ness could instead considered as a spectrum, rather than a black-or-white category,<sup>[https://discord.com/channels/960643023006490684/960643023530762341/1542202781669265540]</sup> such as considering Fermat's Last Theorem as an easier type of Cryptid.<sup>[https://discord.com/channels/960643023006490684/960643023530762341/1542202330794168340]</sup>