TMBR: January 2026: Difference between revisions
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* [[User:Azerty|Azerty]] discovered a new [[BLB|BLB(3,3)]] [[champion]] ({{TM|1RB2RB1LA_2LC0LB2LB_2RC2RA0LC}}) which blanks the tape after running for more than 10<sup>42,745</sup> steps. | * [[User:Azerty|Azerty]] discovered a new [[BLB|BLB(3,3)]] [[champion]] ({{TM|1RB2RB1LA_2LC0LB2LB_2RC2RA0LC}}) which blanks the tape after running for more than 10<sup>42,745</sup> steps. | ||
* Azerty discovered <code>1TB1PA_1PC0PA_1TA0PD_---1TA</code>, a [[TT|TT(4,2)]] TM which runs for 48,186 steps and <code>1TA2PB3TB---_3TA1PB1TA1PA</code>, a [[TT|TT(2,4)]] TM which runs for more than 3.467*10<sup>15</sup> steps. | |||
* A new lower bound of <math>f_{\varepsilon_0 \omega^{\omega^{3}}}\left(4\right)</math> was computed for the [[Busy Beaver for lambda calculus#Champions|BBλ(91)]] champion. | |||
== BB Adjacent == | == BB Adjacent == | ||
* [https://discord.com/channels/960643023006490684/1458010522967609425/1458010522967609425 Uniform-Action Busy Beavers] were introduced, and lower bounds have been given up to BBu(6) (with BBu(3)=17) | * [https://discord.com/channels/960643023006490684/1458010522967609425/1458010522967609425 Uniform-Action Busy Beavers] were introduced, and lower bounds have been given up to BBu(6) (with BBu(3)=17) | ||
== Theory == | |||
@ConePine [https://discord.com/channels/960643023006490684/960643023530762341/1458876275749032232 shared an idea] on how the value of BB(5) can be proved without enumerating Turing machines. | |||
== Holdouts == | == Holdouts == | ||
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** Progress has been made in reducing the list of machines not simulated up to 1e13, by Alistaire: see [https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=806905077#gid=806905077 spreadsheet]. Current count: '''210'''. (Total reduction: '''68'''. 38 machines<sup>[https://discord.com/channels/960643023006490684/1456755170527543420/1456755170527543420 <nowiki>[1]</nowiki>][https://discord.com/channels/960643023006490684/1456757189787127971/1456757189787127971 <nowiki>[2]</nowiki>][https://discord.com/channels/960643023006490684/1456757980203585678/1456757980203585678 <nowiki>[3]</nowiki>][https://discord.com/channels/960643023006490684/1456758622762696815/1456758622762696815 <nowiki>[4]</nowiki>][https://discord.com/channels/960643023006490684/1456759118818971709/1456759118818971709 <nowiki>[5]</nowiki>][https://discord.com/channels/960643023006490684/1456761765688901724/1456761765688901724 <nowiki>[6]</nowiki>][https://discord.com/channels/960643023006490684/1456762231491657830/1456762231491657830 <nowiki>[7]</nowiki>][https://discord.com/channels/960643023006490684/1456310285462802587/1456760768472289321 <nowiki>[8]</nowiki>][https://discord.com/channels/960643023006490684/1239205785913790465/1456932659740545217 <nowiki>[9]</nowiki>][https://discord.com/channels/960643023006490684/1239205785913790465/1456933097009320089 <nowiki>[10]</nowiki>][https://discord.com/channels/960643023006490684/1239205785913790465/1456933714629099593 <nowiki>[11]</nowiki>][https://discord.com/channels/960643023006490684/1239205785913790465/1456934113943621653 <nowiki>[12]</nowiki>][https://discord.com/channels/960643023006490684/1239205785913790465/1457147385309565021 <nowiki>[13]</nowiki>][https://discord.com/channels/960643023006490684/1239205785913790465/1457409447084429594 <nowiki>[11 more]</nowiki>][https://discord.com/channels/960643023006490684/1239205785913790465/1457497643478683770 <nowiki>[4 more]</nowiki>][https://discord.com/channels/960643023006490684/1239205785913790465/1457644806984437760 <nowiki>[10 more]</nowiki>][https://discord.com/channels/960643023006490684/1239205785913790465/1457992404597739672 <nowiki>[11 more]</nowiki>][https://discord.com/channels/960643023006490684/1239205785913790465/1458413343088840734 <nowiki>[17 more]</nowiki>]</sup> simulated out, plus 2 solved machines). | ** Progress has been made in reducing the list of machines not simulated up to 1e13, by Alistaire: see [https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=806905077#gid=806905077 spreadsheet]. Current count: '''210'''. (Total reduction: '''68'''. 38 machines<sup>[https://discord.com/channels/960643023006490684/1456755170527543420/1456755170527543420 <nowiki>[1]</nowiki>][https://discord.com/channels/960643023006490684/1456757189787127971/1456757189787127971 <nowiki>[2]</nowiki>][https://discord.com/channels/960643023006490684/1456757980203585678/1456757980203585678 <nowiki>[3]</nowiki>][https://discord.com/channels/960643023006490684/1456758622762696815/1456758622762696815 <nowiki>[4]</nowiki>][https://discord.com/channels/960643023006490684/1456759118818971709/1456759118818971709 <nowiki>[5]</nowiki>][https://discord.com/channels/960643023006490684/1456761765688901724/1456761765688901724 <nowiki>[6]</nowiki>][https://discord.com/channels/960643023006490684/1456762231491657830/1456762231491657830 <nowiki>[7]</nowiki>][https://discord.com/channels/960643023006490684/1456310285462802587/1456760768472289321 <nowiki>[8]</nowiki>][https://discord.com/channels/960643023006490684/1239205785913790465/1456932659740545217 <nowiki>[9]</nowiki>][https://discord.com/channels/960643023006490684/1239205785913790465/1456933097009320089 <nowiki>[10]</nowiki>][https://discord.com/channels/960643023006490684/1239205785913790465/1456933714629099593 <nowiki>[11]</nowiki>][https://discord.com/channels/960643023006490684/1239205785913790465/1456934113943621653 <nowiki>[12]</nowiki>][https://discord.com/channels/960643023006490684/1239205785913790465/1457147385309565021 <nowiki>[13]</nowiki>][https://discord.com/channels/960643023006490684/1239205785913790465/1457409447084429594 <nowiki>[11 more]</nowiki>][https://discord.com/channels/960643023006490684/1239205785913790465/1457497643478683770 <nowiki>[4 more]</nowiki>][https://discord.com/channels/960643023006490684/1239205785913790465/1457644806984437760 <nowiki>[10 more]</nowiki>][https://discord.com/channels/960643023006490684/1239205785913790465/1457992404597739672 <nowiki>[11 more]</nowiki>][https://discord.com/channels/960643023006490684/1239205785913790465/1458413343088840734 <nowiki>[17 more]</nowiki>]</sup> simulated out, plus 2 solved machines). | ||
** Alistaire found a halting machine in the list mentioned above, see [https://discord.com/channels/960643023006490684/1239205785913790465/1456317703156531211 Discord]. Approximate score: 4e12. Later, he found another halting machine in the same list, see [https://discord.com/channels/960643023006490684/1239205785913790465/1456381492019069192 Discord] - approximate score: 1.5e18. | ** Alistaire found a halting machine in the list mentioned above, see [https://discord.com/channels/960643023006490684/1239205785913790465/1456317703156531211 Discord]. Approximate score: 4e12. Later, he found another halting machine in the same list, see [https://discord.com/channels/960643023006490684/1239205785913790465/1456381492019069192 Discord] - approximate score: 1.5e18. | ||
** @mxdys shared a list of machines that seem to be provable. See [https://discord.com/channels/960643023006490684/1460495597386731643/1460495597386731643 Discord]. | |||
*[[BB(7)]]: | |||
**Andrew Ducharme further continued reducing the number of holdouts, from 20,387,509 to '''20,197,978''' TMs, a 0.93% reduction. This puts the total compute time on the current BB(7) pipeline just over '''50,000''' hours.[https://discord.com/channels/960643023006490684/1369339127652159509/1459719965396566078] | |||
**The holdout count was further reduced to '''19,879,953''', a 1.57% reduction.[https://discord.com/channels/960643023006490684/1369339127652159509/1460718041577951365] | |||
[[Category:This Month in Beaver Research|2025-12]] | [[Category:This Month in Beaver Research|2025-12]] | ||
Latest revision as of 06:54, 14 January 2026
| Prev: December 2025 | This Month in Beaver Research | Next: February 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).
This is the first edition of TMBR in 2026.
Champions
- Azerty discovered a new BLB(3,3) champion (
1RB2RB1LA_2LC0LB2LB_2RC2RA0LC(bbch)) which blanks the tape after running for more than 1042,745 steps. - Azerty discovered
1TB1PA_1PC0PA_1TA0PD_---1TA, a TT(4,2) TM which runs for 48,186 steps and1TA2PB3TB---_3TA1PB1TA1PA, a TT(2,4) TM which runs for more than 3.467*1015 steps. - A new lower bound of was computed for the BBλ(91) champion.
BB Adjacent
- Uniform-Action Busy Beavers were introduced, and lower bounds have been given up to BBu(6) (with BBu(3)=17)
Theory
@ConePine shared an idea on how the value of BB(5) can be proved without enumerating Turing machines.
Holdouts
- BB(6): 2 solved machines.
- Progress has been made in reducing the list of machines not simulated up to 1e13, by Alistaire: see spreadsheet. Current count: 210. (Total reduction: 68. 38 machines[1][2][3][4][5][6][7][8][9][10][11][12][13][11 more][4 more][10 more][11 more][17 more] simulated out, plus 2 solved machines).
- Alistaire found a halting machine in the list mentioned above, see Discord. Approximate score: 4e12. Later, he found another halting machine in the same list, see Discord - approximate score: 1.5e18.
- @mxdys shared a list of machines that seem to be provable. See Discord.
- BB(7):