TMBR: January 2026: Difference between revisions
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RobinCodes (talk | contribs) Added Nick Drozd's article |
→Champions: I didn't find these BLB and TT champions. |
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== Champions == | == Champions == | ||
* | * nickdrozd 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. | ||
* | * creeperman7002 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. | * 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. | ||
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== 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(2)=6, BBu(3)=17 and BBu(4)=29) | ||
== Theory == | == Theory == | ||
Revision as of 09:48, 18 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
- nickdrozd discovered a new BLB(3,3) champion (
1RB2RB1LA_2LC0LB2LB_2RC2RA0LC(bbch)) which blanks the tape after running for more than 1042,745 steps. - creeperman7002 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.
Blog Posts
- 16 Jan 2026. Nick Drozd. AI Reproduction of Lin's Busy Beaver Proof.
BB Adjacent
- Uniform-Action Busy Beavers were introduced, and lower bounds have been given up to BBu(6) (with BBu(2)=6, BBu(3)=17 and BBu(4)=29)
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):
- 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.[1]
- The holdout count was further reduced to 19,879,953 (a 1.57% reduction), which breaks the 20 million barrier.[2]