TMBR: January 2026

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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 10^42,745 steps.
• Azerty discovered 1TB1PA_1PC0PA_1TA0PD_---1TA, a TT(4,2) TM which runs for 48,186 steps and 1TA2PB3TB---_3TA1PB1TA1PA, a TT(2,4) TM which runs for more than 3.467*10¹⁵ steps.

BB Adjacent

• Uniform-Action Busy Beavers were introduced, and lower bounds have been given up to BBu(6) (with BBu(3)=17)

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.