TMBR: March 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 Month in Beaver Research for March 2026. We celebrated bbchallenge's fourth birthday on 8 March. This month was quite a substantial month in Beaver research, as after more than 200 days, the last 3 informally solved BB(3,3) holdouts were formalised by mxdys in Rocq.
TODO: Write a proper introductory paragraph.
Champions
- Discord user 50_ft_lock found a new BB(13) champion which surpasses Graham's number, reducing the upper bound of Graham-beating TMs to 13 states.
Misc
1RB0RB_1LC1RE_1LF0LD_1RA1LD_1RC1RB_---1LC(bbch) was shown to be a probviously non-halting Cryptid similar to Space Needle by DrDisentangle.
Meta
- Famous math Youtuber 2swap made a couple of videos about Turing Machines arranged into grids and colored based on their halting status for BB(2,2), BB(3,2), BB(2,3), BB(4,2) and BB(5,2) respectively, then made a two-hour long Youtube video about the same topic on their second channel.
BB Adjacent
- Fractran: In BBf(21), Claude Opus 4.6 gave a proof that all 140 holdouts do not halt. This tentatively proves that BBf(21) = 31,957,632.
- Fractran: A Cryptid was discovered in BBf(22) with the help of Claude Opus 4.6.
- Fractran: Katelyn Doucette started working on a program to visualize fractran spacetime diagrams just like for TMs:
Holdouts
| Domain | Previous Holdout Count | New Holdout Count | Holdout Reduction | % Reduction |
|---|---|---|---|---|
| BB(6) | 1214 | 1161 | 53 | 4.37% |
| BB(7) | 18,195,192 | 18,036,852 | 158,340 | 0.87% |
| BB(2,5) | 72 | 69 | 3 | 4.17% |
| BB(2,6) | 548,993 | 545,005 | 3,988 | 0.73% |
- BB(6): 1e14 machines: 170. 1e15 machines: 237. 53 solved machines. TODO: Update
- Holdouts lists for machines not simulated to 1e14 and 1e15 steps were created. The holdouts list counts were 178 and 252 respectively. See Spreadsheet for BB6.
- Later, prurq found 10 more machines in the holdouts list that had previously been simulated to 1e15: thus the new 1e15 holdout count was 242.
- Andrew Ducharme solved two machines using FAR.
- prurq found two machines [1][2] to be Translated Cyclers. Shawn Ligocki verified one of them and discovered its preperiod to be over steps. mxdys verified the other. Both were 1e14 and 1e15 holdouts, thus reducing those holdout counts by 2.
- mxdys found four more [3][4] Translated Cyclers in the remaining holdouts and solved one more TM using FAR.
- Andrew Ducharme solved a machine using FAR. This machine was a 1e14 and 1e15 holdout, thus reducing those holdout counts by 1.
- prurq found 3 more machines previously simulated so far in the 1e14 list, and 2 more in the 1e15 list (both were also 1e14). This means 1e14 holdout count was reduced by 3, and 1e15 holdout count was reduced by 2.
- Discord user mammillaria simulated a 1e14 holdout thus far, and then another 9 days later, therefore reducing that holdout count by 2.
- prurq found a machine to be a Translated Cycler.
- mxdys decided a machine using FAR.
- mxdys released a new holdout list of 1161 machines. The new informal holdout count is 1159, and the Rocq-verified holdout count is 1187.
- BB(7):
- Andrew Ducharme reduced the number of holdouts from 18,195,192 to 18,036,852 (a 0.87% reduction) via the mxdys FAR decider.
- BB(2,5):
- Peacemaker II solved a machine using FAR and mxdys confirmed two[5][6] machines to be non-halting. Thus, the new holdout count is 69, or 60 considering informal proofs.
- BB(2,6):
- A new filtering run by Andrew Ducharme has reduced to number of holdouts from 548,993 to 545,005.[7]
- BB(3,3):
- mxdys formalised three remaining informal results (650, 412, 279) into Rocq.