TMBR: November 2025

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This Month in Beaver Research

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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).

In the News

• TODO. Add talk about BB https://discord.com/channels/960643023006490684/960643023530762343/1440090541936214017

Themed Months

There have been two specific BB domain themed months: BB(3,3) month (October) and BB(2,5) month (November). For BB(3,3), this resulted in the clarification of some of the results and techniques on the Discord and Wiki. LegionMammal wrote up a detailed explanation of the probvious halter, see Discord. No further progress on holdouts was made in October due to the limited number of holdouts and the work that's already been put into trying to solve them. For BB(2,5), it was verified that the Wiki was up to date. @mxdys shared some of his old notes on the unanalyzed machines, see source.

Misc

• Discord user Vonhust made a Macro Machine achieving 2 billion steps / s, and is planning even more optimizations. TODO: Sources, details, graph.

BB Adjacent

• 

  All Fractran deciders summarized and their relations, shared by Daniel Yuan on 14 Nov 2025

  Busy Beaver for Fractan, or BBf was introduced on 1 Nov by Jason Yuen, who also solved the first 14 values. Then, all values up to 19 were solved, with 19 requiring 3 programs to be proven by hand. For n = 20, 34 holdouts remain, while for n = 21, 587 holdouts are remaining. Three BB-Cryptids were also transformed into Fractran programs, so we know that n = 29 requires solving Hydra.
• Cyclic Tag was introduced by Discord user Jack on 14 Nov. The first two values, n = 1 and 2 were also solved by him. Then, lower bounds were given for values up to n = 7. CTBB(7) reaches hexation.
• TODO. Add BMS milestone improved by tromp from 350 to 331. (source: https://discord.com/channels/960643023006490684/1355653587824283678/1436844104742076507)
• TODO. Add Busy Beaver for SKI calculus.

Holdouts

• BB(6): Total holdout reduction: 202 TMs, a 12% reduction!
  • @mxdys released a holdouts list consisting of 1534 machines up to equivalence, which is a 6% reduction (84 machines)
  • @mxdys decided a holdout from 50 Random Holdouts by hand, making 11/50 solved. He also decided 5 more machines with a single strategy. (This is not a holdout in the 1534 list, just progress on the 50 Random holdouts).
  • A total of 15 holdouts were solved by a few people (Mainly @mxdys and Alistaire) spanning several days. This is partly a consequence of a new holdouts list, which was created by Robin Rovenszky via searching the Discord server for any results that may have been lost, and thus some results were collected, then verified by @mxdys.
  • At the end of the month, @mxdys released a holdouts list consisting of only 1416 holdout TMs.
  • Right after, Peacemaker decided a TM by hand. @mxdys verified this result using an Inductive decider.
• BB(2,7): Enumeration started!
  • The code provided by mxdys breaks up the BB(2,7) enumeration into 1 million subtasks which each run for ~10 minutes and leave ~2500 holdouts based on an average of the first 1K subtasks. These values are about 5 times longer than and 25 times larger than the ones for BB(7).
  • Terry Ligocki enumerated the first 3 subtasks, resulting in 88,730,540 holdouts, which can be found here.
  • The expected number of holdouts after the enumeration is ~3M TMs.