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).
TODO. Write a summary of what happened during BB(3,3) month (October) and BB(2,5) month (November).
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 2025Busy 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.
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.
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 2 subtasks, resulting in 62,062,284 holdouts, which can be found here.
The expected number of holdouts after the enumeration is ~2'500'000'000.
