TMBR: May 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).

BB Adjacent

General Recursive Functions:

• Some new cryptids were hand-built:
  • Size 56, by Shawn on 2 May (simulating 5x+1 problem starting at 7).^[1]
  • Size 49, by aparker, star and Shawn on 3 May (simulating Brocard's problem).^[2]
• The first non-trivial divergent GRF was found (size 15). It halts iff there exists some n ≥ 1 such that n+3 divides $Tetr(n)=\frac{n(n+1)(n+2)}{6}$.^[3] aparker^[4] and star^[5] proved that there is no such n.

Misc

• mxdys made his inductive decider for history-linear machines compilable into an executable file.^[6]

Holdouts

• BB(2,6)
  • Andrew Ducharme reduced the number of holdouts from 536,112 to 527,232 via Enumerate.py and TM-enum, a 1.66% reduction.^[7][7]
• BB(2,7)
  • Terry Ligocki enumerated 30K more subtasks, increasing the number of holdouts to 775,799,715. A total of 250K subtasks out of the 1 million subtasks (or 25%) have been enumerated.^[8]