TMBR: July 2026

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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).

BB Adjacent

SK Calculus:

• New champions were discovered for BB_SK(12) and BB_SK(13).

Holdouts

• BB(6):
  • On 2 July, mxdys solved three holdouts in rocq.^[1][2]
  • On 3 July, mxdys solved another holdout in rocq using an LLM.
• BB(4,3):
  • Andrew Ducharme reduced the number of holdouts from 4,784,443 to 4,776,646, a 0.16% reduction.^[3]
• BB(2,7):
  • Terry Ligocki enumerated 20K more subtasks, increasing the number of holdouts to 1,686,180,801. A total of 540K subtasks out of the 1 million subtasks (or 54%) have been enumerated.