TMBR: June 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

• Busy Beaver for Lambda Calculus: TODO: BBλ(39) solved

Misc

• TODO: GPU deciders

Holdouts

• BB(6)
  • mxdys solved four TMs with FAR.^[1][2][3][4]
  • prurq solved another four TMs with FAR.^[5][6][7]
  • A TM was shown to be non-halting by hipparcos, which was later confirmed in Rocq by mxdys.
• BB(2,6)
  • Andrew Ducharme reduced the number of holdouts from 413,513 to 412,086, a 0.35% reduction.^[8]
• BB(2,7)
  • Terry Ligocki enumerated 100K more subtasks, increasing the number of holdouts to 1,392,222,673. A total of 450K subtasks out of the 1 million subtasks (or 45%) have been enumerated.