TMBR: October 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). This Month in Beaver Research for October 2026.

BB Adjacent

Register Machine:

• On 1 October, sheep discovered a 12-state, 2-register machine which halts iff 7 converges to 1 under the Collatz-like 5n+1 map, thus showing that MBB(12, 2) is hard.^[1]
• On the same day, @-d enumerated MBB(8), which left 7,891 holdouts after reduction, or 404 holdouts if an ai-created decider is used.^[2]
• On the same day, @mineralli discovered a family of champions for MBB(n, 1).^[3]
• On 2 October, @mineralli discovered a new champion for MBB(10, 2).^[4]
• On the same day, sheep discovered 2 new tetrational champions for MBB(10).^[5][6]
• On the same day, Shawn Ligocki released an MBB(8) holdout list consisting of 145 holdouts,^[7] using another ai-created decider similar to CTL.^[8]
• On 3 October, Shawn Ligocki released another MBB(8) holdout list consisting of 46 holdouts,^[9] later reduced to 6^[10] (from 7^[11]) holdouts.
• On the same day, Shawn Ligocki discovered a cryptid amongst the 6 remaining holdouts, showing MBB(8) is hard.^[12]
• On the same day, sheep analyzed the rest of the holdouts, discovering 4 equivalences and another cryptid,^[13] meaning MBB(8) "probviously" = 3,394.

Misc

• On 1 October, dyuan shared a subset of BB(6) holdouts, consisting of 24 machines which are expected to be easily analyzable by longitudinal analysis.^[14]

Champions

• Jeff Ketchersid constructed a new BB(8) champion 1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_1LC0RH_1RG1LF (bbch), which takes over $>2{\uparrow }^{37}3$ steps to halt. It was constructed by modifying the BB(7) champion, which previously held the BB(8) championship by default.

Holdouts

• BB(2,5)
  • On October 2, prurq claimed to have used Aristotle AI to solve one of the remaining holdouts, reducing the unofficial count to 38 out of initially 60 Rocq-proven.^[15]
• BB(2,7)
  • Terry Ligocki enumerated 20K more subtasks, increasing the number of holdouts to 3,125,433,611. All 1 million subtasks have been enumerated! This enumeration took from November 2025 to October 2026 using the resources I had available to work on this enumeration. Now we can start decreasing the number of holdouts!
• BB(6)
  • On October 7, mxdys released holdouts list of 778 machines up to equivalence.^[16]