TMBR: September 2025

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This Month in Beaver Research

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This Month in Beaver Research for September 2025.

Holdouts

• BB(6):
  • Andrew Ducharme and @mxdys both found a family of 10 halting TMs independently, all halting in around $10^{69}$ steps.
  • @mxdys decided two machines’ fates from the 50 Random Holdouts released in August, making 8/50 machined solved as of this month.
• BB(7): Andrew Ducharme has continued reducing the number of holdouts, from 59,727,905 to 37,514,197 (37.1915% reduction)

BB Adjacent

• John Tromp announced on Discord that a 350-bit $BB\lambda (n)$ function now reaches the limit of BMS, an improvement from the previous 404 bits.

TODO: phrasing. Discord source: https://discord.com/channels/960643023006490684/1355653587824283678/1413637783045542038 and https://github.com/tromp/AIT/blob/master/fast_growing_and_conjectures/bms.lam