TMBR: September 2025: Difference between revisions

Revision as of 15:39, 6 September 2025

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BB(6):
- Andrew Ducharme and @mxdys both found a family of 10 halting TMs independently, all halting in around $1 0^{69}$ steps.
- @mxdys decided yet another machine's fate from the 50 Random Holdouts released in August, making 7/50 machined solved as of this month.
BB(7): Andrew Ducharme has continued reducing the number of holdouts, from 59,727,905 to 45,980,438 (23.02% reduction)

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

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 ** @mxdys [https://discord.com/channels/960643023006490684/1400456788955893840/1413542505772748810 decided yet another machine's fate] from the [[TMBR: August 2025#Misc|50 Random Holdouts released in August]], making 7/50 machined solved as of this month.
 * [[BB(7)|BB(7):]] Andrew Ducharme has continued reducing [https://wiki.bbchallenge.org/wiki/BB(7)#Phase_2 the number of holdouts], from 59,727,905 to 45,980,438                                                                                                     (23.02% reduction)
+==BB Adjacent==
+*John Tromp announced on Discord that a 350-bit <math>BB \lambda (n)</math> 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
 [[Category:This Month in Beaver Research|2025-09]]