TMBR: October 2025: Difference between revisions

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(Started "Holdouts" section. Added Andrew Ducharme's results.)
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* ? Oct 2025.  Katelyn Doucette. [https://katelyndoucette.com/articles/building-the-busy-beaver-ladder Building the Busy Beaver Ladder].
* ? Oct 2025.  Katelyn Doucette. [https://katelyndoucette.com/articles/building-the-busy-beaver-ladder Building the Busy Beaver Ladder].
== Holdouts ==
* BB(7):
** Andrew Ducharme has continued reducing the [[BB(7)#Phase 2|number of holdouts]] with Stage 4 of Phase 2. Initially, in the beginning of the month there were 22,801,601 holdouts, and 22,721,690 holdouts remain. (0.35% reduction)


== Theory ==
== Theory ==

Revision as of 19:12, 1 October 2025

Prev: September 2025 This Month in Beaver Research Next: November 2025

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).

Wily Coyote, a BB(3,3) holdout

Blog Posts

Holdouts

  • BB(7):
    • Andrew Ducharme has continued reducing the number of holdouts with Stage 4 of Phase 2. Initially, in the beginning of the month there were 22,801,601 holdouts, and 22,721,690 holdouts remain. (0.35% reduction)

Theory

TODO: Update this section after studying existing literature a bit more.

Linear-Inequality Affine Transformation Automata (LIATA) were introduced as a generalization of the BMO1 rules:

  • @Bard proved that 3 dimension LIATA are Turing complete: [1]
  • @star proved that 2 dimension LIATA are Turing complete: [2]
  • BMO1 is a 2d-LIATA so this provides some sense for the difficulty of the problem.