TMBR: October 2025

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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).

Wily Coyote, a BB(3,3) holdout

Blog Posts

• ? Oct 2025. Katelyn Doucette. Building the Busy Beaver Ladder.

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 22,721,168 holdouts remain. (0.35% reduction)
• BB(3,4):
  • XnoobSpeakable and Lúkos are running filters in the domain under Phase 2, reducing the holdouts count from 434,787,751 to 64,777,377 (85.1% 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.