TMBR: October 2025
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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).
Misc
TODO: Add the mechanical Turing Machine. discord source: https://discord.com/channels/960643023006490684/1362008236118511758/1425889021653160026 and onwards
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 holdout count from 434,787,751 to 17,983,810 (95.86% reduction).
- BB(4,3):
- Terry Ligocki has begun phase 2 of holdout reduction, reducing the number of holdouts from 460,916,384 to 11,985,999. (97.4% reduction)
- BB(2,6):
- Andrew Ducharme has completed stage 3 of phase 2, reducing the number of holdouts from 873,469 to 870,085. (0.39% reduction)
- TODO: BB(4,3) and BB(6). Also update to wherever 3x4 will be at the time.
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.
Programming
TODO: Add -d's cpp quick_sim project. Discord source: https://discord.com/channels/960643023006490684/1226543091264126976/1426265937455222794