TMBR: July 2025

This is the very first edition of This Month in Beaver Research (TMBR pronounced "timber") for July 2025.

The goal of these pages is to provide a short survey of notable results from each month in Busy Beaver research. So much is happening now that it is hard to keep up with everything. Most of the results come from the bbchallenge Discord server. Contributions are welcome from anyone in the community, please feel free to add a short one sentence blurb for any notable results in a future article. Shawn Ligocki is the editor-in-chief.

This was a busy month in BB research with 3 new BB adjacent problems introduced, significant work on holdout reduction for BB(6) and BB(7), a smattering of new champions discovered and quite a few news articles written about our work.

We are also delighted to have a new piece of fan art to include in this edition: A Lovecraftian Beaver produced by Lauren, a friend of Discord user Fern. We welcome any additional fan art and will gladly add it to future editions!

Champions

(Late June) mxdys found a pair of new BB(6) champions pushing it into the pentational values: 1RB1RA_1RC1RZ_1LD0RF_1RA0LE_0LD1RC_1RA0RE (bbch) (scoring over 2↑↑2↑↑2↑↑10) and 1RB1LC_1LA1RE_0RD0LA_1RZ1LB_1LD0RF_0RD1RB (bbch) (scoring over 10↑↑11010000).
mxdys confirms dyuan's BB(2,5) champion 1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ (bbch). [1]
Nick Drozd discovered a BBi(8) champion running $>6.889\times 10^{1565}$ steps: 1RB1LA------_1RC3LB1RB---_2LA2LC---0LC (bbch). [2]
Shawn Ligocki discovered a BB_rev(6) champion running 537,556 steps.

Holdouts

mxdys announced that BB(6) is down to 2728 holdouts on 29 July. [3]
A large group effort has enumerated BB(7) and filtered it down to less than 86 million holdouts. [4]

BB Adjacent

Instruction-Limited Busy Beaver was introduced and calculated up to BBi(7).
Reversible Turing Machine Busy Beaver values were calculated up to BB_rev(5).
Terminating Turmites (Relative Movement Turing Machines) were introduced.

Blog Posts

28 June 2025. Scott Aaronson. BusyBeaver(6) is really quite large.
3 July 2025. Nick Drozd. Busy Beaver Backwards.
15 July 2025. Nick Drozd. Performance Hacks for Brady's Algorithm.

In the News

1 July 2025. The Quanta Podcast. How Amateurs Solved a Major Computer Science Puzzle.
2 July 2025. Manon Bischoff. Spektrum. Wie der sechste Fleißige Biber die Mathematik an ihre Grenzen bringt.
7 July 2025. Karmela Padavic-Callaghan. New Scientist. Mathematicians are chasing a number that may reveal the edge of maths. (Paywalled)
11 July 2025. New Scientist podcast episode 311. Discusses mxdys's BB(6) pentation result "We’re brushing up against the edge of mathematics".
11 July 2025. Darren Orf. Popular Mechanics. Mathematicians Say There’s a Number So Big, It’s Literally the Edge of Human Knowledge.
18 July 2025 https://francis.naukas.com/2025/07/18/espeluznante-nueva-cota-inferior-para-la-funcion-castor-afanoso-bb6/

Interesting TMs

A collection of interesting TMs that were mentioned on Discord, most because of their space-time diagrams or general behavior.

1RB1LC_1LB0RA_0LD---_1LE0LA_0LF0RG_1LG0LG_0RB1RG (bbch): Tetrational Fractal
1RB1RE_1LC0RA_0RF0LD_1LE1LC_1RA0RC_---0RB (bbch): Skeleton Finger
1RB1RG_1LC1RA_0LD0LC_0RE0RB_1RE1RF_1LD0LC_0LE--- (bbch): Bouncer that transitions into a Counter
1RB1RE_0RC1RG_1LD0LA_0LE0LF_0RA1RC_1LC0LE_---1RE (bbch): Counter that transitions into a Bouncer
1RB2LA2LC---_1LA2RB2RD---_3RB1LC1RD0LA_3LA1RD1LC0RB (bbch): Sneaky almost-Cryptid