TMBR: July 2025

Lovecraftian Beaver fan art made by Lauren

The very first edition of This Month in Beaver Research for July 2025.

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]

Holdout

Number of BB(6) holdouts over time

• 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) was introduced.

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

• 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