BB(2,6)

The 2-state, 6-symbol Busy Beaver problem, BB(2,6), is unsolved. With cryptids like Hydra in the preceding domain BB(2,5), we know that we must solve a Collatz-like problem in order to solve BB(2,6).

The current BB(2,6) champion 1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA (bbch) was discovered by Pavel Kropitz in May 2023, proving the lower bound:

$$S(2,6)>\Sigma (2,6)>10\uparrow \uparrow 10\uparrow \uparrow 10^{10^{115}}>10\uparrow \uparrow \uparrow 3$$

Top Halters

The highest known scoring machines are:

TM	Approximate sigma score	Discoverer
1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA (bbch)	10 ↑↑↑ 3	Pavel Kropitz
1RB3LA4LB0RB1RA3LA_2LA2RA4LA1RA5RB1RZ (bbch)	10 ↑↑ 91	Pavel Kropitz
1RB2LA1RA4LA5RA0LB_1LA3RA2RB1RZ3RB4LA (bbch)	10 ↑↑ 70	Shawn Ligocki
1RB2LB0RA2RA5RA1LB_2LA4RB3LB2RB0RB1RZ (bbch)	10 ↑↑ 54.90	Andrew Ducharme*
1RB3RB1LB5LA2LB1RZ_2LA3RA4RB2LB0LA4RB (bbch)	10 ↑↑ 42.17	Andrew Ducharme*
1RB3LB0RB5RA1LB1RZ_2LB3LA4RA0RB0RA2LB (bbch)	10 ↑↑ 40.07	Andrew Ducharme*
1RB3LB3RB4LA2LA4LA_2LA2RB1LB0RA5RA1RZ (bbch)	10 ↑↑ 21.54	Andrew Ducharme*
1RB2LB3LA1RA0RA1RZ_1LA2RB1LB4RB5RA3LA (bbch)	10 ↑↑ 20.58	Shawn Ligocki
1RB0RA3RB0LB1RA2LA_2LA4LB1RA3LB5LB1RZ (bbch)	10 ↑↑ 17.53	Andrew Ducharme*
1RB0RA3RB0LB5LA2LA_2LA4LB1RA3LB5LB1RZ (bbch)	10 ↑↑ 17.53	Andrew Ducharme*

All decimal places are truncated. Discoverers are asterisked where it is unclear if the TM had been found but unreported by someone previously (namely Shawn Ligocki).

Filtering

Starting from Terry Ligocki's holdouts list of 22,302,296 TMs, Andrew Ducharme has performed the following filtering to get the holdout count down to 18,054,938.

Holdout TMs		% Reduced	Compute Time (core-hours)	TMs Processed per s per core	Description	Source
Input	Output
22,302,296	20,778,101	6.8%	274.6	22.56	Enumerate.py with --no-sim and --lin-steps=10_000	Google Drive
20,778,101	19,257,876	7.3%	~200	~28	lr_enum_continue 1M steps
19,280,508	19,004,377	1.4%	2174.6	2.46	Enumerate.py with --block-multiple=1, max-loops=20_000, and --time=1
19,005,529	18,952,159	0.3%	1952.7	2.70	Enumerate.py with --block-multiple=2, max-loops=20_000, and --time=120
18,952,159	18,054,938	4.7%	4168.4	1.26	CPS_Filter with --block-size=7

A far more efficient pipeline would immediately apply lr_enum_continue out to 1M steps to Terry Ligocki's holdout list. lr_enum_continue, written in C++, is about 400x faster than Enumerate.py at checking for Lin Recursion. Using Enumerate.py meant its Reverse Engineering decider was applied to all holdouts, and solved 74,089 TMs (0.33% of holdouts)...at the cost of roughly 274.1 hours of compute.