BB(7): Difference between revisions

Latest revision as of 10:52, 8 November 2026

The 7-state, 2-symbol Busy Beaver problem, BB(7), refers to the unsolved 7^th value of the Busy Beaver function. With the compilation of the Cryptid machine Bigfoot into a 7-state, 2-symbol machine in May 2024, we now know that we must solve a Collatz-like problem in order to solve BB(7).

The current BB(7) champion 1RB0RG_1RC1RB_0RD1RZ_0LE0LD_0LF1LE_1RA1LF_1LC0RB (bbch) was discovered by Jeff Ketchersid in October 2026, proving the lower bound: $S (7) > Σ (7) > 3 ↑^{20} 3$ .

History

Before 2025, the only known 7-state champions native to BB(7) were produced by hand, not by search. In 1964, Milton Green designed a machine (1LD1LB_1LZ1LA_0LB1LD_0LE0LD_1LF1RC_0LG0LF_1RG1RE (bbch)) that had sigma score 22,961. In 2014, Wythagoras modified a BB(6) champion to produce a machine (1LE---_1RC1RF_1LD0RB_1RE0LC_1LG0RD_1RZ1RC_1RB1LE (bbch)) that had sigma score $> 10 ↑ ↑ 5$ .

In May 2025, mxdys shared C++ code that broke up the BB(7) enumeration into 1 million subtasks, each of which ran for ~2 minutes and left ~100 holdouts. Various folks on Discord investigated different sections of this domain to search for champions.

Within three days of the code's release, the Ligockis found three champions after applying their deciders to enumerator output. Shawn Ligocki found the first two, 1RB0RF_1LC0RE_1RD1LB_1LA1LD_0RA0LE_1RG0LB_1RZ1RB (bbch) and 1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC (bbch), with sigma scores of approximately 10 ↑↑ 22 and 10 ↑↑ 35. That evening, Terry Ligocki found 1RB0LG_1RC0RF_1LD1RZ_1LF0LE_1RA1LD_1LG1RE_0LB0LB (bbch), with sigma score ~10 ↑↑ 46. A few days later, Pavel found 1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch) which outpaces all of them with a sigma score of ~ $2 ↑^{11} 2 ↑^{11} 3$ . Pavel's champion is enumerated in subtask 243308 of Phase 1 (below).

In October 2026, Jeff Ketchersid claimed to have used Gemini 4 Argon to find a new champion (1RB0RG_1RC1RB_0RD1RZ_0LE0LD_0LF1LE_1RA1LF_1LC0RB (bbch)), which runs for $> 3 ↑^{20} 3$ steps.

After the enumeration was completed, deciders were run on the remaining holdouts with various parameters in Phase 2.


Timeline of bounds established for Σ(7) and S(7)^[1]
Month of discovery	Machine	S(7)	Σ(7)	Discoverer	Notes
November 1964	`1LD1LB_1LZ1LA_0LB1LD_0LE0LD_1LF1RC_0LG0LF_1RG1RE` (bbch)	≥ 197,700,005	≥ 22,961	Green, M.	Part of an infinite family of machines now known as Green's machines.
January 1990	`1RB1RA_1LC1LB_0LF1LD_1RA0LE_0RA1LC_1RE1RZ` (bbch)	≥ 13,122,572,797	≥ 136,612	Marxen, H., Buntrock, J.^[2]
January 1990	`1RB1RA_1LC1LB_0RF1LD_1RA0LE_1LZ1LF_0LA0LC` (bbch)	≥ 8,690,333,381,690,951	≥ 95,524,079
July 2000	`1RB0RC_0LA0RD_1RD1RZ_1LE0LD_1RF1LB_1RA1RE` (bbch)	> 5.36 × 10⁴²	> 2.53 × 10²¹
August 2000	`1RB0LC_1LA1RC_1RA0LD_1LE1LC_1RF1RZ_1RA1RE` (bbch)	> 6.12 × 10¹¹⁹	> 1.42 × 10⁶⁰	Marxen, H., Buntrock, J.^[3]
August 2000	`1RB0LB_0RC1LB_1RD0LA_1LE1LF_1LA0LD_1RH1LE` (bbch)	> 6.19 × 10⁹²⁵	> 6.42 × 10⁴⁶²
February 2001	`1RB0LF_0RC0RD_1LD1RE_0LE0LD_0RA1RC_1LA1RZ` (bbch)	> 3.00 × 10^1,730	> 1.29 × 10⁸⁶⁵
November 2007	`1RB0RF_0LB1LC_1LD0RC_1LE1RZ_1LF0LD_1RA0LE` (bbch)	> 8.92 × 10^1,762	> 2.50 × 10⁸⁸¹	Ligocki, T., Ligocki, S.^[4]
December 2007	`1RB0LE_1LC0RA_1LD0RC_1LE0LF_1LA1LC_1LE1RZ` (bbch)	> 2.58 × 10^2,879	> 4.64 × 10^1,439	Ligocki, T., Ligocki, S.^[4]
May 2010	`1RB0LD_1RC0RF_1LC1LA_0LE1RZ_1LA0RB_0RC0RE` (bbch)	> 3.80 × 10^21,132	> 3.18 × 10^10,566	Kropitz, P.^[4]
June 2010	`1RB1LE_1RC1RF_1LD0RB_1RE0LC_1LA0RD_1RZ1RC` (bbch)	> 7.41 × 10^36,534	> 3.51 × 10^18,267	Kropitz, P.^[4]
March 2014	`1LE---_1RC1RF_1LD0RB_1RE0LC_1LG0RD_1RZ1RC_1RB1LE` (bbch)	> 10↑↑5.86		Kropitz, P., Michel, P., Wythagoras^[5]	This machine by Wythagoras is an extension of Pavel Kropitz's former BB(6) champion, based on a tape configuration found by Pascal Michel, proven by Cloudy176.
May 2022	`1RB0LD_1RC0RF_1LC1LA_0LE1RZ_1LF0RB_0RC0RE` (bbch)	> 10↑↑15.60		Kropitz, P.^[6]
May 2025	`1RB0RF_1LC0RE_1RD1LB_1LA1LD_0RA0LE_1RG0LB_1RZ1RB` (bbch)	> 10↑↑22.00		Ligocki, S.^[7]^[8]
	`1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC` (bbch)	> 10↑↑35.09		Ligocki, S.^[7]^[8]
	`1RB0LG_1RC0RF_1LD1RZ_1LF0LE_1RA1LD_1LG1RE_0LB0LB` (bbch)	> 10↑↑46.74		Ligocki, T.^[9]
	`1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF` (bbch)	$> 2 ↑^{11} 2 ↑^{11} 3$		Kropitz, P.^[10]	This was the first example of a 7-state, 2-symbol Ackermann-level machine. 21 minutes later, Terry Ligocki would find `1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ` (bbch), which halts with a score of over 10↑↑286.1658.^[11]
October 2026	`1RB0RG_1RC1RB_0RD1RZ_0LE0LD_0LF1LE_1RA1LF_1LC0RB` (bbch)	$> 3 ↑^{20} 3$		Ketchersid, J.^[12]	Found using Gemini 4 Argon. Not independently verified.

Machines highlighted in blue were inherited from the hunt for BB(6).

Cryptids

BB(7) has not been seriously investigated by hand, so no native BB(7) Cryptids have yet been discovered.

Probviously non-halting Cryptids:

0RB1RB_1LC0RA_1RE1LF_1LF1RE_0RD1RD_1LG0LG_---1LB (bbch), Bigfoot (a BB(3,3) Cryptid) compiled into a 2-symbol TM by Iijil in 2024.

1LG0LD_1RE1RA_1RB1RC_1RC1LD_---0LF_1LC1LF_1LF1LE (bbch), An Antihydra-like cryptid by User:Jacobzheng in Oct 2026.

Top Halters

The scores are given using Knuth's up-arrow notation with an extension to decimal tetration^[13]. The top 20 scoring known machines are:

TM	Approximate runtime	Discoverer
`1RB0RG_1RC1RB_0RD1RZ_0LE0LD_0LF1LE_1RA1LF_1LC0RB` (bbch)	$3 ↑^{20} 3$	Jeff Ketchersid
`1RB0RG_1RC1RB_0RD1RZ_0LE0LD_0LF1LE_1RA1LF_0LD0RB` (bbch)	$3 ↑^{20} 3$	Jeff Ketchersid
`1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF` (bbch)	$2 ↑^{11} 2 ↑^{11} 3$	Pavel Kropitz
`1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE` (bbch)	10 ↑↑ 519.20	Andrew Ducharme
`1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD1LF_1LB0LE` (bbch)	10 ↑↑ 519.20	Andrew Ducharme
`1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD0LG_1LB0LE` (bbch)	10 ↑↑ 519.20	@gerbil5709, Terry Ligocki
`1RB1LB_1LC1RF_1LA0LD_1RE0LG_0RC1RZ_0RB0RD_0RF1LG` (bbch)	10 ↑↑ 403.84	Andrew Ducharme
`1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ` (bbch)	10 ↑↑ 286.17	Terry Ligocki
`1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD` (bbch)	10 ↑↑ 246.32	@Iijil
`1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA1LG_1RZ1LA` (bbch)	10 ↑↑ 246.32	@star, Terry Ligocki
`1RB1RZ_1RC0LE_0RD1RB_1LE1RA_1LF0LG_0LG0RG_1LB1RG` (bbch)	10 ↑↑ 243.88	@Iijil, Andrew Ducharme
`1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ` (bbch)	10 ↑↑ 228.78	Terry Ligocki
`1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RG0LD` (bbch)	10 ↑↑ 192.67	Terry Ligocki
`1RB1LA_1LC0RE_0LD1LB_1RD0LA_1RF0RA_0RG0LA_1RB1RZ` (bbch)	10 ↑↑ 192.67	Terry Ligocki
`1RB1LA_1LC0RE_0LD1LB_1RD0LA_1RF0RA_1RG0LA_0LE1RZ` (bbch)	10 ↑↑ 192.67	Terry Ligocki
`1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG` (bbch)	10 ↑↑ 192.67	Terry Ligocki
`1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RG0LG_1RB1LG` (bbch)	10 ↑↑ 192.67	Terry Ligocki
`1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RC0LD` (bbch)	10 ↑↑ 192.67	Andrew Ducharme
`1RB1LA_1LC0RE_0LD1LB_1RE1LG_1RF0LG_0RA0LA_0RF1RZ` (bbch)	10 ↑↑ 192.67	Andrew Ducharme
`1RB1LA_1LC0RF_0LD0RD_1RF1LE_1LB1RZ_1RG0RA_0RA0LA` (bbch)	10 ↑↑ 192.67	@C7X
`1RB1LA_1LC0RE_0LD1LB_1RE0LA_1RF0RA_0RG0LA_1RB1RZ` (bbch)	10 ↑↑ 192.67	@Iijil, Terry Ligocki
`1RB1LA_1LC0RE_0LD1LB_1RE0LA_1RF0RA_1RG0LA_0LE1RZ` (bbch)	10 ↑↑ 192.67	@Iijil, Terry Ligocki

The top 20 known halters with unique scores are:

TM	Approximate runtime	Discoverer
`1RB0RG_1RC1RB_0RD1RZ_0LE0LD_0LF1LE_1RA1LF_1LC0RB` (bbch)	$3 ↑^{20} 3$	Jeff Ketchersid
`1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF` (bbch)	$2 ↑^{11} 2 ↑^{11} 3$	Pavel Kropitz
`1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE` (bbch)	10 ↑↑ 519.20	Andrew Ducharme
`1RB1LB_1LC1RF_1LA0LD_1RE0LG_0RC1RZ_0RB0RD_0RF1LG` (bbch)	10 ↑↑ 403.84	Andrew Ducharme
`1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ` (bbch)	10 ↑↑ 286.17	Terry Ligocki
`1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD` (bbch)	10 ↑↑ 246.32	@Iijil
`1RB1RZ_1RC0LE_0RD1RB_1LE1RA_1LF0LG_0LG0RG_1LB1RG` (bbch)	10 ↑↑ 243.88	@Iijil, Andrew Ducharme
`1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ` (bbch)	10 ↑↑ 228.78	Terry Ligocki
`1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG` (bbch)	10 ↑↑ 192.67	Terry Ligocki
`1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA` (bbch)	10 ↑↑ 188.28	Terry Ligocki
`1RB0LC_1LC0LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LC` (bbch)	10 ↑↑ 140.28	@stokastic
`1RB0RF_1RC1RZ_0LD1RF_0RA1LE_0LC1LF_1LE0RG_0LE1RA` (bbch)	10 ↑↑ 136.64	Katelyn Doucette, Andrew Ducharme
`1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG` (bbch)	10 ↑↑ 133.85	@poppuncher
`1RB1RZ_1RC0RF_1LD1RB_1RG0LE_1LD0RA_1RE0LD_0RC1LF` (bbch)	10 ↑↑ 129.24	@Iijil
`1RB0RG_1LC0RE_1LF1LD_0LE1LC_1RA1RB_1LD0LF_1RZ0RF` (bbch)	10 ↑↑ 127.52	Andrew Ducharme
`1RB0LC_1RC0RG_1RD0LF_1RE0RF_1LA1RG_1LE1LF_1RZ1RD` (bbch)	10 ↑↑ 126.20	@stokastic
`1RB0LD_1RC1RA_0RD1RG_1LE1LF_0LF1LE_0RA0LD_0RA1RZ` (bbch)	10 ↑↑ 124.86	Terry Ligocki
`1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ` (bbch)	10 ↑↑ 116.98	Terry Ligocki
`1RB0RD_1RC0LA_0LA0LE_1RE1RZ_1RF0RA_1LG0LE_1LC0LG` (bbch)	10 ↑↑ 116.05
`1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ` (bbch)	10 ↑↑ 115.52	@prurq
`1RB0RG_1LC0LE_1LD0LB_0LE1RE_0RA1RF_0RD1RC_1RD1RZ` (bbch)	10 ↑↑ 114.83	Andrew Ducharme

Phase 1

Phase 1's first two stages were carried out from May 2025 to July 2025. The table below summaries some of that activity and was used to coordinate the effort of doing the raw computation. Fourteen people (see below) contributed directly and the overall bbchallenge group participated in discord discussions, etc.

Stage 1, "enumeration" in the table, involved running 1 million subtasks using mxdys's code in 100 batches of 10 thousand subtasks.

Stage 2, "linear rule" in the table, processing the output of Stage 1 using Shawn Ligocki's linear rule code which also used a few other deciders, e.g., a version of CTL.

Stage 3, the final stage of Phase 1, is the compilation, verification, and presentation of the final results from Phase 1. It was completed during August 2025.

(done to reduce column size: $*^{1}$ = enumeration, $*^{2}$ = linear rule)

Task range	Done by	Completed		# holdouts	Maximum Score TM	~Sigma	Source
Task range	Done by	$*^{1}$	$*^{2}$	# holdouts	Maximum Score TM	~Sigma	Source
00-01xxxx	@Iijil	Yes	Yes	1,545,673	`1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD` (bbch)	10 ↑↑ 246.32	Google Drive folder
02-04xxxx	@Iijil Terry Ligocki	Yes	Yes	2,279,734	`1RB0LF_1RC1RA_1RD0RG_1LE1RZ_1LA0LF_1RA1LE_0RE1RG` (bbch)	10 ↑↑ 93.81	@Iijil Terry Ligocki
05-09xxxx	@Iijil Andrew Ducharme	Yes	Yes	3,889,955	`1RB1RZ_1RC0LE_0RD1RB_1LE1RA_1LF0LG_0LG0RG_1LB1RG` (bbch)	10 ↑↑ 243.88	@Iijil Andrew
10-12xxxx	Andrew Ducharme	Yes	Yes	2,708,888	`1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD1LF_1LB0LE` (bbch)	10 ↑↑ 519.20	Google Drive folder
13xxxx	Shawn Ligocki	Yes	Yes	1,192,442	`1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ` (bbch)	10 ↑↑ 114.60	Google Drive folder
14-16xxxx	Andrew Ducharme	Yes	Yes	2,701,637	`1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0LD_0RA1RE_1RZ1LA` (bbch)	10 ↑↑ 188.28	Google Drive folder
17-18xxxx	@gerbil5709 Terry Ligocki	Yes	Yes	1,898,156	`1RB1LA_1LC0RE_0LD1LB_1RE0LA_1RF0RA_0RG0LA_1RB1RZ` (bbch)	10 ↑↑ 192.67	@gerbil5709 Terry Ligocki
19xxxx	Katelyn Doucette Andrew Ducharme	Yes	Yes	1,099,752	`1RB0RF_1RC1RZ_0LD1RF_0RA1LE_0LC1LF_1LE0RG_0LE1RA` (bbch)	10 ↑↑ 136.64	Google Drive folder
20-23xxxx	@C7X	Yes	Yes	4,528,827	`1RB1LA_1LC0RF_0LD0RD_1RF1LE_1LB1RZ_1RG0RA_0RA0LA` (bbch)	10 ↑↑ 192.67	Google Drive folder
24xxxx	Andrew Ducharme	Yes	Yes	712,356	`1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF` (bbch)*	$2 ↑^{11} 2 ↑^{11} 3^{*}$	Google Drive folder
25-34xxxx	@stokastic	Yes	Yes	10,339,816	`1RB0LC_1LC0LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LC` (bbch)	10 ↑↑ 140.28	Google Drive folder
35-39xxxx	Terry Ligocki	Yes	Yes	4,894,047	`1RB1RZ_1LC0RF_0LD1LB_1RD0LE_1RB1LE_1RG0RE_0RA0LE` (bbch)	10 ↑↑ 192.67	Google Drive folder
40-47xxxx	Andrew Ducharme	Yes	Yes	6,181,327	`1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE` (bbch)	10 ↑↑ 519.20	Google Drive folder
48xxxx	@star Terry Ligocki	Yes	Yes	727,875	`1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA1LG_1RZ1LA` (bbch)	10 ↑↑ 246.32	@star Terry Ligocki
49xxxx	Tobiáš Brichta Terry Ligocki	Yes	Yes	804,722	`1RB0LG_1RC0RG_0LD1RE_1RD0RE_1LF1RB_0LA1RZ_1LC1LG` (bbch)	10 ↑↑ 126.20	Tobiáš Brichta Terry Ligocki
50xxxx	@prurq Andrew Ducharme	Yes	Yes	797,224	`1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ` (bbch)	10 ↑↑ 115.52	Google Drive folder
51-53xxxx	@gerbil5709 Terry Ligocki	Yes	Yes	3,016,175	`1RB0LC_1LC0LD_1LA1LB_0LG1RE_0RF0RF_0RA1RE_1RZ1LC` (bbch)	10 ↑↑ 140.28	@gerbil5709 Terry Ligocki
54-59xxxx	Terry Ligocki	Yes	Yes	5,689,850	`1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0RF_0RA1RE_1RZ1LA` (bbch)	10 ↑↑ 188.28	Google Drive folder
60-64xxxx	@gerbil5709 Terry Ligocki	Yes	Yes	3,817,876	`1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD0LG_1LB0LE` (bbch)	10 ↑↑ 519.20	@gerbil5709 Terry Ligocki
65-68xxxx	Terry Ligocki	Yes	Yes	3,076,778	`1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RG0LD` (bbch)	10 ↑↑ 192.67	Google Drive folder
69xxxx	@poppuncher	Yes	Yes	1,053,119	`1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG` (bbch)	10 ↑↑ 133.85	Google Drive folder
70-71xxxx	@hipparcos	Yes	Yes	1,899,094	`1RB1RZ_1LC1RD_0LD0LC_1LE1RA_1LF0LE_1RF0RG_1RG0RD` (bbch)	10 ↑↑ 77.50	Github release
72-79xxxx	Terry Ligocki	Yes	Yes	7,627,514	`1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ` (bbch)	10 ↑↑ 228.78	Google Drive folder
80-81xxxx	XnoobSpeakable	Yes	Yes	1,537,533	`1RB0LA_0RC1RZ_0RD0RG_1LE1RA_1LF1LD_1RG0RG_1RD1RC` (bbch)	10 ↑↑ 74.85	Google Drive folder
82-99xxxx	Terry Ligocki	Yes	Yes	15,673,786	`1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ` (bbch)	10 ↑↑ 286.17	Google Drive folder

*A former BB(7) champion TM 1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch)* was discovered by Pavel Kropitz in the enumeration of subtask 243308. The remaining subtasks in the 24xxxx range were enumerated and filtered by Andrew Ducharme.

Exploration after Phase 1

People are now looking at reducing the number of holdouts (~85M TMs) after Phase 1. They are trying different deciders not used in Phase 1 and different parameters with the deciders used in Phase 1. This table is somewhere they can put the results of these explorations so that there is a record of what is being done. It is hoped that this will inspire everyone to contribute when they can, a reference point for discord discussions, and something that can be questioned and/or verified.

(done to reduce column size: $*^{1}$ = % Reduced, $*^{2}$ = Runtime (hours), $*^{3}$ = Decided, $*^{4}$ = Processed)

Done by	Holdout TMs		$*^{1}$	$*^{2}$	TMs/sec/core		Description	Source
Done by	Input	Output	$*^{1}$	$*^{2}$	$*^{3}$	$*^{4}$	Description	Source
Shawn Ligocki	858,538	733,830	14.5%	5.0	6.9282	47.6966	Translated Cycler and CPS on `7x2_p01_s02_holdouts_rand_13.txt`	Discord link
Andrew Ducharme	872,041	784,099	10.1%	456.4	0.0535	0.5034	Enumerate.py w/ 250k max-loops and block-mult=3 on `7x2_p01_s02_holdouts_rand_72.txt`	Discord link
Terry Ligocki	1,000	982	1.8%	3.3	0.0015	0.0830	MITMWFAR Code with options `-n=10 -m=1 -pm=1` on the first 1,000 TMs in `7x2_p01_s03_holdouts_rand_47.txt`
Andrew Ducharme	800,507	693,348	13.3%	2818.7	0.0106	0.0789	Enumerate.py w/ 1M max-loops and block-mult=4 on holdouts from above Enumerate run on`7x2_p01_s02_holdouts_rand_72.txt`
Andrew Ducharme	70,000	65,615	6.3%	6.6	0.1842	2.9412	Enumerate.py with --no-sim and --lin-steps=100000 on `7x2_p01_s02_holdouts_rand_65.txt`
Terry Ligocki	10,000	N/A	2% - 32%	N/A	N/A	N/A	See the "Source" discussion on the discord channel which includes graphs with quantitative data. A parameter study of a random sample of 10,000 TMs from the Phase 1, Stage 3 holdouts	Discord link

Phase 2

Phase 2 began with Andrew Ducharme's initial decider runs (see Stage 1 in the table). The goal of Phase 2 is to run deciders on the current holdout list (the last in the table) and produce an accessible new holdout list which can then be added to the table. Input Holdout TMs may be unequal to the next row's Output Holdout TMs because more TMs are TNF-enumerated in the process of executing the next row's filtering. Accessing the holdout list can be done through the link "Holdouts" in the "Data" column. The link "Details" leads to additional data/information pertaining to each step. If there isn't a link there it means the data is still being put somewhere everyone can access it.

Stage 1 reduced the number of holdouts by 33.3% from ~86.1M to ~57.5M TMs using the Ligocki's C++/Python codes. In Stage 2, Andrew continued using mxdys' C++ code and reduced the number of holdouts by 51.0% from ~57.5M to ~28.2M TMs. Terry Ligocki then pushed this further using additional deciders/parameters to generate Stage 3 which reduced the number of holdouts by 17.3% from ~28.2M to ~23.3M TMs. Andrew then ran the Ligocki's C++/Python code with larger parameters which reduced the number of holdouts by 2.6% from ~23.3M to ~22.7M TMs. This formed Stage 4. Terry then switched back to the mxdys' C++ code with different deciders/parameters for Stage 5 where the number of holdouts was reduced by 10.2% from ~22.7M to ~20.4M TMs. Stage 6 was Andrew Ducharme running a mix of mxdys and Ligocki deciders, reducing holdouts by 12.7% from ~20.4M to ~17.8M TMs.

This brought the overall reduction in Phase 2 to 79.3% from ~86.1M to ~17.8M TMs. The details are contained in this table:

(done to reduce column size: $*^{1}$ = % Reduced, $*^{2}$ = Compute Time (core-hours), $*^{3}$ = Decided, $*^{4}$ = Processed)

Done by	Holdout TMs		$*^{1}$	$*^{2}$	TMs/sec/core		Description	Source	Data
Done by	Input	Output	$*^{1}$	$*^{2}$	$*^{3}$	$*^{4}$	Description	Source	Data
Stage 1
Andrew Ducharme	86,129,304	82,226,951	4.5%	119.6	9.06	200.04	CPS_Filter with --max-block-size=4	discord	Stage 1 Holdouts Details
Andrew Ducharme	82,226,951	73,751,624	10.3%	120.0	19.62	190.34	lr_enum_continue 1M steps	discord
Andrew Ducharme	73,751,624	72,470,054	1.7%	1040.0	0.34	19.70	lr_enum_continue 3M steps	discord
Andrew Ducharme	72,470,054	69,347,610	4.3%	1113.4	0.78	18.08	CPS_Filter with --min-block-size=5, --max-block-size=6	discord
Andrew Ducharme	69,347,610	68,695,205	0.9%	1491.8	0.12	12.92	CPS_Filter with --block-size=7	discord
Andrew Ducharme	68,695,205	61,875,401	10.6%	1726.7	1.17	11.11	Enumerate.py with --block-multiple=12, max-loops=100_000, and --time=0.1	discord
Andrew Ducharme	61,875,401	60,986,231	1.5%	1660.7	0.15	10.35	Enumerate.py with --block-multiple=8, max-loops=100_000, and --time=0.1	discord
Andrew Ducharme	60,986,231	60,765,943	0.4%	1619.4	0.04	10.46	Enumerate.py with --block-multiple=16, max-loops=100_000, and --time=0.1	discord
Andrew Ducharme	60,765,943	59,727,905	1.7%	2329.4	0.12	7.25	CPS_Filter with --block-size=8	discord
Andrew Ducharme	59,727,905	57,452,672	3.9%	2472.2	0.26	6.71	Enumerate.py with --block-multiple=5, max-loops=200_000, and time=0.2	discord
Stage 1 Cumulative	86,129,304	57,452,672	33.3%	13693.2	---	---	---	---
Stage 2
Andrew Ducharme	57,452,672	52,605,872	8.4%	150.0	8.98	106.39	chr_LRUH 20 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3	discord	Stage 2 Holdouts Details
Andrew Ducharme	52,605,872	50,268,427	4.4%	100.0	6.49	146.13	chr_LRUH 8 chr_H 4 MitM_CTL NG maxT 10000 NG_n 3	discord
Andrew Ducharme	50,268,427	45,980,438	8.5%	250.0			MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 2 n 8	discord
Andrew Ducharme	45,980,438	43,870,806	4.5%	220.0			MitM_CTL RWL_mod sim 1001 maxT 10000 H 8 mod 3 n 6	discord
Andrew Ducharme	43,870,806	42,700,370	2.6%	80.0			chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 30000 NG_n 2	discord
Andrew Ducharme	42,700,370	41,926,200	1.8%	20.0			MitM_CTL RWL_mod sim 1001 maxT 10000 H 3 mod 3 n 1	discord
Andrew Ducharme	41,926,200	41,590,605	0.8%	50.0			MitM_CTL RWL_mod sim 1001 maxT 3000 H 6 mod 2 n 6	discord
Andrew Ducharme	41,590,605	40,481,477	2.6%	75.0			chr_LRUH 14 chr_H 12 MitM_CTL NG maxT 10000 NG_n 2	discord
Andrew Ducharme	40,481,477	38,641,627	4.5%	200.0			MitM_CTL RWL_mod sim 1001 maxT 10000 H 3 mod 1 n 12	discord
Andrew Ducharme	38,641,627	37,514,197	2.9%	80.0			chr_LRUH 18 chr_H 8 MitM_CTL NG maxT 10000 NG_n 5	discord
Andrew Ducharme	37,514,197	36,273,782	3.3%	90.0			MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 8 H 1 tH 1 n 4	discord
Andrew Ducharme	36,273,782	35,984,179	0.8%	20.0			MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 4 H 2 tH 0 n 2	discord
Andrew Ducharme	35,984,179	31,811,445	11.6%	800.0			chr_LRUH 24 chr_H 24 MitM_CTL NG maxT 100000 NG_n 8	discord
Andrew Ducharme	31,811,445	30,638,201	3.6%	1150.0			chr_LRUH 28 chr_H 28 MitM_CTL NG maxT 100000 NG_n 10	discord
Andrew Ducharme	30,638,201	29,781,771	2.8%	630.0			MitM_CTL RWL_mod sim 1001 maxT 30000 H 12 mod 2 n 12	discord
Andrew Ducharme	29,781,771	29,670,310	0.37%	30.0			chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n [1-7]	discord
Andrew Ducharme	29,670,310	29,629,503	0.14%	75.0			chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n [8-10]
Andrew Ducharme	29,629,503	29,380,949	0.84%	90.0			MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 2 n 6
Andrew Ducharme	29,380,949	28,543,434	2.85%	600.0			MitM_CTL RWL_mod sim 1001 maxT 10000 H 3 mod 1 n [2-10,2]
Andrew Ducharme	28,543,434	28,189,617	1.24%	550.0			MitM_CTL RWL_mod sim 1001 maxT 10000 H 3 mod 1 n [1-11,2]	discord
Stage 2 Cumulative	57,452,672	28,189,617	51.00%	5260.0	---	---	---	---
Stage 3
Terry Ligocki	28,189,617	28,109,540	0.28%	5.3	4.2	1,479.75	MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 3 n 1 run		Stage 3 Holdouts Details
Terry Ligocki	28,109,540	27,804,922	1.08%	8.3	10.18	938.98	MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 6 n 1 run
Terry Ligocki	27,804,922	27,747,435	0.21%	14.9	1.07	518.17	MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 3 n 1 run
Terry Ligocki	27,747,435	27,616,006	0.47%	65.7	0.56	117.33	chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
Terry Ligocki	27,616,006	27,552,018	0.23%	56.9	0.31	134.81	MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 4 H 1 tH 0 n 3 run
Terry Ligocki	27,552,018	27,222,303	1.2%	92.3	0.99	82.96	MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 6 n 2 run
Terry Ligocki	27,222,303	26,626,978	2.19%	140.5	1.18	53.8	MitM_CTL RWL_mod sim 1001 maxT 30000 H 6 mod 2 n 2 run
Terry Ligocki	26,626,978	26,518,327	0.41%	126.9	0.24	58.31	MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 3 run
Terry Ligocki	26,518,327	26,334,644	0.69%	99.4	0.51	74.14	MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 0 tH 2 n 4 run
Terry Ligocki	26,334,644	26,076,261	0.98%	336.9	0.21	21.72	MitM_CTL RWL_mod sim 1001 maxT 100000 H 6 mod 6 n 1 run
Terry Ligocki	26,076,261	25,828,854	0.95%	146.8	0.47	49.35	MitM_CTL RWL_mod sim 1001 maxT 30000 H 6 mod 4 n 2 run
Terry Ligocki	25,828,854	25,659,775	0.65%	203.4	0.23	35.28	chr_LRUH 8 chr_H 0 MitM_CTL NG maxT 30000 NG_n 6 run
Terry Ligocki	25,659,775	25,532,914	0.49%	194.4	0.18	36.66	MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 6 H 2 tH 2 n 5 run
Terry Ligocki	25,532,914	25,318,355	0.84%	252.8	0.24	28.06	chr_LRUH 8 chr_H 6 MitM_CTL NG maxT 100000 NG_n 3 run
Terry Ligocki	25,318,355	24,914,333	1.6%	446.1	0.25	15.77	chr_LRUH 14 chr_H 12 MitM_CTL NG maxT 100000 NG_n 2 run
Terry Ligocki	24,914,333	24,648,140	1.07%	258.6	0.29	26.76	MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 2 tH 2 n 6 run
Terry Ligocki	24,648,140	24,596,755	0.21%	322.7	0.04	21.21	MitM_CTL RWL_mod sim 1001 maxT 30000 H 16 mod 3 n 5 run
Terry Ligocki	24,596,755	24,505,987	0.37%	292.0	0.09	23.4	MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 6 H 1 tH 1 n 10 run
Terry Ligocki	24,505,987	24,343,456	0.66%	1,067.8	0.04	6.37	chr_LRUH 20 chr_H 12 MitM_CTL NG maxT 100000 NG_n 6 run
Terry Ligocki	24,343,456	24,116,020	0.93%	574.2	0.11	11.78	MitM_CTL RWL_mod sim 1001 maxT 100000 H 4 mod 2 n 4 run
Terry Ligocki	24,116,020	24,008,284	0.45%	1,754.3	0.02	3.82	MitM_CTL RWL_mod sim 1001 maxT 100000 H 12 mod 1 n 4 run
Terry Ligocki	24,008,284	23,502,214	2.11%	1,941.6	0.07	3.43	chr_LRUH 28 chr_LRUn 2 MitM_CTL NG maxT 100000 NG_n 8 run
Terry Ligocki	23,502,214	23,332,229	0.72%	3,413.9	0.01	1.91	chr_LRUH 18 chr_H 8 MitM_CTL NG maxT 100000 NG_n 12 run
Terry Ligocki	23,332,229	23,314,388	0.08%	1,182.1	0.0	5.48	chr_LRUH 9 chr_H 1 MitM_CTL NG maxT 100000 NG_n 13 run
Stage 3 Cumulative	28,189,617	23,314,388	17.3%	12997.8	---	---	---	---
Stage 4
Andrew Ducharme	23,314,388	23,281,839	0.14%	2,227.8		343.7	Enumerate.py with --block-multiple=1, max-loops=250_000, and --time=0.5.	discord	Stage 4 Holdouts Details
Andrew Ducharme	23,281,839	22,801,601	2.06%	~1,400			lr_enum_continue 10M steps	discord
Andrew Ducharme	22,801,601	22,721,690	0.35%	3,334.6			Enumerate.py with --block-mult=3, --max-loops=250k, and --time=0.2.	discord
Andrew Ducharme	22,721,690	22,721,168	0.002%	3393.5			Enumerate.py with --block-mult=2, --max-loops=250k, and --time=0.2.	discord
Stage 4 Cumulative	23,314,388	22,721,168	2.55%	10,355.9	---	---	---	---
Stage 5
Terry Ligocki	22,721,168	20,405,295	10.19%	4,903.2	0.13	1.29	MitM_CTL RWL_mod sim 1001 maxT 100000 H 8 mod 3 n 12 run MitM_CTL RWL_mod sim 1001 maxT 100000 H 6 mod 2 n 12 run chr_LRUH 18 chr_H 16 MitM_CTL NG maxT 100000 NG_n 3 run MitM_CTL CPS_LRU sim 1001 maxT 1000000 LRUH 20 H 2 tH 4 n 2 run chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 1000000 NG_n 1 run MitM_CTL RWL_mod sim 1001 maxT 30000 H 6 mod 4 n 4 run MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 9 n 1 run MitM_CTL RWL_mod sim 1001 maxT 30000 H 12 mod 3 n 3 run MitM_CTL RWL_mod sim 1001 maxT 300000 H 3 mod 2 n 2 run MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 1 tH 1 n 4 run chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 100000 NG_n 2 run MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 1 run MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 2 run MitM_CTL RWL_mod sim 1001 maxT 30000 H 4 mod 2 n 2 run MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 4 H 1 tH 1 n 3 run		Stage 5 Holdouts Details
Stage 5 Cumulative	22,721,168	20,405,295	10.19%	4903.2	---	---	---	---
Stage 6
Andrew Ducharme	20,405,295	20,387,509	0.09%	1797.2			Enumerate.py with --block-mult=5, --max-loops=250k, --tape-limit=5000, and --time=0.3.	discord	Details
Andrew Ducharme	20,387,509	20,197,978	0.93%	6394.7			Enumerate.py with --block-mult=20, --max-loops=1M, --tape-limit=5000, --max-steps-per-macro=100k, and --time=1.	discord
Andrew Ducharme	20,197,978	19,879,953	1.57%	5748.1			Enumerate.py with --block-mult=18, --max-loops=1M, --tape-limit=5000, --max-steps-per-macro=100k, and --time=1.	discord
Andrew Ducharme	19,879,953	19,781,295	0.50%	6269.7			Enumerate.py with --block-mult=21, --max-loops=1M, --tape-limit=5000, --max-steps-per-macro=100k, and --time=1.	discord
Andrew Ducharme	19,781,295	19,303,801	2.41%	~2000			FAR CPS_LRU maxT 1000000 LRUH 2 H 0 tH 0 n [1-10]	discord
Andrew Ducharme	19,303,801	18,306,497	5.17%	~7000			FAR CPS_LRU maxT 100000 LRUH 3 H 0 tH 0 n [1-31]	discord
Andrew Ducharme	18,306,497	18,254,547	0.28%	~3200			LRUH 1 H [0,1] tH [0,1] n [1-31]	discord
Andrew Ducharme	18,254,547	18,195,716	0.32%	~4000			maxT 100000 remaining parameters w/ LRUH 2	discord
Andrew Ducharme	18,195,716	18,037,417	0.87%	~2200			maxT 100000 remaining parameters w/ LRUH 3	discord
Andrew Ducharme	18,037,417	17,823,260	1.19%	~7200			maxT 100000 LRUH 4	discord
Stage 6 Cumulative	20,405,295	17,823,260	12.65%	45809.7	---	---	---	---
Overall
Overall Cumulative	86,129,304	17,823,260	79.31%	93019.8	---	---	---	---

Phase 3

Phase 3 is characterized by significant reductions hiding TMs improperly dropped from the holdout list. It began with @David SG using novel GPU-based direct simulation to eliminate halting TMs with step counts under 10^12. However, when a TM with multiple undefined transitions was found to halt, this decider did not enumerate new TNF children, causing the accepted number of holdouts (~16.9M) to be an undercount. Andrew Ducharme applied more mxdys C++ code to eliminate further non-halting TMs. @finlay ran the mxdys inductive decider on the generally accepted holdout list, eliminating a very impressive three million holdouts, a 19.4% reduction. This run also generated, but did not expand, new halting TMs with multiple undefined transitions. This finally triggered an effort reunify the holdout list.

The three main deciders were performed on three different computer clusters with different (and in the case of the GPU run, unknown) number of cores, so the TMs/sec/core columns have been removed. This brought the overall reduction in Phase 2 is so far 28.78%, from ~17.8M to ~12.7M TMs. The details are contained in this table:

Done by	Holdout TMs		% Reduced	Compute Time (core-hours)	Description	Source	Data
Done by	Input	Output	% Reduced	Compute Time (core-hours)	Description	Source	Data
@David SG	17,823,260	16,949,557	4.90%	Unknown	Direct simulation by custom GPU code	discord	Google Drive
Andrew Ducharme	16,949,557	15,743,264	7.12%	~120,000	FAR RWL_mod maxT 100000 H [1-4,6,8,12,16] mod [1-6] n [1-10]	discord
@finlay	15,743,264	12,693,129	19.37%	29,000	decider --maxT 100000 --exploop --arithseq	Discord
Stage 7 Cumulative	17,823,260	12,693,129	28.78%	>150,000	---	---	---

Of the 870,000 some TMs found to halt by David SG, 12,378 had multiple undefined transitions. As each transition can represent one of 28 possible rules in BB(7), this meant a growth in the holdout list by 346,584 TMs. Enumeration would have taken significantly, significantly longer without the assistance of @GameDungeon. Roughly 22.5% were removed by the reverse engineer filter, i.e., were trivial to solve. Reductions have been performed by Andrew Ducharme. Not all deciders between the point of enumeration and the current holdout list have been run yet.

Holdout TMs		% Reduced	Compute Time	Description
Input	Output	% Reduced	Compute Time	Description
346,584	268,680	22.47%	5 s	Reverse_Engineer_Filter.py
268,680	66,136	75.38%	~500 hours	FAR RWL_mod maxT 100000 H [1-4,6,8,12,16] mod [1-6] n [1-10]

Only 301 TMs found to halt by @finlay required enumeration, adding 8,428 holdouts. Reductions have been performed by Andrew Ducharme. Not all deciders between the point of enumeration and the current holdout list have been run yet.

Holdout TMs		% Reduced	Compute Time	Description
Input	Output	% Reduced	Compute Time	Description
8,428	6,508	22.47%	<1 s	Reverse_Engineer_Filter.py
6,508				decider --maxT 100000 --exploop --arithseq

References

[:PMH-1] Pascal Michel. (last updated 2026). The Busy Beaver Competition: a historical survey. https://bbchallenge.org/~pascal.michel/ha#tm72

[:12-2] ttps://turbotm.de/~heiner/BB/bb-list

[3] ttps://turbotm.de/~heiner/BB/bb-6list

[:22-4] 4.0 ^4.1 https://web.archive.org/web/20160420171959/http://www.drb.insel.de/~heiner/BB/bbsimtab.html

[5] ttps://googology.fandom.com/wiki/User:Wythagoras/Rado's_sigma_function/BB(7)

[6] ttps://www.sligocki.com/2022/06/21/bb-6-2-t15.html

[7] ttps://discord.com/channels/960643023006490684/1369339127652159509/1370058177277722784

[8] ttps://discord.com/channels/960643023006490684/1369339127652159509/1370080317481943152

[9] ttps://discord.com/channels/960643023006490684/1369339127652159509/1370191445247524964

[10] ttps://discord.com/channels/960643023006490684/1369339127652159509/1370678203395604562

[11] ttps://discord.com/channels/960643023006490684/1369339127652159509/1370683302176096347

[12] ttps://github.com/jeff87654/busy-beaver/commit/9d9a1a4fcaa5dbabc19e887e0fd834cb79567081

[13] Shawn Ligocki. 2022. "Extending Up-arrow Notation"

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[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

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BB(7): Difference between revisions

Latest revision as of 10:52, 8 November 2026

Contents

History

Cryptids

Top Halters

Phase 1

Exploration after Phase 1

Phase 2

Phase 3

References

Navigation menu

@@ Line 1: / Line 1: @@
-The 7-state, 2-symbol Busy Beaver problem '''BB(7)''' is a mostly unexplored domain with only preliminary information.
+The 7-state, 2-symbol Busy Beaver problem, '''BB(7)''', refers to the unsolved 7<sup>th</sup> value of the [[Busy Beaver function]]. With the compilation of the [[Cryptid]] machine [[Bigfoot]] into a 7-state, 2-symbol machine in May 2024, we now know that we must solve a [[Collatz-like]] problem in order to solve BB(7).
-The current BB(7) champion is {{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}} discovered by Pavel Kropitz in 2025 proving the lower bound:<math display="block">S(7) > \Sigma(7) > 2 \uparrow^{11} 2 \uparrow^{11} 3</math>
+The current BB(7) [[champion]] {{TM|1RB0RG_1RC1RB_0RD1RZ_0LE0LD_0LF1LE_1RA1LF_1LC0RB|halt}} was discovered by Jeff Ketchersid in October 2026, proving the lower bound: <math display="block">S(7) > \Sigma(7) > 3 \uparrow^{20} 3</math>.
 == History ==
-Before 2025, the only known BB(7) champions were produced by hand, not by search. Example, Milton Green designed a machine in 1964 that had [[sigma score]] 22,961 and Wythagoras modified a BB(6) champion in 2014 to produce a machine that had sigma score <math>> 10 \uparrow\uparrow 5</math>.
+Before 2025, the only known 7-state champions native to BB(7) were produced by hand, not by search. In 1964, Milton Green designed a machine ({{TM|1LD1LB_1LZ1LA_0LB1LD_0LE0LD_1LF1RC_0LG0LF_1RG1RE|halt}}) that had [[sigma score]] 22,961. In 2014, Wythagoras modified a BB(6) champion to produce a machine ({{TM|1LE---_1RC1RF_1LD0RB_1RE0LC_1LG0RD_1RZ1RC_1RB1LE|halt}}) that had sigma score <math>> 10 \uparrow\uparrow 5</math>.
-In May 2025, mxdys shared [https://github.com/ccz181078/TM C++ code] that breaks up the BB(7) enumeration into 1 million subtasks which each run for about 2 minutes and leave ~100 holdouts each. Various folks on Discord have been investigating different sections of this domain to search for champions.
+In May 2025, mxdys shared [https://github.com/ccz181078/TM C++ code] that broke up the BB(7) enumeration into 1 million subtasks, each of which ran for ~2 minutes and left ~100 [[Holdouts lists|holdouts]]. Various folks on Discord investigated different sections of this domain to search for champions.
-Within three days of the code's release, the Ligockis found three champions after applying their deciders to enumerator output. Shawn Ligocki found the first two, {{TM|1RB0RF_1LC0RE_1RD1LB_1LA1LD_0RA0LE_1RG0LB_1RZ1RB}} and {{TM|1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC}}, with sigma scores of approximately 10 ↑↑ 22 and 10 ↑↑ 35. That evening, Terry Ligocki found {{TM|1RB0LG_1RC0RF_1LD1RZ_1LF0LE_1RA1LD_1LG1RE_0LB0LB}}, with sigma score ~10 ↑↑ 46. These were all outpaced by Pavel's champion.
+Within three days of the code's release, the Ligockis found three champions after applying their deciders to enumerator output. Shawn Ligocki found the first two, {{TM|1RB0RF_1LC0RE_1RD1LB_1LA1LD_0RA0LE_1RG0LB_1RZ1RB|halt}} and {{TM|1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC|halt}}, with sigma scores of approximately 10 ↑↑ 22 and 10 ↑↑ 35. That evening, Terry Ligocki found {{TM|1RB0LG_1RC0RF_1LD1RZ_1LF0LE_1RA1LD_1LG1RE_0LB0LB|halt}}, with sigma score ~10 ↑↑ 46. A few days later, Pavel found {{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF|halt}} which outpaces all of them with a sigma score of ~<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>. Pavel's champion is enumerated in subtask 243308 of Phase 1 (below).
+In October 2026, Jeff Ketchersid claimed to have used Gemini 4 Argon to find a new champion ({{TM|1RB0RG_1RC1RB_0RD1RZ_0LE0LD_0LF1LE_1RA1LF_1LC0RB|halt}}), which runs for <math> > 3 \uparrow^{20} 3</math> steps.
+After the enumeration was completed, deciders were run on the remaining holdouts with various parameters in Phase 2.
+{| class="wikitable mw-collapsible"
+|+
+! colspan="6" |Timeline of bounds established for Σ(7) and S(7)<ref name=":PMH">Pascal Michel. (last updated 2026). The Busy Beaver Competition: a historical survey. [https://bbchallenge.org/~pascal.michel/ha#tm62 https://bbchallenge.org/~pascal.michel/ha#tm72] </ref>
+|-
+!Month of discovery
+!Machine
+!S(7)
+!Σ(7)
+!Discoverer
+!Notes
+|-
+|November 1964
+|{{TM|1LD1LB_1LZ1LA_0LB1LD_0LE0LD_1LF1RC_0LG0LF_1RG1RE|halt}}
+|≥ 197,700,005
+|≥ 22,961
+|Green, M.
+|Part of an infinite family of machines now known as [[Green's machines]].
+|-
+| rowspan="2" |January 1990
+| style="background: #CCFFFF;" |{{TM|1RB1RA_1LC1LB_0LF1LD_1RA0LE_0RA1LC_1RE1RZ|halt}}
+|≥ 13,122,572,797
+|≥ 136,612
+| rowspan="3" |Marxen, H., Buntrock, J.<ref name=":12">https://turbotm.de/~heiner/BB/bb-list</ref>
+|
+|-
+| style="background: #CCFFFF;" |{{TM|1RB1RA_1LC1LB_0RF1LD_1RA0LE_1LZ1LF_0LA0LC|halt}}
+|≥&nbsp;8,690,333,381,690,951
+|≥ 95,524,079
+|
+|-
+|July 2000
+| style="background: #CCFFFF;" |{{TM|1RB0RC_0LA0RD_1RD1RZ_1LE0LD_1RF1LB_1RA1RE|halt}}
+|> 5.36 × 10<sup>42</sup>
+|> 2.53 × 10<sup>21</sup>
+|
+|-
+| rowspan="2" |August 2000
+| style="background: #CCFFFF;" |{{TM|1RB0LC_1LA1RC_1RA0LD_1LE1LC_1RF1RZ_1RA1RE|halt}}
+|> 6.12 × 10<sup>119</sup>
+|> 1.42 × 10<sup>60</sup>
+| rowspan="3" |Marxen, H., Buntrock, J.<ref>https://turbotm.de/~heiner/BB/bb-6list</ref>
+|
+|-
+| style="background: #CCFFFF;" |{{TM|1RB0LB_0RC1LB_1RD0LA_1LE1LF_1LA0LD_1RH1LE|halt}}
+|> 6.19 × 10<sup>925</sup>
+|> 6.42 × 10<sup>462</sup>
+|
+|-
+|February 2001
+| style="background: #CCFFFF;" |{{TM|1RB0LF_0RC0RD_1LD1RE_0LE0LD_0RA1RC_1LA1RZ|halt}}
+|> 3.00 × 10<sup>1,730</sup>
+|> 1.29 × 10<sup>865</sup>
+|
+|-
+|November&nbsp;2007
+| style="background: #CCFFFF;" |{{TM|1RB0RF_0LB1LC_1LD0RC_1LE1RZ_1LF0LD_1RA0LE|halt}}
+|> 8.92 × 10<sup>1,762</sup>
+|> 2.50 × 10<sup>881</sup>
+| rowspan="2" |Ligocki, T., Ligocki, S.<ref name=":22">https://web.archive.org/web/20160420171959/http://www.drb.insel.de/~heiner/BB/bbsimtab.html</ref>
+|
+|-
+|December 2007
+| style="background: #CCFFFF;" |{{TM|1RB0LE_1LC0RA_1LD0RC_1LE0LF_1LA1LC_1LE1RZ|halt}}
+|> 2.58 × 10<sup>2,879</sup>
+|> 4.64 × 10<sup>1,439</sup>
+|
+|-
+|May 2010
+| style="background: #CCFFFF;" |{{TM|1RB0LD_1RC0RF_1LC1LA_0LE1RZ_1LA0RB_0RC0RE|halt}}
+|> 3.80 × 10<sup>21,132</sup>
+|> 3.18 × 10<sup>10,566</sup>
+| rowspan="2" |Kropitz, P.<ref name=":22" />
+|
+|-
+|June 2010
+| style="background: #CCFFFF;" |{{TM|1RB1LE_1RC1RF_1LD0RB_1RE0LC_1LA0RD_1RZ1RC|halt}}
+|> 7.41 × 10<sup>36,534</sup>
+|>&nbsp;3.51&nbsp;×&nbsp;10<sup>18,267</sup>
+|
+|-
+|March 2014
+|{{TM|1LE---_1RC1RF_1LD0RB_1RE0LC_1LG0RD_1RZ1RC_1RB1LE|halt}}
+| colspan="2" | > 10&uparrow;&uparrow;5.86
+|Kropitz, P., Michel, P., Wythagoras<ref>https://googology.fandom.com/wiki/User:Wythagoras/Rado's_sigma_function/BB(7)</ref>
+|This machine by Wythagoras is an extension of Pavel Kropitz's former BB(6) champion, based on a tape configuration found by Pascal Michel, proven by Cloudy176.
+|-
+|May 2022
+| style="background: #CCFFFF;" |{{TM|1RB0LD_1RC0RF_1LC1LA_0LE1RZ_1LF0RB_0RC0RE|halt}}
+| colspan="2" |> 10↑↑15.60
+|Kropitz, P.<ref>https://www.sligocki.com/2022/06/21/bb-6-2-t15.html</ref>
+|
+|-
+| rowspan="4" | May 2025
+|{{TM|1RB0RF_1LC0RE_1RD1LB_1LA1LD_0RA0LE_1RG0LB_1RZ1RB|halt}}
+| colspan="2" | > 10&uparrow;&uparrow;22.00
+| rowspan="2" |Ligocki, S.<ref>https://discord.com/channels/960643023006490684/1369339127652159509/1370058177277722784</ref><ref>https://discord.com/channels/960643023006490684/1369339127652159509/1370080317481943152</ref>
+|
+|-
+|{{TM|1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC|halt}}
+| colspan="2" | > 10&uparrow;&uparrow;35.09
+|
+|-
+|{{TM|1RB0LG_1RC0RF_1LD1RZ_1LF0LE_1RA1LD_1LG1RE_0LB0LB|halt}}
+| colspan="2" | > 10&uparrow;&uparrow;46.74
+|Ligocki, T.<ref>https://discord.com/channels/960643023006490684/1369339127652159509/1370191445247524964</ref>
+|
+|-
+|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF|halt}}
+| colspan="2" | <math> > 2 \uparrow^{11} 2 \uparrow^{11} 3</math>
+|Kropitz, P.<ref>https://discord.com/channels/960643023006490684/1369339127652159509/1370678203395604562</ref>
+|This was the first example of a 7-state, 2-symbol Ackermann-level machine.
+minutes later, Terry Ligocki would find {{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ|halt}}, which halts with a score of over 10↑↑286.1658.<ref>https://discord.com/channels/960643023006490684/1369339127652159509/1370683302176096347</ref>
+|-
+|October 2026
+|{{TM|1RB0RG_1RC1RB_0RD1RZ_0LE0LD_0LF1LE_1RA1LF_1LC0RB|halt}}
+| colspan="2" | <math> > 3 \uparrow^{20} 3</math>
+|Ketchersid,&nbsp;J.<ref>https://github.com/jeff87654/busy-beaver/commit/9d9a1a4fcaa5dbabc19e887e0fd834cb79567081</ref>
+|Found using Gemini 4 Argon.
+Not independently verified.
+|}
+Machines highlighted in <span style="background: #CCFFFF">blue</span> were inherited from the hunt for BB(6).
+== Cryptids ==
+BB(7) has not been seriously investigated by hand, so no native BB(7) [[Cryptids]] have yet been discovered.
+[[Probviously]] non-halting Cryptids:
+{{TM|0RB1RB_1LC0RA_1RE1LF_1LF1RE_0RD1RD_1LG0LG_---1LB}}, [[Bigfoot]] (a [[BB(3,3)]] Cryptid) compiled into a 2-symbol TM by Iijil in 2024.
+{{TM|1LG0LD_1RE1RA_1RB1RC_1RC1LD_---0LF_1LC1LF_1LF1LE}}, An [[Antihydra]]-like cryptid by [[User:Jacobzheng]] in Oct 2026.
 == Top Halters ==
-Based on limited search through a subset of the 1 million subtasks from mxdys's code, the top 20 scoring known machines are:
+The scores are given using [[wikipedia:Knuth's_up-arrow_notation|Knuth's up-arrow notation]] with an extension to decimal tetration<ref>Shawn Ligocki. 2022. [https://www.sligocki.com/2022/06/25/ext-up-notation.html "Extending Up-arrow Notation"]</ref>. The top 20 scoring known machines are:
-{| class="wikitable"
+{| class="wikitable sortable"
 !TM
-!Approximate sigma score
+!Approximate runtime
 !Discoverer
 |-
-|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
+|{{TM|1RB0RG_1RC1RB_0RD1RZ_0LE0LD_0LF1LE_1RA1LF_1LC0RB|halt}}
-|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
+|data-sort-value="10 ↑↑ 9999"|<math>3 \uparrow^{20} 3</math>
+|Jeff Ketchersid
+|-
+|{{TM|1RB0RG_1RC1RB_0RD1RZ_0LE0LD_0LF1LE_1RA1LF_0LD0RB|halt}}
+|data-sort-value="10 ↑↑ 9999"|<math>3 \uparrow^{20} 3</math>
+|Jeff Ketchersid
+|-
+|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF|halt}}
+|data-sort-value="10 ↑↑ 9998"|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
 |Pavel Kropitz
 |-
-|{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE}}
+|{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE|halt}}
 |10 ↑↑ 519.20
 |Andrew Ducharme
 |-
-|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}}
+|{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD1LF_1LB0LE|halt}}
+|10 ↑↑ 519.20
+|Andrew Ducharme
+|-
+|{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD0LG_1LB0LE|halt}}
+|10 ↑↑ 519.20
+|@gerbil5709, Terry Ligocki
+|-
+|{{TM|1RB1LB_1LC1RF_1LA0LD_1RE0LG_0RC1RZ_0RB0RD_0RF1LG|halt}}
+|10 ↑↑ 403.84
+|Andrew Ducharme
+|-
+|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ|halt}}
 |10 ↑↑ 286.17
 |Terry Ligocki
 |-
-|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD}}
+|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD|halt}}
 |10 ↑↑ 246.32
 |@Iijil
 |-
-|{{TM|1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RC0LD}}
+|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA1LG_1RZ1LA|halt}}
-|10 ↑↑ 192.67
+|10 ↑↑ 246.32
-|Andrew Ducharme
+|@star, Terry Ligocki
+|-
+|{{TM|1RB1RZ_1RC0LE_0RD1RB_1LE1RA_1LF0LG_0LG0RG_1LB1RG|halt}}
+|10 ↑↑ 243.88
+|@Iijil, Andrew Ducharme
 |-
-|{{TM|1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RG0LD}}
+|{{TM|1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ|halt}}
-|10 ↑↑ 192.67
+|10 ↑↑ 228.78
 |Terry Ligocki
 |-
-|{{TM|1RB1LA_1LC0RE_0LD1LB_1RD0LA_1RF0RA_0RG0LA_1RB1RZ}}
+|{{TM|1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RG0LD|halt}}
 |10 ↑↑ 192.67
 |Terry Ligocki
 |-
-|{{TM|1RB1LA_1LC0RE_0LD1LB_1RD0LA_1RF0RA_1RG0LA_0LE1RZ}}
+|{{TM|1RB1LA_1LC0RE_0LD1LB_1RD0LA_1RF0RA_0RG0LA_1RB1RZ|halt}}
 |10 ↑↑ 192.67
 |Terry Ligocki
 |-
-|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG}}
+|{{TM|1RB1LA_1LC0RE_0LD1LB_1RD0LA_1RF0RA_1RG0LA_0LE1RZ|halt}}
 |10 ↑↑ 192.67
 |Terry Ligocki
 |-
-|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RG0LG_1RB1LG}}
+|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG|halt}}
 |10 ↑↑ 192.67
 |Terry Ligocki
 |-
-|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LG_1RF0RG_0RA0LG_1RB1LG}}
+|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RG0LG_1RB1LG|halt}}
 |10 ↑↑ 192.67
 |Terry Ligocki
 |-
-|{{TM|1RB1RZ_1LC0RF_0LD1LB_1RD0LE_1RB1LE_1RG0RE_0RA0LE}}
+|{{TM|1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RC0LD|halt}}
 |10 ↑↑ 192.67
-|Terry Ligocki
+|Andrew Ducharme
 |-
-|{{TM|1RB0LC_1LC1LD_1LA1LB_1LG1RE_1LD0RF_0RA1RE_1RZ0RA}}
+|{{TM|1RB1LA_1LC0RE_0LD1LB_1RE1LG_1RF0LG_0RA0LA_0RF1RZ|halt}}
-|10 ↑↑ 188.28
+|10 ↑↑ 192.67
-|@XnoobSpeakable, @Peacemaker II
+|Andrew Ducharme
 |-
-|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0LF_0RA1RE_1RZ1LA}}
+|{{TM|1RB1LA_1LC0RF_0LD0RD_1RF1LE_1LB1RZ_1RG0RA_0RA0LA|halt}}
-|10 ↑↑ 188.28
+|10 ↑↑ 192.67
-|Terry Ligocki
+|@C7X
 |-
-|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA}}
+|{{TM|1RB1LA_1LC0RE_0LD1LB_1RE0LA_1RF0RA_0RG0LA_1RB1RZ|halt}}
-|10 ↑↑ 188.28
+|10 ↑↑ 192.67
-|Terry Ligocki
+|@Iijil, Terry Ligocki
 |-
-|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LF0RF_0RA1RE_1RZ0RE}}
+|{{TM|1RB1LA_1LC0RE_0LD1LB_1RE0LA_1RF0RA_1RG0LA_0LE1RZ|halt}}
-|10 ↑↑ 188.28
+|10 ↑↑ 192.67
-|Terry Ligocki
+|@Iijil, Terry Ligocki
-|-
-|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LF0RF_0RA1RE_1RZ1LA}}
-|10 ↑↑ 188.28
-|Terry Ligocki
-|-
-|{{TM|1RB0LC_1LC1LD_1LA1LB_1LG1RE_0RF0LF_0RA1RE_1RZ0LE}}
-|10 ↑↑ 188.28
-|Terry Ligocki
-|-
-|{{TM|1RB0LC_1LC1LD_1LA1LB_1LG1RE_0RF0LF_0RA1RE_1RZ0RA}}
-|10 ↑↑ 188.28
-|Terry Ligocki
-|-
-|{{TM|1RB0LC_1LC1LD_1LA1LB_1LG1RE_1LF0RF_0RA1RE_1RZ0RA}}
-|10 ↑↑ 188.28
-|Terry Ligocki
 |}
 The top 20 known halters with unique scores are:
-{| class="wikitable"
+{| class="wikitable sortable"
 !TM
-!Approximate sigma score
+!Approximate runtime
 !Discoverer
 |-
-|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
+|{{TM|1RB0RG_1RC1RB_0RD1RZ_0LE0LD_0LF1LE_1RA1LF_1LC0RB|halt}}
-|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
+|data-sort-value="10 ↑↑ 9999"|<math>3 \uparrow^{20} 3</math>
+|Jeff Ketchersid
+|-
+|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF|halt}}
+|data-sort-value="10 ↑↑ 9998"|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
 |Pavel Kropitz
 |-
-|{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE}}
+|{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE|halt}}
 |10 ↑↑ 519.20
 |Andrew Ducharme
 |-
-|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}}
+|{{TM|1RB1LB_1LC1RF_1LA0LD_1RE0LG_0RC1RZ_0RB0RD_0RF1LG|halt}}
+|10 ↑↑ 403.84
+|Andrew Ducharme
+|-
+|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ|halt}}
 |10 ↑↑ 286.17
 |Terry Ligocki
 |-
-|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD}}
+|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD|halt}}
 |10 ↑↑ 246.32
 |@Iijil
 |-
-|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG}}
+|{{TM|1RB1RZ_1RC0LE_0RD1RB_1LE1RA_1LF0LG_0LG0RG_1LB1RG|halt}}
+|10 ↑↑ 243.88
+|@Iijil, Andrew Ducharme
+|-
+|{{TM|1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ|halt}}
+|10 ↑↑ 228.78
+|Terry Ligocki
+|-
+|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG|halt}}
 |10 ↑↑ 192.67
 |Terry Ligocki
 |-
-|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA}}
+|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA|halt}}
 |10 ↑↑ 188.28
 |Terry Ligocki
 |-
-|{{TM|1RB0LC_1LC0LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LC}}
+|{{TM|1RB0LC_1LC0LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LC|halt}}
 |10 ↑↑ 140.28
 |@stokastic
 |-
-|{{TM|1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG}}
+|{{TM|1RB0RF_1RC1RZ_0LD1RF_0RA1LE_0LC1LF_1LE0RG_0LE1RA|halt}}
+|10 ↑↑ 136.64
+|Katelyn Doucette, Andrew Ducharme
+|-
+|{{TM|1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG|halt}}
 |10 ↑↑ 133.85
 |@poppuncher
 |-
-|{{TM|1RB1RZ_1RC0RF_1LD1RB_1RG0LE_1LD0RA_1RE0LD_0RC1LF}}
+|{{TM|1RB1RZ_1RC0RF_1LD1RB_1RG0LE_1LD0RA_1RE0LD_0RC1LF|halt}}
 |10 ↑↑ 129.24
 |@Iijil
 |-
-|{{TM|1RB0LC_1RC0RG_1RD0LF_1RE0RF_1LA1RG_1LE1LF_1RZ1RD}}
+|{{TM|1RB0RG_1LC0RE_1LF1LD_0LE1LC_1RA1RB_1LD0LF_1RZ0RF|halt}}
+|10 ↑↑ 127.52
+|Andrew Ducharme
+|-
+|{{TM|1RB0LC_1RC0RG_1RD0LF_1RE0RF_1LA1RG_1LE1LF_1RZ1RD|halt}}
 |10 ↑↑ 126.20
 |@stokastic
 |-
-|{{TM|1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ}}
+|{{TM|1RB0LD_1RC1RA_0RD1RG_1LE1LF_0LF1LE_0RA0LD_0RA1RZ|halt}}
+|10 ↑↑ 124.86
+|Terry Ligocki
+|-
+|{{TM|1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ|halt}}
 |10 ↑↑ 116.98
 |Terry Ligocki
 |-
-|{{TM|1RB0RD_1RC0LA_0LA0LE_1RE1RZ_1RF0RA_1LG0LE_1LC0LG}}
+|{{TM|1RB0RD_1RC0LA_0LA0LE_1RE1RZ_1RF0RA_1LG0LE_1LC0LG|halt}}
 |10 ↑↑ 116.05
 |
 |-
-|{{TM|1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ}}
+|{{TM|1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ|halt}}
 |10 ↑↑ 115.52
 |@prurq
 |-
-|{{TM|1RB0RF_1RC0RB_0RD0RF_1LE0LG_1LC0RD_1LA0LD_1LF1RZ}}
+|{{TM|1RB0RG_1LC0LE_1LD0LB_0LE1RE_0RA1RF_0RD1RC_1RD1RZ|halt}}
-|10 ↑↑ 114.61
+|10 ↑↑ 114.83
-|Andrew Ducharme
-|-
-|{{TM|1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ}}
-|10 ↑↑ 114.60
-|Shawn Ligocki
-|-
-|{{TM|1RB0RE_0RC1LC_0LD1LF_1LE0LG_1RA0RC_0LB1LA_1LB1RZ}}
-|10 ↑↑ 114.57
-|Andrew Ducharme
-|-
-|{{TM|1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ}}
-|10 ↑↑ 113.38
-|Terry Ligocki
-|-
-|{{TM|1RB1RZ_1RC1RA_1RD0RB_1LE0RC_1LF0LD_1RG0LF_1RC0LG}}
-|10 ↑↑ 108.77
-|Terry Ligocki
-|-
-|{{TM|1RB0LA_1RC0RA_0RD0RB_1LE0RC_0LD1LF_0LA1LG_0LC1RZ}}
-|10 ↑↑ 105.37
-|Terry Ligocki
-|-
-|{{TM|1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG}}
-|10 ↑↑ 93.81
 |Andrew Ducharme
 |}
-== Current Progress ==
+== Phase 1 ==
-This is a summary of the 1 million subtasks from mxdys's code that have been processed, including further processing by Shawn Ligocki's linear rule code ("TBD" = "To Be Determined", "TBE" = "To Be Entered"):
+Phase 1's first two stages were carried out from May 2025 to July 2025. The table below summaries some of that activity and was used to coordinate the effort of doing the raw computation. Fourteen people (see below) contributed directly and the overall bbchallenge group participated in [https://discord.com/channels/960643023006490684/1369339127652159509 discord discussions], etc.
-{| class="wikitable defaultleft"
-!rowspan="2"|Task range
+Stage 1, "enumeration" in the table, involved running 1 million subtasks using mxdys's code in 100 batches of 10 thousand subtasks.
-!rowspan="2"|Done by
-!colspan="2"|Completed
+Stage 2, "linear rule" in the table, processing the output of Stage 1 using Shawn Ligocki's linear rule code which also used a few other deciders, e.g., a version of CTL.
-!rowspan="2"|# holdouts
-!rowspan="2"|Maximum Score TM
+Stage 3, the final stage of Phase 1, is the compilation, verification, and presentation of the final results from Phase 1. It was completed during August 2025.
-!rowspan="2"|~Sigma
-!rowspan="2"|Source
+(done to reduce column size:
+<math>*^1</math>= enumeration,
+<math>*^2</math>= linear rule)
+{| class="wikitable sortable"
+! rowspan="2" |Task range
+! rowspan="2" |Done by
+! colspan="2" |Completed
+! rowspan="2" |# holdouts
+! rowspan="2" |Maximum Score TM
+! rowspan="2" |~Sigma
+! rowspan="2" |Source
 |-
-!enumeration
+!<math>*^1</math>
-!linear rule
+!<math>*^2</math>
 |-
-|00xxxx
+|00-01xxxx
-|rowspan="10"|@Iijil
+|@Iijil
 |Yes
 |Yes
-|728,495
+|1,545,673
-|{{TM|1RB0RF_1RC1LF_0RD0RD_1LE0LB_1RA1RZ_1LG1RA_1LD0RC}}
+|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD|halt}}
-|10 ↑↑ 45.64
+|10 ↑↑ 246.32
-|rowspan="10"|[https://drive.google.com/drive/folders/1wniwrAuvsHfkvro8Tg65WAMNZEuIekzD Google Drive folder]
+|[https://drive.google.com/drive/folders/1wniwrAuvsHfkvro8Tg65WAMNZEuIekzD Google Drive folder]
 |-
-|01xxxx
+|02-04xxxx
+|
+@Iijil<br/>
+Terry Ligocki
 |Yes
 |Yes
-|817,178
+|2,279,734
-|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD}}
+|{{TM|1RB0LF_1RC1RA_1RD0RG_1LE1RZ_1LA0LF_1RA1LE_0RE1RG|halt}}
-|10 ↑↑ 246.32
+|10 ↑↑ 93.81
+|
+[https://drive.google.com/drive/folders/1wniwrAuvsHfkvro8Tg65WAMNZEuIekzD @Iijil]<br/>
+[https://drive.google.com/drive/folders/1kJ6tlmX8_7AQ8qpR1mSQ-Fz4-fPfwYBn?usp=drive_link Terry Ligocki]
 |-
-|02xxxx
+|05-09xxxx
+|
+@Iijil<br/>
+Andrew Ducharme
 |Yes
-|No
-|963,486
-|TBD
-|TBD
-|-
-|03xxxx
 |Yes
-|No
+|3,889,955
-|1,052,504
+|{{TM|1RB1RZ_1RC0LE_0RD1RB_1LE1RA_1LF0LG_0LG0RG_1LB1RG|halt}}
-|TBD
+|10 ↑↑ 243.88
-|TBD
+|
+[https://drive.google.com/drive/folders/1wniwrAuvsHfkvro8Tg65WAMNZEuIekzD @Iijil]<br/>
+[https://drive.google.com/drive/folders/16uDjgOahkhAMWv3v-YWmxJG7xxsBvj4h?usp=sharing Andrew]
 |-
-|04xxxx
+|10-12xxxx
+|Andrew Ducharme
 |Yes
-|No
-|955,711
-|TBD
-|TBD
-|-
-|05xxxx
 |Yes
-|No
+|2,708,888
-|1,056,745
+|{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD1LF_1LB0LE|halt}}
-|TBD
+|10 ↑↑ 519.20
-|TBD
+|[https://drive.google.com/drive/folders/16uDjgOahkhAMWv3v-YWmxJG7xxsBvj4h?usp=sharing Google Drive folder]
 |-
-|06xxxx
+|13xxxx
+|Shawn Ligocki
 |Yes
-|No
-|950,271
-|TBD
-|TBD
-|-
-|07xxxx
 |Yes
-|No
+|1,192,442
-|1,053,750
+|{{TM|1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ|halt}}
-|TBD
+|10 ↑↑ 114.60
-|TBD
+|[https://drive.google.com/drive/folders/1lyYN2wznnrfM0dg-dKprHODeYaTxdtzP?usp=drive_link Google Drive folder]
 |-
-|08xxxx
+|14-16xxxx
+|Andrew Ducharme
 |Yes
-|No
-|951,114
-|TBD
-|TBD
-|-
-|09xxxx
 |Yes
-|No
+|2,701,637
-|1,052,362
+|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0LD_0RA1RE_1RZ1LA|halt}}
-|TBD
+|10 ↑↑ 188.28
-|TBD
+|[https://drive.google.com/drive/folders/16uDjgOahkhAMWv3v-YWmxJG7xxsBvj4h?usp=sharing Google Drive folder]
 |-
-|13xxxx
+|17-18xxxx
-|Shawn Ligocki
+|
+@gerbil5709<br/>
+Terry Ligocki
 |Yes
 |Yes
-|1,192,442
+|1,898,156
-|{{TM|1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ}}
+|{{TM|1RB1LA_1LC0RE_0LD1LB_1RE0LA_1RF0RA_0RG0LA_1RB1RZ|halt}}
-|10 ↑↑ 114.60
+|10 ↑↑ 192.67
-|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
+|
+[https://drive.google.com/drive/folders/1kAvBebeF09CEVocCk5bGKlDJfRN8co_i?usp=sharing @gerbil5709]<br/>
+[https://drive.google.com/drive/folders/1kJ6tlmX8_7AQ8qpR1mSQ-Fz4-fPfwYBn?usp=drive_link Terry Ligocki]
 |-
+|19xxxx
 |
-xxxx -<br/>
+Katelyn Doucette<br/>
-xxxx
+Andrew Ducharme
-|@C7X
+|Yes
 |Yes
-|No
+|1,099,752
-|2,972,747
+|{{TM|1RB0RF_1RC1RZ_0LD1RF_0RA1LE_0LC1LF_1LE0RG_0LE1RA|halt}}
-|TBD
+|10 ↑↑ 136.64
-|TBD
+|[https://drive.google.com/drive/folders/1-eGxVc3kmGIEJFShG4olPX3sGci2SPaA?usp=sharing Google Drive folder]
-|[https://drive.google.com/drive/folders/11iGTKsvu2Y7aFrwOcWS1LYvcN6i_7-JM?usp=sharing Google Drive folder]
 |-
-|243308
+|20-23xxxx
-|@uni
+| @C7X
+|Yes
 |Yes
-|No
+|4,528,827
-|TBE
+|{{TM|1RB1LA_1LC0RF_0LD0RD_1RF1LE_1LB1RZ_1RG0RA_0RA0LA|halt}}
-|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
+|10 ↑↑ 192.67
-|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
+| [https://drive.google.com/drive/folders/11iGTKsvu2Y7aFrwOcWS1LYvcN6i_7-JM?usp=sharing Google Drive folder]
-|[https://discord.com/channels/960643023006490684/1369339127652159509/1373660959960469545 Discord post]
 |-
-|25xxxx
+|24xxxx
-|rowspan="10"|@stokastic
+|Andrew Ducharme
 |Yes
 |Yes
-|815,919
+|712,356
-|{{TM|1RB1RZ_1LC0LE_0LD0LC_0RE1LB_1RF0RG_0LD1RB_1RD1RA}}
+|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF|halt}}*
-|10 ↑↑ 31.33
+|data-sort-value="10 ↑↑ 9999"|<math>2 \uparrow^{11} 2 \uparrow^{11} 3^*</math>
-|rowspan="10"|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
+|[https://drive.google.com/drive/folders/16uDjgOahkhAMWv3v-YWmxJG7xxsBvj4h?usp=sharing Google Drive folder]
 |-
-|26xxxx
+|25-34xxxx
+|@stokastic
 |Yes
 |Yes
-|731,995
+|10,339,816
-|{{TM|1RB1RZ_0LC1RB_0LE0LD_1LE1LD_0RF0LC_0RG1RF_1RD0RA}}
+|{{TM|1RB0LC_1LC0LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LC|halt}}
-|10 ↑↑ 36.26
+|10 ↑↑ 140.28
+|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
 |-
-|27xxxx
+|35-39xxxx
+|Terry Ligocki
 |Yes
 |Yes
-|811,486
+|4,894,047
-|{{TM|1RB0RG_1LC1LB_0RE0LD_0LC1RF_0RA1RE_0LF0LB_1RF1RZ}}
+|{{TM|1RB1RZ_1LC0RF_0LD1LB_1RD0LE_1RB1LE_1RG0RE_0RA0LE|halt}}
-|10 ↑↑ 63.56
+|10 ↑↑ 192.67
+|[https://drive.google.com/drive/folders/1kJ6tlmX8_7AQ8qpR1mSQ-Fz4-fPfwYBn?usp=drive_link Google Drive folder]
 |-
-|28xxxx
+|40-47xxxx
+|Andrew Ducharme
 |Yes
 |Yes
-|956,935
+|6,181,327
-|{{TM|1RB1RZ_0LC1RC_0RE1RD_0RB1RG_1RF0RA_1LG0LC_1LB0LF}}
+|{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE|halt}}
-|10 ↑↑ 114.57
+|10 ↑↑ 519.20
+|[https://drive.google.com/drive/folders/16uDjgOahkhAMWv3v-YWmxJG7xxsBvj4h?usp=sharing Google Drive folder]
 |-
-|29xxxx
+|48xxxx
+|
+@star<br/>
+Terry Ligocki
 |Yes
 |Yes
-|1,052,415
+|727,875
-|{{TM|1RB1LA_1RC1RD_0LA1LG_1RZ0LE_1RB1RF_1RE0LC_0RE1LF}}
+|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA1LG_1RZ1LA|halt}}
-|10 ↑↑ 31.67
+|10 ↑↑ 246.32
+|
+[https://drive.google.com/file/d/1HbIX46_6V-etFWTv4FvWZmb7AHIiWB1v/view?usp=sharing @star]<br/>
+[https://drive.google.com/drive/folders/1lyYN2wznnrfM0dg-dKprHODeYaTxdtzP?usp=drive_link Terry Ligocki]
 |-
-|30xxxx
+|49xxxx
+|
+Tobiáš Brichta<br/>
+Terry Ligocki
 |Yes
 |Yes
-|1,032,095
+|804,722
-|{{TM|1RB0LC_1RC0RG_1RD0LF_1RE0RF_1LA1RG_1LE1LF_1RZ1RD}}
+|{{TM|1RB0LG_1RC0RG_0LD1RE_1RD0RE_1LF1RB_0LA1RZ_1LC1LG|halt}}
 |10 ↑↑ 126.20
+|
+[https://drive.google.com/drive/folders/1-csgJ5uSIX3SKlqTkSnhkUuEYLKgCw81 Tobiáš Brichta]<br/>
+[https://drive.google.com/drive/folders/1kJ6tlmX8_7AQ8qpR1mSQ-Fz4-fPfwYBn?usp=drive_link Terry Ligocki]
 |-
-|31xxxx
+|50xxxx
+|
+@prurq<br/>
+Andrew Ducharme
 |Yes
 |Yes
-|1,436,970
+|797,224
-|{{TM|1RB1LD_1LC0RF_0RA0LB_0LE1RZ_1LA0LE_1RG1LA_0RC0RF}}
+|{{TM|1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ|halt}}
-|10 ↑↑ 50.27
+|10 ↑↑ 115.52
+|[https://drive.google.com/drive/folders/145H4sT4F9KJYGSrlIETZdBOIMR7krLQm Google Drive folder]
 |-
-|32xxxx
+|51-53xxxx
+|
+@gerbil5709<br/>
+Terry Ligocki
 |Yes
 |Yes
-|1,036,950
+|3,016,175
-|{{TM|1RB1RD_1LC0RF_0LE0LD_1LE1LE_1RF0LB_1RB0RG_1RA1RZ}}
+|{{TM|1RB0LC_1LC0LD_1LA1LB_0LG1RE_0RF0RF_0RA1RE_1RZ1LC|halt}}
-|10 ↑↑ 50.28
+|10 ↑↑ 140.28
+|
+[https://drive.google.com/drive/folders/1kAvBebeF09CEVocCk5bGKlDJfRN8co_i?usp=sharing @gerbil5709]<br/>
+[https://drive.google.com/drive/folders/1kJ6tlmX8_7AQ8qpR1mSQ-Fz4-fPfwYBn?usp=drive_link Terry Ligocki]
 |-
-|33xxxx
+|54-59xxxx
+|Terry Ligocki
 |Yes
-|No
+|Yes
-|1,432,081
+|5,689,850
-|{{TM|1RB0LC_1LC0LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LC}}
+|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0RF_0RA1RE_1RZ1LA|halt}}
-|10 ↑↑ 140.28
+|10 ↑↑ 188.28
+|[https://drive.google.com/drive/folders/1lyYN2wznnrfM0dg-dKprHODeYaTxdtzP?usp=drive_link Google Drive folder]
 |-
-|34xxxx
+|60-64xxxx
+|
+@gerbil5709<br/>
+Terry Ligocki
+|Yes
 |Yes
-|No
+|3,817,876
-|1,032,970
+||{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD0LG_1LB0LE|halt}}
-|TBD
+|10 ↑↑ 519.20
-|TBD
+|
+[https://drive.google.com/drive/folders/1kAvBebeF09CEVocCk5bGKlDJfRN8co_i?usp=sharing @gerbil5709]<br/>
+[https://drive.google.com/drive/folders/1kJ6tlmX8_7AQ8qpR1mSQ-Fz4-fPfwYBn?usp=drive_link Terry Ligocki]
 |-
-|
+|65-68xxxx
-xxxx -<br/>
-xxxx
 |Terry Ligocki
 |Yes
 |Yes
-|4,894,047
+|3,076,778
-|{{TM|1RB1RZ_1LC0RF_0LD1LB_1RD0LE_1RB1LE_1RG0RE_0RA0LE}}
+|{{TM|1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RG0LD|halt}}
 |10 ↑↑ 192.67
-|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
+|[https://drive.google.com/drive/folders/1lyYN2wznnrfM0dg-dKprHODeYaTxdtzP?usp=drive_link Google Drive folder]
 |-
-|40xxxx
+|69xxxx
-| rowspan="8" |Andrew Ducharme
+|@poppuncher
 |Yes
 |Yes
-|730,310
+|1,053,119
-|{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE}}
+|{{TM|1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG|halt}}
-|10 ↑↑ 519.20
+|10 ↑↑ 133.85
-| rowspan="8" |[https://drive.google.com/drive/folders/16uDjgOahkhAMWv3v-YWmxJG7xxsBvj4h?usp=sharing Google Drive folder]
+|[https://drive.google.com/drive/folders/1KlCZqXxqVPuBPkDcCBocuMPA8paq9b8P?usp=drive_link Google Drive folder]
 |-
-|41xxxx
+|70-71xxxx
+|@hipparcos
 |Yes
 |Yes
-|814,075
+|1,899,094
-|{{TM|1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RC0LD}}
+|{{TM|1RB1RZ_1LC1RD_0LD0LC_1LE1RA_1LF0LE_1RF0RG_1RG0RD|halt}}
-|10 ↑↑ 192.67
+|10 ↑↑ 77.50
+|[https://github.com/jhuang97/bb7x2/releases Github release]
 |-
-|42xxxx
+|72-79xxxx
+|Terry Ligocki
 |Yes
 |Yes
-|739,729
+|7,627,514
-|{{TM|1RB1LD_0RC1RF_1LD0LE_0LE0LA_1LA1LE_1RG0LA_1RZ1RA}}
+|{{TM|1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ|halt}}
-|10 ↑↑ 46.26
+|10 ↑↑ 228.78
+|[https://drive.google.com/drive/folders/1kJ6tlmX8_7AQ8qpR1mSQ-Fz4-fPfwYBn?usp=drive_link Google Drive folder]
 |-
-|43xxxx
+|80-81xxxx
+|[[User:XnoobSpeakable|XnoobSpeakable]]
 |Yes
 |Yes
-|817,332
+|1,537,533
-|{{TM|1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG}}
+|{{TM|1RB0LA_0RC1RZ_0RD0RG_1LE1RA_1LF1LD_1RG0RG_1RD1RC|halt}}
-|10 ↑↑ 93.81
+|10 ↑↑ 74.85
+|[https://drive.google.com/drive/folders/1TpuEC7KottEmvsFnCREugnlVMPaY5ZHi?usp=sharing Google Drive folder]
 |-
-|44xxxx
+|82-99xxxx
+|Terry Ligocki
 |Yes
 |Yes
-|729,686
+|15,673,786
-|{{TM|1RB1LC_1RC0RC_1RD1LA_0RE1RF_1LC0LG_1LA1LE_1RZ1LF}}
+|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ|halt}}
-|10 ↑↑ 76.36
+|10 ↑↑ 286.17
+|[https://drive.google.com/drive/folders/1kJ6tlmX8_7AQ8qpR1mSQ-Fz4-fPfwYBn?usp=drive_link Google Drive folder]
+|}
+<nowiki>*</nowiki>A former BB(7) champion TM {{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF|halt}}* was discovered by Pavel Kropitz in the enumeration of subtask 243308. The remaining subtasks in the 24xxxx range were enumerated and filtered by Andrew Ducharme.
+== Exploration after Phase 1 ==
+People are now looking at reducing the number of holdouts (~85M TMs) after Phase 1. They are trying different deciders not used in Phase 1 and different parameters with the deciders used in Phase 1. This table is somewhere they can put the results of these explorations so that there is a record of what is being done. It is hoped that this will inspire everyone to contribute when they can, a reference point for [https://discord.com/channels/960643023006490684/1369339127652159509 discord discussions], and something that can be questioned and/or verified.
+(done to reduce column size:
+<math>*^1</math>= % Reduced,
+<math>*^2</math>= Runtime (hours),
+<math>*^3</math>= Decided,
+<math>*^4</math>= Processed)
+{| class="wikitable sortable" style="text-align: right"
+! style="width: 10%" rowspan="2" |Done by
+! colspan="2" |Holdout TMs
+! rowspan="2" |<math>*^1</math>
+! rowspan="2" |<math>*^2</math>
+! colspan="2" |TMs/sec/core
+! style="width: 50%" rowspan="2" |Description
+! rowspan="2" |Source
+|-
+!Input
+!Output
+!<math>*^3</math>
+!<math>*^4</math>
+|-
+|style="text-align:center" |Shawn Ligocki
+|858,538
+|733,830
+|14.5%
+|5.0
+|6.9282
+|47.6966
+|style="text-align:left" |[[Translated Cycler]] and [[CPS]] on <code>7x2_p01_s02_holdouts_rand_13.txt</code>
+|style="text-align:left" |[https://discord.com/channels/960643023006490684/1369339127652159509/1403423336293208164 Discord link]
+|-
+|style="text-align:center" |Andrew Ducharme
+|872,041
+|784,099
+|10.1%
+|456.4
+|0.0535
+|0.5034
+|style="text-align:left" |Enumerate.py w/ 250k max-loops and block-mult=3 on <code>7x2_p01_s02_holdouts_rand_72.txt</code>
+|style="text-align:left" |[https://discord.com/channels/960643023006490684/1369339127652159509/1403236957298884679 Discord link]
+|-
+|style="text-align:center" |Terry Ligocki
+|1,000
+|982
+|1.8%
+|3.3
+|0.0015
+|0.0830
+|style="text-align:left" |[[MITMWFAR]] [https://github.com/Iijil1/MITMWFAR Code] with options <code>-n=10 -m=1 -pm=1</code> on the first 1,000 TMs in <code>7x2_p01_s03_holdouts_rand_47.txt</code>
+|style="text-align:left" |
+|-
+|style="text-align:center" |Andrew Ducharme
+|800,507
+|693,348
+|13.3%
+|2818.7
+|0.0106
+|0.0789
+|style="text-align:left" |Enumerate.py w/ 1M max-loops and block-mult=4 on holdouts from above Enumerate run on<code>7x2_p01_s02_holdouts_rand_72.txt</code>
+|style="text-align:left" |
+|-
+|style="text-align:center" |Andrew Ducharme
+|70,000
+|65,615
+|6.3%
+|6.6
+|0.1842
+|2.9412
+|style="text-align:left" |Enumerate.py with --no-sim and --lin-steps=100000 on <code>7x2_p01_s02_holdouts_rand_65.txt</code>
+|style="text-align:left" |
+|-
+|style="text-align:center" |Terry Ligocki
+|10,000
+|N/A
+|2% - 32%
+|N/A
+|N/A
+|N/A
+|style="text-align:left" |See the "Source" discussion on the discord channel which includes graphs with quantitative data. A parameter study of a random sample of 10,000 TMs from the Phase 1, Stage 3 holdouts
+|style="text-align:left" |[https://discord.com/channels/960643023006490684/1369339127652159509/1407090465097908245 Discord link]
+|}
+== Phase 2 ==
+Phase 2 began with Andrew Ducharme's initial decider runs (see Stage 1 in the table). The goal of Phase 2 is to run deciders on the current holdout list (the last in the table) and produce an accessible new holdout list which can then be added to the table. Input Holdout TMs may be unequal to the next row's Output Holdout TMs because more TMs are TNF-enumerated in the process of executing the next row's filtering. Accessing the holdout list can be done through the link "Holdouts" in the "Data" column. The link "Details" leads to additional data/information pertaining to each step. If there isn't a link there it means the data is still being put somewhere everyone can access it.
+Stage 1 reduced the number of holdouts by 33.3% from ~86.1M to ~57.5M TMs using the Ligocki's C++/Python codes. In Stage 2, Andrew continued using mxdys' C++ code and reduced the number of holdouts by 51.0% from ~57.5M to ~28.2M TMs. Terry Ligocki then pushed this further using additional deciders/parameters to generate Stage 3 which reduced the number of holdouts by 17.3% from ~28.2M to ~23.3M TMs. Andrew then ran the Ligocki's C++/Python code with larger parameters which reduced the number of holdouts by 2.6% from ~23.3M to ~22.7M TMs. This formed Stage 4. Terry then switched back to the mxdys' C++ code with different deciders/parameters for Stage 5 where the number of holdouts was reduced by 10.2% from ~22.7M to ~20.4M TMs. Stage 6 was Andrew Ducharme running a mix of mxdys and Ligocki deciders, reducing holdouts by 12.7% from ~20.4M to ~17.8M TMs.
+This brought the overall reduction in Phase 2 to 79.3% from ~86.1M to ~17.8M TMs. The details are contained in this table:
+(done to reduce column size:
+<math>*^1</math>= % Reduced,
+<math>*^2</math>= Compute Time (core-hours),
+<math>*^3</math>= Decided,
+<math>*^4</math>= Processed)
+{| class="wikitable sortable" style="text-align: right"
+!rowspan="2" |Done by
+!colspan="2" |Holdout TMs
+!rowspan="2" |<math>*^1</math>
+!rowspan="2" |<math>*^2</math>
+!colspan="2" |TMs/sec/core
+!rowspan="2" |Description
+!rowspan="2" |Source
+!rowspan="2" |Data
+|-
+!Input
+!Output
+!<math>*^3</math>
+!<math>*^4</math>
+|-
+|colspan="20" style="text-align:center"|'''Stage 1'''
+|-
+|style="text-align:center" |Andrew Ducharme
+|86,129,304
+|82,226,951
+|4.5%
+|119.6
+|9.06
+|200.04
+|style="text-align:left" |CPS_Filter with --max-block-size=4
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1407167730121052231 discord]
+|rowspan="11" style="text-align:left" |Stage 1<br>
+[https://drive.google.com/file/d/1LXUKxqRhwW_Q1QGxWuRheV3sZu18hgOK/view?usp=drive_link Holdouts]<br>
+[https://drive.google.com/drive/u/0/folders/17U0BRpJHTMLtB0poBlOSZhGGp4FkCHIO Details]
+|-
+|style="text-align:center" |Andrew Ducharme
+|82,226,951
+|73,751,624
+|10.3%
+|120.0
+|19.62
+|190.34
+|style="text-align:left" |lr_enum_continue 1M steps
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1407809787734786159 discord]
+|-
+|style="text-align:center" |Andrew Ducharme
+|73,751,624
+|72,470,054
+|1.7%
+|1040.0
+|0.34
+|19.70
+|style="text-align:left" |lr_enum_continue 3M steps
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1408119196931330190 discord]
+|-
+|style="text-align:center" |Andrew Ducharme
+|72,470,054
+|69,347,610
+|4.3%
+|1113.4
+|0.78
+|18.08
+|style="text-align:left" |CPS_Filter with --min-block-size=5, --max-block-size=6
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1408517862485917826 discord]
+|-
+|style="text-align:center" |Andrew Ducharme
+|69,347,610
+|68,695,205
+|0.9%
+|1491.8
+|0.12
+|12.92
+|style="text-align:left" |CPS_Filter with --block-size=7
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1409227033715933244 discord]
+|-
+|style="text-align:center" |Andrew Ducharme
+|68,695,205
+|61,875,401
+|10.6%
+|1726.7
+|1.17
+|11.11
+|style="text-align:left" |Enumerate.py with --block-multiple=12, max-loops=100_000, and --time=0.1
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1409590262644215828 discord]
+|-
+|style="text-align:center" |Andrew Ducharme
+|61,875,401
+|60,986,231
+|1.5%
+|1660.7
+|0.15
+|10.35
+|style="text-align:left" |Enumerate.py with --block-multiple=8, max-loops=100_000, and --time=0.1
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1409939131701792788 discord]
+|-
+|style="text-align:center" |Andrew Ducharme
+|60,986,231
+|60,765,943
+|0.4%
+|1619.4
+|0.04
+|10.46
+|style="text-align:left" |Enumerate.py with --block-multiple=16, max-loops=100_000, and --time=0.1
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1413962201676517396 discord]
+|-
+|style="text-align:center" |Andrew Ducharme
+|60,765,943
+|59,727,905
+|1.7%
+|2329.4
+|0.12
+|7.25
+|style="text-align:left" |CPS_Filter with --block-size=8
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1411505653599572008 discord]
+|-
+|style="text-align:center" |Andrew Ducharme
+|59,727,905
+|57,452,672
+|3.9%
+|2472.2
+|0.26
+|6.71
+|style="text-align:left" |Enumerate.py with --block-multiple=5, max-loops=200_000, and time=0.2
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1412882390774321172 discord]
+|-
+|style="text-align:center" |'''Stage 1 Cumulative'''
+|'''86,129,304'''
+|'''57,452,672'''
+|'''33.3%'''
+| '''13693.2'''
+| ---
+| ---
+|style="text-align:left"   | ---
+|style="text-align:center" | ---
+|-
+|colspan="20" style="text-align:center"|'''Stage 2'''
+|-
+|style="text-align:center" |Andrew Ducharme
+|57,452,672
+|52,605,872
+|8.4%
+|150.0
+|8.98
+|106.39
+|style="text-align:left" |chr_LRUH 20 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1413022512568074341 discord]
+|rowspan=21" style="text-align:left" |Stage 2<br>
+[https://drive.google.com/file/d/18G2ofUaMZIKFwNCNVHxTRjasV6p39Wr2/view?usp=drive_link Holdouts]<br>
+[https://drive.google.com/drive/folders/1tdJVC0OvUF8-Ql__xPKoSHKm5Lf5VoUd?usp=drive_link Details]
+|-
+|style="text-align:center" |Andrew Ducharme
+|52,605,872
+|50,268,427
+|4.4%
+|100.0
+|6.49
+|146.13
+|style="text-align:left" |chr_LRUH 8 chr_H 4 MitM_CTL NG maxT 10000 NG_n 3
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1413589351933153352 discord]
+|-
+|style="text-align:center" |Andrew Ducharme
+|50,268,427
+|45,980,438
+|8.5%
+|250.0
+|
+|
+|style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 2 n 8
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1413652363599810660 discord]
+|-
+|style="text-align:center" |Andrew Ducharme
+|45,980,438
+|43,870,806
+|4.5%
+|220.0
+|
+|
+|style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 10000 H 8 mod 3 n 6
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1413942432533446706 discord]
+|-
+|style="text-align:center" |Andrew Ducharme
+|43,870,806
+|42,700,370
+|2.6%
+|80.0
+|
+|
+|style="text-align:left" |chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 30000 NG_n 2
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1413942432533446706 discord]
+|-
+|style="text-align:center" |Andrew Ducharme
+|42,700,370
+|41,926,200
+|1.8%
+|20.0
+|
+|
+|style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 10000 H 3 mod 3 n 1
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1413942432533446706 discord]
+|-
+|style="text-align:center" |Andrew Ducharme
+|41,926,200
+|41,590,605
+|0.8%
+|50.0
+|
+|
+|style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 3000 H 6 mod 2 n 6
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1413942432533446706 discord]
+|-
+|style="text-align:center" |Andrew Ducharme
+|41,590,605
+|40,481,477
+|2.6%
+|75.0
+|
+|
+|style="text-align:left" |chr_LRUH 14 chr_H 12 MitM_CTL NG maxT 10000 NG_n 2
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1413942432533446706 discord]
+|-
+|style="text-align:center" |Andrew Ducharme
+|40,481,477
+|38,641,627
+|4.5%
+|200.0
+|
+|
+|style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 10000 H 3 mod 1 n 12
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1413942432533446706 discord]
+|-
+|style="text-align:center" |Andrew Ducharme
+|38,641,627
+|37,514,197
+|2.9%
+|80.0
+|
+|
+|style="text-align:left" |chr_LRUH 18 chr_H 8 MitM_CTL NG maxT 10000 NG_n 5
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1413966380377833552 discord]
+|-
+|style="text-align:center" |Andrew Ducharme
+|37,514,197
+|36,273,782
+|3.3%
+|90.0
+|
+|
+|style="text-align:left" |MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 8 H 1 tH 1 n 4
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1414167850180018317 discord]
+|-
+|style="text-align:center" |Andrew Ducharme
+|36,273,782
+|35,984,179
+|0.8%
+|20.0
+|
+|
+|style="text-align:left" |MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 4 H 2 tH 0 n 2
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1414167850180018317 discord]
+|-
+|style="text-align:center" |Andrew Ducharme
+|35,984,179
+|31,811,445
+|11.6%
+|800.0
+|
+|
+|style="text-align:left" |chr_LRUH 24 chr_H 24 MitM_CTL NG maxT 100000 NG_n 8
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1414167850180018317 discord]
+|-
+|style="text-align:center" |Andrew Ducharme
+|31,811,445
+|30,638,201
+|3.6%
+|1150.0
+|
+|
+|style="text-align:left" |chr_LRUH 28 chr_H 28 MitM_CTL NG maxT 100000 NG_n 10
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1414385826099495004 discord]
+|-
+|style="text-align:center" |Andrew Ducharme
+|30,638,201
+|29,781,771
+|2.8%
+|630.0
+|
+|
+|style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 30000 H 12 mod 2 n 12
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1414654007149989978 discord]
+|-
+|style="text-align:center" |Andrew Ducharme
+|29,781,771
+|29,670,310
+|0.37%
+|30.0
+|
+|
+|style="text-align:left" |chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n [1-7]
+| rowspan="4" |[https://discord.com/channels/960643023006490684/1369339127652159509/1416506454965227773 discord]
+|-
+|style="text-align:center" |Andrew Ducharme
+|29,670,310
+|29,629,503
+|0.14%
+|75.0
+|
+|
+|style="text-align:left" |chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n [8-10]
+|-
+|style="text-align:center" |Andrew Ducharme
+|29,629,503
+|29,380,949
+|0.84%
+|90.0
+|
+|
+|style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 2 n 6
+|-
+|style="text-align:center" |Andrew Ducharme
+|29,380,949
+|28,543,434
+|2.85%
+|600.0
+|
+|
+|style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 10000 H 3 mod 1 n [2-10,2]
+|-
+|style="text-align:center" |Andrew Ducharme
+|28,543,434
+|28,189,617
+|1.24%
+|550.0
+|
+|
+|style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 10000 H 3 mod 1 n [1-11,2]
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1417199742361927690 discord]
+|-
+| style="text-align:center" |'''Stage 2 Cumulative'''
+|'''57,452,672'''
+|'''28,189,617'''
+|'''51.00%'''
+| '''5260.0'''
+| ---
+| ---
+| style="text-align:left" | ---
+| style="text-align:center" | ---
+|-
+|colspan="20" style="text-align:center"|'''Stage 3'''
+|-
+|style="text-align:center" |Terry Ligocki
+|28,189,617
+|28,109,540
+|0.28%
+|5.3
+|4.2
+|1,479.75
+|style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 3 n 1 run
+|
+|rowspan="25" style="text-align:left" |Stage 3<br>
+[https://drive.google.com/file/d/1VEC5hum9Z9nkDhOhAw1bWsS8yLalrGWC/view?usp=drive_link Holdouts]<br>
+[https://drive.google.com/drive/folders/1DPO_aJ25bqHYB6zzjPYkvnhEtVGsY9iZ?usp=drive_link Details]
+|-
+|style="text-align:center" |Terry Ligocki
+|28,109,540
+|27,804,922
+|1.08%
+|8.3
+|10.18
+|938.98
+|style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 6 n 1 run
+|
+|-
+|style="text-align:center" |Terry Ligocki
+|27,804,922
+|27,747,435
+|0.21%
+|14.9
+|1.07
+|518.17
+|style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 3 n 1 run
+|
+|-
+|style="text-align:center" |Terry Ligocki
+|27,747,435
+|27,616,006
+|0.47%
+|65.7
+|0.56
+|117.33
+|style="text-align:left" |chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
+|
+|-
+|style="text-align:center" |Terry Ligocki
+|27,616,006
+|27,552,018
+|0.23%
+|56.9
+|0.31
+|134.81
+|style="text-align:left" |MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 4 H 1 tH 0 n 3 run
+|
+|-
+|style="text-align:center" |Terry Ligocki
+|27,552,018
+|27,222,303
+|1.2%
+|92.3
+|0.99
+|82.96
+|style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 6 n 2 run
+|
+|-
+|style="text-align:center" |Terry Ligocki
+|27,222,303
+|26,626,978
+|2.19%
+|140.5
+|1.18
+|53.8
+|style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 30000 H 6 mod 2 n 2 run
+|
+|-
+|style="text-align:center" |Terry Ligocki
+|26,626,978
+|26,518,327
+|0.41%
+|126.9
+|0.24
+|58.31
+|style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 3 run
+|
+|-
+|style="text-align:center" |Terry Ligocki
+|26,518,327
+|26,334,644
+|0.69%
+|99.4
+|0.51
+|74.14
+|style="text-align:left" |MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 0 tH 2 n 4 run
+|
+|-
+|style="text-align:center" |Terry Ligocki
+|26,334,644
+|26,076,261
+|0.98%
+|336.9
+|0.21
+|21.72
+|style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 100000 H 6 mod 6 n 1 run
+|
+|-
+|style="text-align:center" |Terry Ligocki
+|26,076,261
+|25,828,854
+|0.95%
+|146.8
+|0.47
+|49.35
+|style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 30000 H 6 mod 4 n 2 run
+|
+|-
+|style="text-align:center" |Terry Ligocki
+|25,828,854
+|25,659,775
+|0.65%
+|203.4
+|0.23
+|35.28
+|style="text-align:left" |chr_LRUH 8 chr_H 0 MitM_CTL NG maxT 30000 NG_n 6 run
+|
+|-
+|style="text-align:center" |Terry Ligocki
+|25,659,775
+|25,532,914
+|0.49%
+|194.4
+|0.18
+|36.66
+|style="text-align:left" |MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 6 H 2 tH 2 n 5 run
+|
+|-
+|style="text-align:center" |Terry Ligocki
+|25,532,914
+|25,318,355
+|0.84%
+|252.8
+|0.24
+|28.06
+|style="text-align:left" |chr_LRUH 8 chr_H 6 MitM_CTL NG maxT 100000 NG_n 3 run
+|
+|-
+|style="text-align:center" |Terry Ligocki
+|25,318,355
+|24,914,333
+|1.6%
+|446.1
+|0.25
+|15.77
+|style="text-align:left" |chr_LRUH 14 chr_H 12 MitM_CTL NG maxT 100000 NG_n 2 run
+|
+|-
+|style="text-align:center" |Terry Ligocki
+|24,914,333
+|24,648,140
+|1.07%
+|258.6
+|0.29
+|26.76
+|style="text-align:left" |MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 2 tH 2 n 6 run
+|
+|-
+|style="text-align:center" |Terry Ligocki
+|24,648,140
+|24,596,755
+|0.21%
+|322.7
+|0.04
+|21.21
+|style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 30000 H 16 mod 3 n 5 run
+|
+|-
+|style="text-align:center" |Terry Ligocki
+|24,596,755
+|24,505,987
+|0.37%
+|292.0
+|0.09
+|23.4
+|style="text-align:left" |MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 6 H 1 tH 1 n 10 run
+|
+|-
+|style="text-align:center" |Terry Ligocki
+|24,505,987
+|24,343,456
+|0.66%
+|1,067.8
+|0.04
+|6.37
+|style="text-align:left" |chr_LRUH 20 chr_H 12 MitM_CTL NG maxT 100000 NG_n 6 run
+|
+|-
+|style="text-align:center" |Terry Ligocki
+|24,343,456
+|24,116,020
+|0.93%
+|574.2
+|0.11
+|11.78
+|style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 100000 H 4 mod 2 n 4 run
+|
+|-
+|style="text-align:center" |Terry Ligocki
+|24,116,020
+|24,008,284
+|0.45%
+|1,754.3
+|0.02
+|3.82
+|style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 100000 H 12 mod 1 n 4 run
+|
+|-
+|style="text-align:center" |Terry Ligocki
+|24,008,284
+|23,502,214
+|2.11%
+|1,941.6
+|0.07
+|3.43
+|style="text-align:left" |chr_LRUH 28 chr_LRUn 2 MitM_CTL NG maxT 100000 NG_n 8 run
+|
+|-
+|style="text-align:center" |Terry Ligocki
+|23,502,214
+|23,332,229
+|0.72%
+|3,413.9
+|0.01
+|1.91
+|style="text-align:left" |chr_LRUH 18 chr_H 8 MitM_CTL NG maxT 100000 NG_n 12 run
+|
+|-
+|style="text-align:center" |Terry Ligocki
+|23,332,229
+|23,314,388
+|0.08%
+|1,182.1
+|0.0
+|5.48
+|style="text-align:left" |chr_LRUH 9 chr_H 1 MitM_CTL NG maxT 100000 NG_n 13 run
+|
+|-
+| style="text-align:center" |'''Stage 3 Cumulative'''
+|'''28,189,617'''
+|'''23,314,388'''
+|'''17.3%'''
+| '''12997.8'''
+| ---
+| ---
+| style="text-align:left" | ---
+| style="text-align:center" | ---
 |-
-|45xxxx
+|colspan="20" style="text-align:center"|'''Stage 4'''
-|Yes
+|-
-|Yes
+|style="text-align:center" |Andrew Ducharme
-|812,973
+|23,314,388
-|{{TM|1RB0RE_0RC1LC_0LD1LF_1LE0LG_1RA0RC_0LB1LA_1LB1RZ}}
+|23,281,839
-|10 ↑↑ 114.57
+|0.14%
+|2,227.8
+|
+|343.7
+|style="text-align:left" |Enumerate.py with --block-multiple=1, max-loops=250_000, and --time=0.5.
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1421974799604912188 discord]
+| rowspan="5" style="text-align:left"|Stage 4<br>
+[https://drive.google.com/file/d/1N-vMMupgrsmIXe38sFczZRcF0t8XvgLT/view?usp=drive_link Holdouts]<br>
+[https://drive.google.com/drive/folders/1FP7b5GHL9D-WQJ7E4XX3BnMBNuJUBmt1?usp=sharing Details]
+|-
+|style="text-align:center" |Andrew Ducharme
+|23,281,839
+|22,801,601
+|2.06%
+|~1,400
+|
+|
+|style="text-align:left" |lr_enum_continue 10M steps
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1422298181693079743 discord]
+|-
+|style="text-align:center" |Andrew Ducharme
+|22,801,601
+|22,721,690
+|0.35%
+|3,334.6
+|
+|
+|style="text-align:left" |Enumerate.py with --block-mult=3, --max-loops=250k, and --time=0.2.
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1423019804985655418 discord]
+|-
+|style="text-align:center" |Andrew Ducharme
+|22,721,690
+|22,721,168
+|0.002%
+|3393.5
+|
+|
+|style="text-align:left" |Enumerate.py with --block-mult=2, --max-loops=250k, and --time=0.2.
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1423806362072256676 discord]
+|-
+| style="text-align:center" |'''Stage 4 Cumulative'''
+|'''23,314,388'''
+|'''22,721,168'''
+|'''2.55%'''
+|'''10,355.9'''
+| ---
+| ---
+| ---
+| ---
+|-
+|colspan="20" style="text-align:center"|'''Stage 5'''
 |-
-|46xxxx
+|style="text-align:center" |Terry Ligocki
-|No
+|22,721,168
-|No
+|20,405,295
-|TBD
+|10.19%
-|TBD
+|4,903.2
-|TBD
+|0.13
+|1.29
+|style="text-align:left" |
+MitM_CTL RWL_mod sim 1001 maxT 100000 H 8 mod 3 n 12 run <br/>
+MitM_CTL RWL_mod sim 1001 maxT 100000 H 6 mod 2 n 12 run <br/>
+chr_LRUH 18 chr_H 16 MitM_CTL NG maxT 100000 NG_n 3 run <br/>
+MitM_CTL CPS_LRU sim 1001 maxT 1000000 LRUH 20 H 2 tH 4 n 2 run <br/>
+chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 1000000 NG_n 1 run <br/>
+MitM_CTL RWL_mod sim 1001 maxT 30000 H 6 mod 4 n 4 run <br/>
+MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 9 n 1 run <br/>
+MitM_CTL RWL_mod sim 1001 maxT 30000 H 12 mod 3 n 3 run <br/>
+MitM_CTL RWL_mod sim 1001 maxT 300000 H 3 mod 2 n 2 run <br/>
+MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 1 tH 1 n 4 run <br/>
+chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 100000 NG_n 2 run <br/>
+MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 1 run <br/>
+MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 2 run <br/>
+MitM_CTL RWL_mod sim 1001 maxT 30000 H 4 mod 2 n 2 run <br/>
+MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 4 H 1 tH 1 n 3 run <br/>
+|
+|rowspan="1" style="text-align:left"|Stage 5<br>
+[https://drive.google.com/file/d/1jTyRvblSJnRDTwsfSCqD7kK0T4zxgU2A/view?usp=drive_link Holdouts]<br>
+[https://drive.google.com/drive/folders/1APe-Vl8vcZOk4VMqRXHbPPxLanvKTmhA?usp=drive_link Details]
 |-
-|47xxxx
+| style="text-align:center" |'''Stage 5 Cumulative'''
-|No
+|'''22,721,168'''
-|No
+|'''20,405,295'''
-|TBD
+|'''10.19%'''
-|TBD
+|'''4903.2'''
-|TBD
+| ---
+| ---
+| ---
+| ---
+|
 |-
-|49xxxx
+| colspan="20" style="text-align:center"|'''Stage 6'''
-|Tobiáš Brichta
-|No
-|No
-|TBD
-|TBD
-|TBD
-|[https://drive.google.com/drive/folders/1-csgJ5uSIX3SKlqTkSnhkUuEYLKgCw81 Google Drive folder]
 |-
-|500xxx
+|style="text-align:center"| Andrew Ducharme
-|rowspan="2"|@prurq
+|20,405,295
-|Yes
+|20,387,509
-|Yes
+|0.09%
-|120,520
+|1797.2
-|{{TM|1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ}}
+|
-|10 ↑↑ 115.52
+|
-|rowspan="2"|[https://drive.google.com/drive/folders/145H4sT4F9KJYGSrlIETZdBOIMR7krLQm Google Drive folder]
+|style="text-align:left" |Enumerate.py with --block-mult=5, --max-loops=250k, --tape-limit=5000, and --time=0.3.
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1452727708479127633 discord]
+| rowspan="10" |[https://drive.google.com/drive/folders/16uQS2oF136VO7-2znEjaACOWQiHHQFeX?usp=share_link Details]
 |-
-|501xxx
+|style="text-align:center"| Andrew Ducharme
-|Yes
+|20,387,509
-|No
+|20,197,978
-|96,102
+|0.93%
-|TBD
+|6394.7
-|TBD
+|
+|
+|style="text-align:left" |Enumerate.py with --block-mult=20, --max-loops=1M, --tape-limit=5000, --max-steps-per-macro=100k, and --time=1.
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1459719965396566078 discord]
 |-
-|60xxxx
+|style="text-align:center"| Andrew Ducharme
-| rowspan="5" |@gerbil5709
+|20,197,978
-|Yes
+|19,879,953
-|No
+|1.57%
-|957,769
+|5748.1
-|TBD
+|
-|TBD
+|
-| rowspan="5" |[https://drive.google.com/drive/folders/1kAvBebeF09CEVocCk5bGKlDJfRN8co_i?usp=sharing Google Drive folder]
+|style="text-align:left" |Enumerate.py with --block-mult=18, --max-loops=1M, --tape-limit=5000, --max-steps-per-macro=100k, and --time=1.
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1460718041577951365 discord]
 |-
-|61xxxx
+|style="text-align:center"| Andrew Ducharme
-|Yes
+|19,879,953
-|No
+|19,781,295
-|1,052,047
+|0.50%
-|TBD
+|6269.7
-|TBD
+|
+|
+|style="text-align:left" |Enumerate.py with --block-mult=21, --max-loops=1M, --tape-limit=5000, --max-steps-per-macro=100k, and --time=1.
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1461993117921054720 discord]
 |-
-|62xxxx
+|style="text-align:center"|Andrew Ducharme
-|Yes
+|19,781,295
-|No
+|19,303,801
-|959,753
+|2.41%
-|TBD
+|~2000
-|TBD
+|
+|
+|style="text-align:left" |FAR CPS_LRU maxT 1000000 LRUH 2 H 0 tH 0 n [1-10]
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1464763753072427230 discord]
 |-
-|63xxxx
+|Andrew Ducharme
-|Yes
+|19,303,801
-|No
+|18,306,497
-|1,051,882
+|5.17%
-|TBD
+|~7000
-|TBD
+|
+|
+|style="text-align:left" |FAR CPS_LRU maxT 100000 LRUH 3 H 0 tH 0 n [1-31]
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1469398962325684373 discord]
 |-
-|64xxxx
+|Andrew Ducharme
-|No
+|18,306,497
-|No
+|18,254,547
-|TBD
+|0.28%
-|TBD
+|~3200
-|TBD
+|
+|
+|style="text-align:left" |LRUH 1 H [0,1] tH [0,1] n [1-31]
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1470510369687601375 discord]
 |-
+|Andrew Ducharme
+|18,254,547
+|18,195,716
+|0.32%
+|~4000
 |
-xxxx -<br/>
+|
-xxxx
+|style="text-align:left" |maxT 100000 remaining parameters w/ LRUH 2
-|Terry Ligocki
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1472115313683202189 discord]
-|Yes
-|Yes
-|3,076,778
-|{{TM|1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RG0LD}}
-|10 ↑↑ 192.67
-|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
 |-
-|69xxxx
+|Andrew Ducharme
-|@poppuncher
+|18,195,716
-|Yes
+|18,037,417
-|Yes
+|0.87%
-|1,053,119
+|~2200
-|{{TM|1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG}}
+|
-|10 ↑↑ 133.85
+|
-|[https://drive.google.com/drive/folders/1KlCZqXxqVPuBPkDcCBocuMPA8paq9b8P?usp=drive_link Google Drive folder]
+|style="text-align:left" |maxT 100000 remaining parameters w/ LRUH 3
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1481889113232904295 discord]
 |-
-|70xxxx
+|Andrew Ducharme
-|@hipparcos
+|18,037,417
-|Yes
+|17,823,260
-|Yes
+|1.19%
-|798,304
+|~7200
+|
 |
-{{TM|1RB0LF_1RC1LE_0RD1RA_1RE1RG_0LA1LB_1LE1RG_0RC1RZ}}<br/>
+|maxT 100000 LRUH 4
-{{TM|1RB0LF_1LC1LE_1RE0LD_0LC0LA_1LB1RA_0LG0RC_1RZ0LA}}
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1489495196180942881 discord]
+|-
+| style="text-align:center" |'''Stage 6 Cumulative'''
+|'''20,405,295'''
+|'''17,823,260'''
+|'''12.65%'''
+|'''45809.7'''
+| ---
+| ---
+| ---
+| ---
 |
-↑↑ 33.81<br/>
-↑↑ 26.63
-|[https://github.com/jhuang97/bb7x2/releases/tag/70xxxx Github release]
 |-
-|71xxxx
+| colspan="20" style="text-align:center"|'''Overall'''
-|@hipparcos
+|-
-|No
+| style="text-align:center" |'''Overall Cumulative'''
-|No
+|'''86,129,304'''
-|TBD
+|'''17,823,260'''
-|TBD
+|'''79.31%'''
-|TBD
+|'''93019.8'''
+| ---
+| ---
+| ---
+| ---
 |
 |-
-|75xxxx
+|}
-|Terry Ligocki
-|Yes
+== Phase 3 ==
-|Yes
+Phase 3 is characterized by significant reductions hiding TMs improperly dropped from the holdout list. It began with @David SG using novel GPU-based direct simulation to eliminate halting TMs with step counts under 10^12. However, when a TM with multiple undefined transitions was found to halt, this decider did not enumerate new TNF children, causing the accepted number of holdouts (~16.9M) to be an undercount. Andrew Ducharme applied more mxdys C++ code to eliminate further non-halting TMs. @finlay ran the mxdys inductive decider on the generally accepted holdout list, eliminating a very impressive three million holdouts, a 19.4% reduction. This run also generated, but did not expand, new halting TMs with multiple undefined transitions. This finally triggered an effort reunify the holdout list.
-|1,103,089
-|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0LF_0RA1RE_1RZ1LA}}
+The three main deciders were performed on three different computer clusters with different (and in the case of the GPU run, unknown) number of cores, so the TMs/sec/core columns have been removed. This brought the overall reduction in Phase 2 is so far 28.78%, from ~17.8M to ~12.7M TMs. The details are contained in this table:
-|10 ↑↑ 188.28
+{| class="wikitable sortable" style="text-align: right"
-|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
+! rowspan="2" |Done by
+! colspan="2" |Holdout TMs
+! rowspan="2" |% Reduced
+! rowspan="2" |Compute Time
+(core-hours)
+! rowspan="2" |Description
+! rowspan="2" |Source
+! rowspan="2" |Data
+|-
+!Input
+!Output
+|-
+| style="text-align:center" |@David SG
+|17,823,260
+|16,949,557
+|4.90%
+|Unknown
+|Direct simulation by custom GPU code
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1512553945837605016 discord]
+| rowspan="3" |[https://drive.google.com/drive/folders/1YZNpzqhmVuopX5Qgz8vvcpnY1c7EXax4?usp=sharing Google Drive]
+|-
+| style="text-align:center" |Andrew Ducharme
+|16,949,557
+|15,743,264
+|7.12%
+|~120,000
+| style="text-align:left" |FAR RWL_mod maxT 100000 H [1-4,6,8,12,16] mod [1-6] n [1-10]
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1516364912375627816 discord]
+|-
+|@finlay
+|15,743,264
+|12,693,129
+|19.37%
+|29,000
+|decider --maxT 100000 --exploop --arithseq
+|[https://discord.com/channels/960643023006490684/1369339127652159509/1563950872000467005 Discord]
+|-
+| style="text-align:center" |'''Stage 7 Cumulative'''
+|'''17,823,260'''
+|'''12,693,129'''
+|'''28.78%'''
+|'''>150,000'''
+| ---
+| ---
+| ---
+|}
+Of the 870,000 some TMs found to halt by David SG, 12,378 had multiple undefined transitions. As each transition can represent one of 28 possible rules in BB(7), this meant a growth in the holdout list by 346,584 TMs. Enumeration would have taken significantly, significantly longer without the [https://discord.com/channels/960643023006490684/1369339127652159509/1566834448803045478 assistance of @GameDungeon]. Roughly 22.5% were removed by the reverse engineer filter, i.e., were trivial to solve. Reductions have been performed by Andrew Ducharme. Not all deciders between the point of enumeration and the current holdout list have been run yet.
+{| class="wikitable sortable" style="text-align: right"
+! colspan="2" |Holdout TMs
+! rowspan="2" |% Reduced
+! rowspan="2" |Compute Time
+! rowspan="2" |Description
+|-
+!Input
+!Output
 |-
-|80xxxx
+|346,584
-|@xnoobspeakable
+|268,680
-|Yes
+|22.47%
-|No
+|5 s
-|964,396
+|Reverse_Engineer_Filter.py
-|TBD
-|TBD
-| rowspan="2" |[https://drive.google.com/drive/folders/1TpuEC7KottEmvsFnCREugnlVMPaY5ZHi?usp=sharing Google Drive folder]
 |-
-|81xxxx
+|268,680
-|@xnoobspeakable
+|66,136
-|No
+|75.38%
-|No
+|~500 hours
-|TBD
+| style="text-align:left" |FAR RWL_mod maxT 100000 H [1-4,6,8,12,16] mod [1-6] n [1-10]
-|TBD
+|}
-|TBD
+Only 301 TMs found to halt by @finlay required enumeration, adding 8,428 holdouts. Reductions have been performed by Andrew Ducharme. Not all deciders between the point of enumeration and the current holdout list have been run yet.
+{| class="wikitable sortable" style="text-align: right"
+! colspan="2" |Holdout TMs
+! rowspan="2" |% Reduced
+! rowspan="2" |Compute Time
+! rowspan="2" |Description
 |-
-|83xxxx
+!Input
-|Terry Ligocki
+!Output
-|Yes
-|No
-|1,053,621
-|TBD
-|TBD
-|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
 |-
-|84xxxx
+|8,428
-|Terry Ligocki
+|6,508
-|Yes
+|22.47%
-|Yes
+|<1 s
-|728,138
+|Reverse_Engineer_Filter.py
-|{{TM|1RB0RE_0RC0RB_1LD1LG_1LE0LC_1RA0LF_1LE1LC_1LC1RZ}}
-|10 ↑↑ 47.75
-|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
 |-
+|6,508
 |
-xxxx -<br/>
+|
-xxxxx
+|
-|Terry Ligocki
+| style="text-align:left" |decider --maxT 100000 --exploop --arithseq
-|Yes
-|Yes
-|13,396,923
-|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}}
-|10 ↑↑ 286.17
-|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
 |}
-[[Category:BB Domain]]
+== References ==
+[[Category:BB Domains]][[Category:BB(7)]]
+<references />

BB(7): Difference between revisions

Latest revision as of 10:52, 8 November 2026

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