User:RobinCodes/Work on BB Domains

Progress by domain

As of 26 November 2025:

Only domains with active filtering going on (decider-wise): BB(3x4) Xnoob and Lúkos

Domain	2-state	3-state	4-state	5-state	6-state	7-state	8-state
2-symbol	0	0	0	0 July 2, 2024	1,527 Holdouts list (2+5 informal) Exhausted 15+3 Cryptids found (3 probable)	20,405,295 No Handwork Andrew Ducharme, Terry Ligocki Phase 2, Stage 5	Enumeration started!
3-symbol	0	4+3 Holdouts list Exhausted (3 informal) 1 Cryptid	9,401,447 No Handwork Terry Ligocki Phase 2, Stage 2	???
4-symbol	0 Aug. 22, 2024	15,136,283 No Handwork XnoobSpeakable,Lúkos Phase 2, Stage 8 (in progress)	???
5-symbol	64 Holdouts list Exhausted (11 informal) 2+4 Cryptids (4 probable)	???
6-symbol	870,085 No Handwork Exhausted	???
7-symbol	Enumeration started! 01xxx done (2/100) Expected no. of holdouts: 2'500'000'000
8-symbol

I also wanted to study at what point are domains infeasible with reasonable resources and time, but this is for the future of this page. ???? And after are almost completely unexplored.

Informal and unverified proofs by domain

Unconfirmed, informal proofs of machines for each domain by equivalence class:

Domain	2-state	3-state	4-state	5-state	6-state
2-symbol	0	0	0	0	2
3-symbol	0	4	----	---	---
4-symbol	0	---	---	---	---
5-symbol	9	---	---	---	---

15 total by eqv. class and proof count. 18 by individual machine.

BB(6): 15 November 2025

3 informal (2 informal by eqv. class)

• Racheline:
  1. >1RB0RB_1LB0LC_1RD1LC_1RE0RA_1RF0RB_---1LB
  2. 1RB0RB_1LB0LC_1RD1LC_1RE0RA_0RF0RB_---0LA (equivalence)
• Shawn, star, Pomme, @mxdys: BMO 7

BB(3,3): 25 October 2025

3 informal, 1 unconfirmed by eqv. class and individual

• Legion: (long. analysis) informal
  1. 1RB2LB0LC_2LA2RA1RB_---2LA1LC (1)
  2. 1RB1LC1LC_1LA2RB0RB_2LB---0LA (2)
  3. 1RB0RC---_2RC0LB1LB_2LC2RA2RB (3)

• @furnleaf: 1RB1LB2LC_1LA2RB1RB_---0LA2LA (397) erroneous, currently attempting fix

BB(2,5): 25 October 2025

9 informal, 2 unverified (8 informal, 1 unverified by eqv. class)

• Dyuan:
  1. BMO 3 (2 machines in 1 eqv. class) (source)
  2. 1RB4LA1LB2LA0RB_2LB3RB4LA---1RA (source)
  3. Dekaheptoid, unverified: 1RB3RB1LB---2RB_2LA1RA4LB2LA2RA (source), equivalently 1RB3RA2LB1LB1RB_2LA2RA4LA1LA---
  4. BMO 3 variant: 1RB0RA3LA4LA2RA_2LB3LA---4RA3RB (source)
• Legion:
  1. 1RB2RA3LA4LA2RB_2LA---1LA1RA3RA (1)
  2. 1RB3LA4LA1LA2RA_2LA4RB---0RA0LA (2)
  3. 1RB3LA4LA2RB1LA_2LA4RB---3RA3LA (3)
• Racheline: 1RB2LB---4LB0RB_1LA3RB4RB4RA1LB
• Peacemaker II: 1RB2LA0LB1LA2RA_0LA3RA1RA4LB---