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

Work on BB Domains

	2-state	3-state	4-state	5-state	6-state	7-state
2-symbol	BB(2) = 6	BB(3) = 21	BB(4) = 107	BB(5) = 47,176,870 2 Jul 2024	1414 Holdouts list 16+8 Cryptids, Exhausted	20,405,295 No Handwork Andrew Ducharme, Terry Ligocki Phase 2, Stage 5
3-symbol	BB(2,3) = 38	4 Holdouts list (3 informal) 1 Cryptid, Exhausted	9,401,447 No Handwork Terry Ligocki Phase 2, Stage 2
4-symbol	BB(2,4) = 3,932,964	15,136,283 No Handwork XnoobSpeakable, Lúkos Phase 2, Stage 8 (in progress)
5-symbol	64 Holdouts list (11 informal) 2+4 Cryptids
6-symbol	870,085 No Handwork, Exhausted
7-symbol	Enumeration started! 02xxx done (3/100) Expected no. of holdouts: 3B

Informal and unverified proofs by domain

Unconfirmed, informal proofs of machines for each domain by equivalence class: 15 total

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

14+6 total by eqv. class and proof count. 16+6 by individual machine.

BB(6): 29 November 2025

2+6 informal

• Likely correct: (2)
  • Shawn, star, Pomme, @mxdys: BMO 7
  • mxdys, Pomme, Autumn Pan, vyx^[1][2][3][4]: 1RB1LA_1RC1RE_1LD0RB_1LA0LC_0RF0RD_0RB---
• Very unlikely to be correct: (6), see spreadsheet (Search term: "unverified result").

BB(3,3): 25 October 2025

3 informal

• 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---