User:RobinCodes/Work on BB Domains

Progress by domain

As of 30 December 2025:

Domains with active filtering going on (decider-wise): BB(2,6), BB(7) - Andrew Ducharme

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	1201 Holdouts list 16+6 Cryptids, Exhausted	18,036,852 No Handwork Andrew Ducharme, Terry Ligocki Phase 2, Stage 6
3-symbol	BB(2,3) = 38	4 Holdouts list 1 Cryptid, Exhausted	9,401,447 No Handwork Terry Ligocki Phase 2, Stage 2
4-symbol	BB(2,4) = 3,932,964	12,435,284 No Handwork XnoobSpeakable, Lúkos Phase 2, Stage 10C
5-symbol	60 Holdouts list (11 informal) 2+4 Cryptids	BB(3,5)
6-symbol	548,993 Andrew Ducharme, Terry Ligocki No Handwork, Exhausted
7-symbol	Enumeration started! 09xxx done (10/100) Expected no. of holdouts: 3B Current: 300M

Enumeration

The enumeration process for BB(2,7) has started, and 5% has so far been completed. BB(8) is (tested from a random sample) even harder to enumerate. These processes will take a very long time and much collaborative work to complete. As for BB(3x5), BB(4x4), BB(5x3), enumeration may still be possible, but also incredibly difficult. Any domains after these are probably complete out-of-reach of current technology.

Informal and unverified proofs by domain

Unconfirmed, informal proofs of machines for each domain by equivalence class: 13 total

Domain	2-state	3-state	4-state	5-state	6-state
2-symbol	0	0	0	0	2
3-symbol	0	0	----	---	---
4-symbol	0	---	---	---	---
5-symbol	11	---	---	---	---

13 by individual machine. 11 total by eqv. class and proof count.

BB(6): 1 March 2026

2 informal

• Likely correct: (2)
  • Shawn, star, Pomme, @mxdys: BMO 7 verified
  • mxdys, Pomme, Autumn Pan, vyx^[1][2][3][4]: 1RB1LA_1RC1RE_1LD0RB_1LA0LC_0RF0RD_0RB---
  • 1RB0RC_0LC0LB_0LD1LC_0LE1LA_0LF---_1RF1RA (halt, Racheline)

BB(3,3): 1 March 2026

None

BB(2,5): 1 March 2026

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---