User:RobinCodes/Work on BB Domains

Progress by domain

As of 26 November 2025:

Only domains with active filtering going on (decider-wise): None

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	1342 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	14,518,243 No Handwork XnoobSpeakable, Lúkos Phase 2, Stage 8
5-symbol	64 Holdouts list (11 informal) 2+4 Cryptids
6-symbol	870,085 No Handwork, Exhausted
7-symbol	Enumeration started! 04xxx done (5/100) Expected no. of holdouts: 3B Current: 150M

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	1+6
3-symbol	0	3	----	---	---
4-symbol	0	---	---	---	---
5-symbol	9	---	---	---	---

13+6=19 total by eqv. class and proof count. 15+6=21 by individual machine.

BB(6): 16 December 2025

1+6 informal

• Likely correct: (1)
  • 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---