User:RobinCodes/Work on BB Domains

Progress by domain

As of 25 October 2025:

Only domains with active filtering going on (decider-wise): BB(7) Terry Ligocki

Domain	2-state	3-state	4-state	5-state	6-state	7-state	8-state
2-symbol	0	0	0	0 July 2, 2024	1,616 (2 informal) Exhausted 15 Cryptids found	22,721,168 Phase 2, Stage 4	???
3-symbol	0	4+3 Exhausted (3 informal) 1 Cryptid	9,401,447 Terry Ligocki Phase 2, Stage 2	???
4-symbol	0 Aug. 22, 2024	15,564,491 XnoobSpeakable and Lúkos currently filtering Phase 2, Stage 6	???
5-symbol	66 Exhausted (9 informal) 2+4 Cryptids (4 probable)	???
6-symbol	870,085 Exhausted	???
7-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	3
3-symbol	0	1	----	---	---
4-symbol	0	---	---	---	---
5-symbol	9	---	---	---	---

13 total by eqv. class

BB(6): 25 October 2025

3 informal, 1 unconfirmed (2 informal 1 unconfirmed by eqv. class)

• Bricks / Shawn Ligocki: 1RB1RF_0LC1RC_1RD1LC_---0RE_1RA1LF_1RA0LE NONHALT (verified by quick_sim.py)
• Racheline:
  1. >1RB0RB_1LB0LC_1RD1LC_1RE0RA_1RF0RB_---1LB
  2. 1RB0RB_1LB0LC_1RD1LC_1RE0RA_0RF0RB_---0LA (equivalence)
• Shawn, star, Pomme, @mxdys: BMO 7, unconfirmed

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. Skelet 17-like 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---