User:RobinCodes/Work on BB Domains: Difference between revisions

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== Progress by domain ==
== Progress by domain ==
As of 26 November 2025:
As of 30 December 2025:
 
<code>Domains with active filtering going on (decider-wise): BB(2,6), BB(7) - Andrew Ducharme</code> 


<code>Only domains with active filtering going on (decider-wise): BB(3x4) Xnoob and Lúkos</code> 
{| class="wikitable"
{| class="wikitable"
|+
|+ Work on BB Domains
!Domain
! !!2-state!!3-state !!4-state!!5-state!!6-state  
!2-state
!3-state
!4-state
!5-state
!6-state
!7-state
!7-state
!'''8-state'''
|-
|-
! 2-symbol  
!2-symbol
| [[BB(2)]] = 6
|0
| [[BB(3)]] = 21
|0
| [[BB(4)]] = 107
|0
| [[BB(5)]] = 47,176,870
|0
2 Jul 2024
July 2, 2024
| style="background: orange;" | 1299
|1,527
[https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=1330361301#gid=1330361301 Holdouts list]
[https://docs.google.com/spreadsheets/d/10y2aMp9yZVLyN-nXAxgA25rw4EA_lJqn3Vxy2kB-m-U/ Holdouts list]
16+8 Cryptids, Exhausted
(2+5 informal)
| style="background: orange;" | 18,195,192
Exhausted
 
15+3 Cryptids found
 
(3 probable)
|20,405,295
No Handwork
No Handwork
Andrew Ducharme,
Andrew Ducharme,
Terry Ligocki
Terry Ligocki
Phase 2, Stage 5
Phase 2, Stage 6
|Enumeration started!
|-
|-
!3-symbol
! 3-symbol
|0
| [[BB(2,3)]] = 38
|4+3
| style="background: orange;" | 4
[[BB(3,3)#Holdouts|Holdouts list]]
[[BB(3,3)#Holdouts|Holdouts list]]  
Exhausted
 
(3 informal)
(3 informal)
 
1 Cryptid, Exhausted
1 Cryptid
| style="background: #ffe4b2;" | 9,401,447
| 9,401,447
No Handwork  
No Handwork  
Terry Ligocki Phase 2, Stage 2
Terry Ligocki Phase 2, Stage 2
|???
| style="background: #ffe4b2;" |
|
| style="background: #ffe4b2;" |
|
| style="background: #ffe4b2;" |
|
|-
|-
!4-symbol
! 4-symbol
|0
| [[BB(2,4)]] = 3,932,964
Aug. 22, 2024
| style="background: #ffe4b2;" | 12,435,284
|15,136,283
No Handwork  
No Handwork  
[[User:XnoobSpeakable|XnoobSpeakable,]][[User:WarpedWartWars|Lúkos]]
[[User:XnoobSpeakable|XnoobSpeakable,]] [[User:WarpedWartWars|Lúkos]]


Phase 2, Stage 8 (in progress)
Phase 2, Stage 10C
|???
| style="background: #ffe4b2;" |
|
| style="background: #ffe4b2;" |
|
| style="background: #ffe4b2;" |
|
| style="background: #ffe4b2;" |
|
|-
|-
!5-symbol
! 5-symbol  
|64
| style="background: orange;" | 61
[[BB(2,5)#Holdouts|Holdouts list]]
[[BB(2,5)#Holdouts|Holdouts list]]
Exhausted
(11 informal)
(11 informal)


2+4 Cryptids (4 probable)
2+4 Cryptids
|???
| style="background: #ffe4b2;" |[[BB(3,5)]]
|
| style="background: #ffe4b2;" |
|
| style="background: #ffe4b2;" |
|
| style="background: #ffe4b2;" |
|
| style="background: #ffe4b2;" |
|
|-
|-
!6-symbol
! 6-symbol  
|870,085
| style="background: #ffe4b2;" | 556,814
No Handwork
Andrew Ducharme,
Exhausted
Terry Ligocki
|???
No Handwork, Exhausted
|
| style="background: #ffe4b2;" |
|
| style="background: #ffe4b2;" |
|
| style="background: #ffe4b2;" |
|
| style="background: #ffe4b2;" |
|
| style="background: #ffe4b2;" |
|-
|-
!7-symbol
!7-symbol
|Enumeration started!
| style="background: #ffe4b2;" |Enumeration started!
00xxx done.
09xxx done
Expected no. of holdouts: 2'500'000'000
 
|
(10/100)
|
 
|
Expected no. of holdouts: 3B
|
 
|
Current: 300M
|
| style="background: #ffe4b2;" |
|-
| style="background: #ffe4b2;" |
!8-symbol
| style="background: #ffe4b2;" |
|
| style="background: #ffe4b2;" |
|
| style="background: #ffe4b2;" |
|
|
|
|
|
|}
|}
<small>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.</small>
 
== 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 ==
== Informal and unverified proofs by domain ==
'''Unconfirmed, informal proofs of machines for each domain by equivalence class:'''
'''Unconfirmed, informal proofs of machines for each domain by equivalence class: 16 total'''
{| class="wikitable"
{| class="wikitable"
!Domain
!Domain
Line 128: Line 106:
|0
|0
|0
|0
|2
|'''4'''
|-
|-
!3-symbol
!3-symbol
|0
|0
|4
|'''3'''
| ----
| ----
| ---
| ---
Line 145: Line 123:
|-
|-
!5-symbol
!5-symbol
|9
|'''9'''
| ---
| ---
| ---
| ---
Line 151: Line 129:
| ---
| ---
|}
|}
<small>15 total by eqv. class and proof count. 18 by individual machine.</small>
<small>'''16''' total by eqv. class and proof count. 18 by individual machine.</small>


=== [[BB(6)]]: 15 November 2025 ===
=== [[BB(6)]]: 7 February 2025 ===


===== 3 informal (2 informal by eqv. class) =====
===== 4 informal =====


* [https://discord.com/channels/960643023006490684/1239205785913790465/1431225455557611611 Racheline]:
* Likely correct: (4)
*# >1RB0RB_1LB0LC_1RD1LC_1RE0RA_1RF0RB_---1LB
** <s>[https://discord.com/channels/960643023006490684/1421782442213376000/1431483206208852001 Shawn, star, Pomme, @mxdys]: BMO 7 verified</s>
*# 1RB0RB_1LB0LC_1RD1LC_1RE0RA_0RF0RB_---0LA (equivalence)
** mxdys, Pomme, Autumn Pan, vyx<sup>[https://discord.com/channels/960643023006490684/1239205785913790465/1441124403801755730 <nowiki>[1]</nowiki>][https://discord.com/channels/960643023006490684/1443295684878143579/1443295684878143579 <nowiki>[2]</nowiki>][https://discord.com/channels/960643023006490684/1443295684878143579/1444047803935490190 <nowiki>[3]</nowiki>][https://discord.com/channels/960643023006490684/1443295684878143579/1444051070186819836 <nowiki>[4]</nowiki>]</sup>: <code>1RB1LA_1RC1RE_1LD0RB_1LA0LC_0RF0RD_0RB---</code>
* [https://discord.com/channels/960643023006490684/1421782442213376000/1431483206208852001 Shawn, star, Pomme, @mxdys]: BMO 7
** 3 more machines that halt. (See [https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=1330361301#gid=1330361301 spreadsheet] labeled as (?))


=== [[BB(3,3)]]: 25 October 2025 ===
=== [[BB(3,3)]]: 25 October 2025 ===


===== 3 informal, 1 unconfirmed by eqv. class and individual =====
===== 3 informal =====


* Legion: ([[Longitudinal Analysis|long. analysis]]) informal
* Legion: ([[Longitudinal Analysis|long. analysis]]) informal
Line 171: Line 149:
*# 1RB0RC---_2RC0LB1LB_2LC2RA2RB ([https://discord.com/channels/960643023006490684/1084047886494470185/1256729514076016733 3])
*# 1RB0RC---_2RC0LB1LB_2LC2RA2RB ([https://discord.com/channels/960643023006490684/1084047886494470185/1256729514076016733 3])


* [https://discord.com/channels/960643023006490684/1259770474897080380/1430531925315031172 @furnleaf]: 1RB1LB2LC_1LA2RB1RB_---0LA2LA (397) erroneous, [https://discord.com/channels/960643023006490684/1259770474897080380/1430557898269790248 currently attempting fix]
* [https://discord.com/channels/960643023006490684/1259770474897080380/1430531925315031172 @furnleaf]: 1RB1LB2LC_1LA2RB1RB_---0LA2LA (397) ''erroneous'', [https://discord.com/channels/960643023006490684/1259770474897080380/1430557898269790248 currently attempting fix]


=== [[BB(2,5)]]: 25 October 2025 ===
=== [[BB(2,5)]]: 25 October 2025 ===

Latest revision as of 18:45, 15 February 2026

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

1299

Holdouts list 16+8 Cryptids, Exhausted

18,195,192

No Handwork Andrew Ducharme, Terry Ligocki Phase 2, Stage 6

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 12,435,284

No Handwork XnoobSpeakable, Lúkos

Phase 2, Stage 10C

5-symbol 61

Holdouts list (11 informal)

2+4 Cryptids

BB(3,5)
6-symbol 556,814

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: 16 total

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

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

BB(6): 7 February 2025

4 informal

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)

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---
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