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

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Page to collect the BB Domains and their status. Holdout counts are machines that do not have a formal Rocq proof.
== Progress by domain ==
As of 26 November 2025:


As of 28/09/2025
<code>Only domains with active filtering going on (decider-wise): BB(3x4) Xnoob and Lúkos</code> 
 
{| class="wikitable"
|+ 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
| style="background: orange;" | 1414
[https://docs.google.com/spreadsheets/d/10y2aMp9yZVLyN-nXAxgA25rw4EA_lJqn3Vxy2kB-m-U/ Holdouts list]
16+8 Cryptids, Exhausted
| style="background: orange;" | 20,405,295
No Handwork
Andrew Ducharme,
Terry Ligocki
Phase 2, Stage 5
|-
! 3-symbol
| [[BB(2,3)]] = 38
| style="background: orange;" | 4
[[BB(3,3)#Holdouts|Holdouts list]]
(3 informal)
1 Cryptid, Exhausted
| style="background: #ffe4b2;" | 9,401,447
No Handwork
Terry Ligocki Phase 2, Stage 2
| style="background: #ffe4b2;" |
| style="background: #ffe4b2;" |
| style="background: #ffe4b2;" |
|-
! 4-symbol 
| [[BB(2,4)]] = 3,932,964
| style="background: #ffe4b2;" | 15,136,283
No Handwork
[[User:XnoobSpeakable|XnoobSpeakable,]] [[User:WarpedWartWars|Lúkos]]
 
Phase 2, Stage 8 (in progress)
| style="background: #ffe4b2;" |
| style="background: #ffe4b2;" |
| style="background: #ffe4b2;" |
| style="background: #ffe4b2;" |
|-
! 5-symbol
| style="background: orange;" | 64
[[BB(2,5)#Holdouts|Holdouts list]]
(11 informal)
 
2+4 Cryptids
| style="background: #ffe4b2;" |
| style="background: #ffe4b2;" |
| style="background: #ffe4b2;" |
| style="background: #ffe4b2;" |
| style="background: #ffe4b2;" |
|-
! 6-symbol
| style="background: #ffe4b2;" | 870,085
No Handwork, Exhausted
| style="background: #ffe4b2;" |
| style="background: #ffe4b2;" |
| style="background: #ffe4b2;" |
| style="background: #ffe4b2;" |
| style="background: #ffe4b2;" |
|-
!7-symbol
| style="background: #ffe4b2;" |Enumeration started!
02xxx done
 
(3/100)
 
Expected no. of holdouts: 3B
| style="background: #ffe4b2;" |
| style="background: #ffe4b2;" |
| style="background: #ffe4b2;" |
| style="background: #ffe4b2;" |
| style="background: #ffe4b2;" |
|}
== Informal and unverified proofs by domain ==
'''Unconfirmed, informal proofs of machines for each domain by equivalence class: 15 total'''
{| class="wikitable"
{| class="wikitable"
|+
!Domain
!Domain
!2-state
!2-state
<nowiki>------------------</nowiki>
!3-state
!3-state
!4-state
!4-state
!5-state
!5-state
!6-state
!6-state
!7-state
!'''8-state'''
!'''9-state'''
!'''10-state'''
|-
|-
!2-symbol
!2-symbol
|0 Holdouts
|0
|0 Holdouts
|0
|0 Holdouts
|0
|0 Holdouts
|0
July 2, 2024
|2+6
|1,691 Holdouts
|23,314,388 Holdouts, Phase 2 Stage 3 completed.
|Unexplored
|Unexplored
|???
|-
|-
!3-symbol
!3-symbol
|0 Holdouts
|0
|4+4 Holdouts BB3x3 month October
|3
(4 informal [[Longitudinal Analysis|longitudinal]] proofs by @Legion)
| ----
1 Cryptid
| ---
|88,914,343
| ---
|???
|
|
|
|
|
|-
|-
!4-symbol
!4-symbol
|0 Holdouts
|0
Aug. 22, 2024
| ---
|434,787,751[[User:XnoobSpeakable|XnoobSpeakable]] and Lúkos currently filtering
| ---
|???
| ---
|
| ---
|
|
|
|
|
|-
|-
!5-symbol
!5-symbol
|75 Holdouts
|9
Exhausted (decider-wise)
| ---
Some informal proofs exist
| ---
2+4 Cryptids (4 probable)
| ---
|???
| ---
|
|
|
|
|
|
|
|-
!6-symbol
|873,469 Holdouts
Exhausted (decider-wise)
|???
|
|
|
|
|
|
|
|-
!7-symbol
|????
|
|
|
|
|
|
|
|
|}
|}
<small>'''14'''+6 total by eqv. class and proof count. 16+6 by individual machine.</small>
=== [[BB(6)]]: 29 November 2025 ===
===== 2+6 informal =====
* Likely correct: (2)
** [https://discord.com/channels/960643023006490684/1421782442213376000/1431483206208852001 Shawn, star, Pomme, @mxdys]: BMO 7
** 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>: 1RB1LA_1RC1RE_1LD0RB_1LA0LC_0RF0RD_0RB---
* Very unlikely to be correct: (6), see [https://docs.google.com/spreadsheets/d/10y2aMp9yZVLyN-nXAxgA25rw4EA_lJqn3Vxy2kB-m-U spreadsheet] (Search term: "unverified result").
=== [[BB(3,3)]]: 25 October 2025 ===
===== 3 informal =====
* Legion: ([[Longitudinal Analysis|long. analysis]]) informal
*# 1RB2LB0LC_2LA2RA1RB_---2LA1LC ([https://discord.com/channels/960643023006490684/1259770474897080380/1290044219481657476 <small>1</small>])
*# 1RB1LC1LC_1LA2RB0RB_2LB---0LA ([https://discord.com/channels/960643023006490684/1259770474897080380/1279055891559223399 2])
*# 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]
=== [[BB(2,5)]]: 25 October 2025 ===
===== 9 informal, 2 unverified (8 informal, 1 unverified by eqv. class) =====
* Dyuan:
*# [[Beaver Math Olympiad#3. 1RB0RB3LA4LA2RA 2LB3RA---3RA4RB (bbch) and 1RB1RB3LA4LA2RA 2LB3RA---3RA4RB (bbch)|BMO 3]] (2 machines in 1 eqv. class) ([https://discord.com/channels/960643023006490684/1084047886494470185/1252634913220591728 source])
*# 1RB4LA1LB2LA0RB_2LB3RB4LA---1RA ([https://discord.com/channels/960643023006490684/1259770421046411285/1290449717536489622 source])
*# Dekaheptoid, unverified: [[1RB3RB1LB---2RB_2LA1RA4LB2LA2RA]] ([https://discord.com/channels/960643023006490684/1259770421046411285/1267650177389432913 source]), equivalently 1RB3RA2LB1LB1RB_2LA2RA4LA1LA---
*# BMO 3 variant: 1RB0RA3LA4LA2RA_2LB3LA---4RA3RB ([https://discord.com/channels/960643023006490684/1259770421046411285/1415337575543214132 source])
* Legion:
*# 1RB2RA3LA4LA2RB_2LA---1LA1RA3RA (<small>[https://discord.com/channels/960643023006490684/1084047886494470185/1254518334406266964 1]</small>)
*# 1RB3LA4LA1LA2RA_2LA4RB---0RA0LA ([https://discord.com/channels/960643023006490684/1084047886494470185/1254518334406266964 2])
*# 1RB3LA4LA2RB1LA_2LA4RB---3RA3LA ([https://discord.com/channels/960643023006490684/1084047886494470185/1254518334406266964 3])
* [https://discord.com/channels/960643023006490684/1259770421046411285/1329663999700111471 Racheline]: 1RB2LB---4LB0RB_1LA3RB4RB4RA1LB
* [https://discord.com/channels/960643023006490684/1259770421046411285/1428501877947109437 Peacemaker II]: 1RB2LA0LB1LA2RA_0LA3RA1RA4LB---

Latest revision as of 11:59, 29 November 2025

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

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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