User:XnoobSpeakable/Holdouts-temp: Difference between revisions

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The top table may or may not match the one found at [[Holdouts lists]] depending on the timing of when these lists get updated. I will keep track of the list on this page seperately. The bottom list will include unfinished work that I have noticed on Discord that will not be in other wiki pages.
== Main tables: ==
Top table: compilation of finished work that is almost certainly correct. This table might miss out on more recent changes and small reduction, especially if unverified.
 
Bottom table: compilation of latest progress, even if from unfinished work. More representative of the current state of the various BB domains, however, more likely to include mistakes or unverified work.
 
Note that both tables are full of compromises, some of which are explained in the footnotes. Soon there will be more tables in the "Specialized Tables" section that should solve this problem.
 
'''If you must refer to a single table, you probably want to use the bottom table. The top table can be very outdated.'''
 
CURRENTLY BOTH ARE LIKELY OUTDATED, I WILL UPDATE NOVEMBER 3RD
{| class="wikitable"
{| class="wikitable"
|+Number of holdouts (latest exact counts)
|+Number of holdouts (latest exact counts)
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|-
|-
!2-symbol
!2-symbol
|0
|0<ref name=":2" />
|0
|0<ref name=":2" />
|0
|0<ref name=":2" />
|0
|0<ref name=":2">https://arxiv.org/pdf/2509.12337</ref>
|1691*
|1618*<ref name=":4" />
|23,314,388
|20,405,295<ref name=":3">https://drive.google.com/drive/folders/1-_JHOR89vCIH9RzwDCcoX8JHIz2GwRn0?usp=drive_link</ref>
|-
|-
!3-symbol
!3-symbol
|0
|0<ref name=":2" />
|6***
|6**<ref name=":5">[[BB(3,3)]]</ref>
|97,701,052
|9,401,447<ref name=":6">[[BB(4,3)]]</ref>
|
|
|
|
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|-
|-
!4-symbol
!4-symbol
|0
|0<ref name=":2" />
|434,787,751
|15,136,283<ref name=":3" />
|
|
|
|
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|-
|-
!5-symbol
!5-symbol
|75
|75<ref name=":0">https://discord.com/channels/960643023006490684/1259770421046411285/1411512242498961458</ref>
|
|
|
|
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|-
!6-symbol
!6-symbol
|873,469
|870,085<ref name=":1">https://discord.com/channels/960643023006490684/1084047886494470185/1424584096818135072</ref>
|
|
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<nowiki>*</nowiki>The 1691 holdouts are based on equivalence classes. The amount of individual unsolved TMs in TNF is currently 3171. The holdouts for every other entry use the unsolved TNF TM count as well.
<nowiki>*</nowiki>This count is based on equivalence classes. For the top table, the amount of individual unsolved TMs in TNF is currently 3067. The holdouts for every other entry use the unsolved TNF TM count.
{| class="wikitable"
{| class="wikitable"
|+Number of holdouts (in-progress and approximate values)
|+Number of holdouts (in-progress and approximate values)
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|-
|-
!2-symbol
!2-symbol
|0
|0<ref name=":2" />
|0
|0<ref name=":2" />
|0
|0<ref name=":2" />
|0
|0<ref name=":2" />
|1689* / 3169*
|1615*'''◊''' / 3063*'''◊'''<ref name=":4">https://discord.com/channels/960643023006490684/1239205785913790465/1429892916763033601</ref><ref name=":8">https://discord.com/channels/960643023006490684/1421782442213376000/1431483206208852001</ref><ref name=":7">https://discord.com/channels/960643023006490684/1239205785913790465/1431299260099461140</ref>
|23,314,388
|20,405,295<ref name=":3" />
|-
|-
!3-symbol
!3-symbol
|0
|0<ref name=":2" />
|6***
|6**<ref name=":5" />
|88,914,343
|9,401,447<ref name=":6" />
|
|
|
|
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|-
!4-symbol
!4-symbol
|0
|0<ref name=":2" />
|<434,787,751**
|15,136,283<ref name=":3" />
|
|
|
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|-
!5-symbol
!5-symbol
|75
|75 / 64'''†'''<ref name=":0" /><ref>https://discord.com/channels/960643023006490684/1259770421046411285/1428501877947109437</ref>
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!6-symbol
!6-symbol
|873,469
|870,083'''††'''<ref name=":1" />
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<nowiki>**</nowiki>I am currently working on BB(3,4) and have removed some holdouts, however, the partial progress has not been merged and the reduction has not been counted.
After the work is done, I will upload my results and update the value in the table. I suspect a reduction to ~65M will be achievable.
Said work was supposed to be done by the end of this week as I am typing (which is tomorrow, 2025-09-28), however, I have delayed it to the end of next week, which is 2025-10-05 to those reading in the future.
'''Other technicalities:'''
'''Other technicalities:'''


<nowiki>***</nowiki>This addendum applies to both tables. For BB(3,3), the most commonly accepted value is 6 holdouts<ref>https://discord.com/channels/960643023006490684/1084047886494470185/1421447666889523260</ref>, however, there are other values that I want to highlight in the table below:
<nowiki>**</nowiki>This addendum applies to both tables. For BB(3,3), the most commonly accepted value is 6 holdouts<ref>https://discord.com/channels/960643023006490684/1084047886494470185/1421447666889523260</ref>, however, there are other values that I want to highlight in the table below:
{| class="wikitable"
{| class="wikitable"
!BB(3,3) holdouts
!BB(3,3) holdouts
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|-
|-
!By TNF
!By TNF
|6
|6<ref name=":5" />
|10
|9<ref name=":5" />
|-
!By Equivalence Classes
|4<ref name=":5" />
|7<ref name=":5" />
|}
'''†'''Formal / Informal.
 
'''◊'''For BB(6), it is quite difficult to keep track of in-progress holdout changes, as they are usually posted sporadically or not posted at all. I cannot guarantee the accuracy of these values in the 2nd table. Also note that in table 1, the values are proven (formally verified), but in table 2, some fraction of the reduction in holdouts might be formally verified, while the rest won't be. BB(6) also has the same problem as BB(3,3), with multiple conflicting values, however, I could not find a consensus for the most commonly accepted one.
{| class="wikitable"
!BB(6) holdouts
!Unproven
!Proven
|-
!By TNF
|3063<ref name=":4" /><ref name=":8" /><ref name=":7" />
|3067<ref name=":4" />
|-
|-
!By Equivalence Classes
!By Equivalence Classes
|4
|1615<ref name=":4" /><ref name=":8" /><ref name=":7" />
|Not Applied Yet.
|1618<ref name=":4" />
|}
|}
'''††'''The top two halters have not been solved by automated tools and so are not part of the 870,085 holdouts list, but they are indeed known to halt.<ref>[[BB(2,6)]]</ref>
(A great source for holdouts lists is [https://drive.google.com/drive/folders/1-_JHOR89vCIH9RzwDCcoX8JHIz2GwRn0?usp=drive_link tjligocki's Google Drive folder])
<references />
== Specialized tables: ==
Coming eventually

Latest revision as of 20:41, 2 November 2025

Main tables:

Top table: compilation of finished work that is almost certainly correct. This table might miss out on more recent changes and small reduction, especially if unverified.

Bottom table: compilation of latest progress, even if from unfinished work. More representative of the current state of the various BB domains, however, more likely to include mistakes or unverified work.

Note that both tables are full of compromises, some of which are explained in the footnotes. Soon there will be more tables in the "Specialized Tables" section that should solve this problem.

If you must refer to a single table, you probably want to use the bottom table. The top table can be very outdated.

CURRENTLY BOTH ARE LIKELY OUTDATED, I WILL UPDATE NOVEMBER 3RD

Number of holdouts (latest exact counts)
2-state 3-state 4-state 5-state 6-state 7-state
2-symbol 0[1] 0[1] 0[1] 0[1] 1618*[2] 20,405,295[3]
3-symbol 0[1] 6**[4] 9,401,447[5]
4-symbol 0[1] 15,136,283[3]
5-symbol 75[6]
6-symbol 870,085[7]

*This count is based on equivalence classes. For the top table, the amount of individual unsolved TMs in TNF is currently 3067. The holdouts for every other entry use the unsolved TNF TM count.

Number of holdouts (in-progress and approximate values)
2-state 3-state 4-state 5-state 6-state 7-state
2-symbol 0[1] 0[1] 0[1] 0[1] 1615*◊ / 3063*◊[2][8][9] 20,405,295[3]
3-symbol 0[1] 6**[4] 9,401,447[5]
4-symbol 0[1] 15,136,283[3]
5-symbol 75 / 64†[6][10]
6-symbol 870,083††[7]

Other technicalities:

**This addendum applies to both tables. For BB(3,3), the most commonly accepted value is 6 holdouts[11], however, there are other values that I want to highlight in the table below:

BB(3,3) holdouts Unproven Proven
By TNF 6[4] 9[4]
By Equivalence Classes 4[4] 7[4]

†Formal / Informal.

◊For BB(6), it is quite difficult to keep track of in-progress holdout changes, as they are usually posted sporadically or not posted at all. I cannot guarantee the accuracy of these values in the 2nd table. Also note that in table 1, the values are proven (formally verified), but in table 2, some fraction of the reduction in holdouts might be formally verified, while the rest won't be. BB(6) also has the same problem as BB(3,3), with multiple conflicting values, however, I could not find a consensus for the most commonly accepted one.

BB(6) holdouts Unproven Proven
By TNF 3063[2][8][9] 3067[2]
By Equivalence Classes 1615[2][8][9] 1618[2]

††The top two halters have not been solved by automated tools and so are not part of the 870,085 holdouts list, but they are indeed known to halt.[12]

(A great source for holdouts lists is tjligocki's Google Drive folder)

  1. ↑ 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 https://arxiv.org/pdf/2509.12337
  2. ↑ 2.0 2.1 2.2 2.3 2.4 2.5 https://discord.com/channels/960643023006490684/1239205785913790465/1429892916763033601
  3. ↑ 3.0 3.1 3.2 3.3 https://drive.google.com/drive/folders/1-_JHOR89vCIH9RzwDCcoX8JHIz2GwRn0?usp=drive_link
  4. ↑ 4.0 4.1 4.2 4.3 4.4 4.5 BB(3,3)
  5. ↑ 5.0 5.1 BB(4,3)
  6. ↑ 6.0 6.1 https://discord.com/channels/960643023006490684/1259770421046411285/1411512242498961458
  7. ↑ 7.0 7.1 https://discord.com/channels/960643023006490684/1084047886494470185/1424584096818135072
  8. ↑ 8.0 8.1 8.2 https://discord.com/channels/960643023006490684/1421782442213376000/1431483206208852001
  9. ↑ 9.0 9.1 9.2 https://discord.com/channels/960643023006490684/1239205785913790465/1431299260099461140
  10. ↑ https://discord.com/channels/960643023006490684/1259770421046411285/1428501877947109437
  11. ↑ https://discord.com/channels/960643023006490684/1084047886494470185/1421447666889523260
  12. ↑ BB(2,6)

Specialized tables:

Coming eventually

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