User:XnoobSpeakable/Holdouts-temp: Difference between revisions

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Temporary page for keeping track of holdouts
== 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.
{| class="wikitable"
{| class="wikitable"
|+Number of holdouts (latest exact counts)
|+Number of holdouts (latest exact counts)
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|0
|0
|0
|0
|0
|0<ref>https://arxiv.org/pdf/2509.12337</ref>
|1691
|1691*<ref>https://discord.com/channels/960643023006490684/1239205785913790465/1419290767767240734</ref>
|23,314,388
|22,801,601<ref>https://discord.com/channels/960643023006490684/1369339127652159509/1422298181693079743</ref>
|-
|-
!3-symbol
!3-symbol
|0
|0
|6
|6***
|460,916,384
|97,701,052<ref>https://drive.google.com/drive/folders/11ei0G8izILonMHH62e8ev0F8ur8S5Yft</ref>
|
|
|
|
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!4-symbol
!4-symbol
|0
|0
|434,787,751
|434,787,751<ref>https://drive.google.com/drive/folders/1bZxl7jg5q9IVvHQNZwItx1kPusAWznZk</ref>
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|-
!5-symbol
!5-symbol
|83
|75<ref name=":0">https://discord.com/channels/960643023006490684/1259770421046411285/1411512242498961458</ref>
|
|
|
|
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|-
|-
!6-symbol
!6-symbol
|873,469
|873,469<ref name=":1">https://discord.com/channels/960643023006490684/1084047886494470185/1419506101912866937</ref>
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<nowiki>*</nowiki>The 1691 holdouts are based on equivalence classes. For the top table, the amount of individual unsolved TMs in TNF is currently 3171. The holdouts for every other entry use the unsolved TNF TM count.
{| class="wikitable"
{| class="wikitable"
|+Number of holdouts (in-progress and approximate values)
!
!
!2-state
!2-state
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|0
|0
|0
|0
|1691
|1684*'''◊''' / 3164*'''◊'''
|23,314,388
|22,801,601
|-
|-
!3-symbol
!3-symbol
|0
|0
|6
|6***
|~96.6M
|50,835,926<ref>https://discord.com/channels/960643023006490684/1084047886494470185/1422325962980196392</ref>
|
|
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!4-symbol
!4-symbol
|0
|0
|434,787,751
|<434,787,751**<ref>https://discord.com/channels/960643023006490684/1084047886494470185/1419658118505169039</ref>
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!5-symbol
!5-symbol
|83
|75 / 68'''†'''<ref name=":0" />
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!6-symbol
!6-symbol
|873,469
|873,468<ref name=":1" /><ref>https://discord.com/channels/960643023006490684/1084047886494470185/1422203693268205699</ref>
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<nowiki>**</nowiki>[[User:WarpedWartWars|Lúkos]]<ref>https://discord.com/channels/960643023006490684/1084047886494470185/1419663299640823828</ref> and I are 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, we will upload our 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 2025-09-28, however, I have delayed the deadline to 2025-10-05.
'''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:
{| class="wikitable"
!BB(3,3) holdouts
!Unproven
!Proven
|-
!By TNF
|6
|10
|-
!By Equivalence Classes
|4
|Not Applied Yet.
|}
'''†'''For BB(2,5), the situation is similar to BB(3,3), but the other way around. The most commonly accepted value is 75, the formally proven value, and the 68 value uses informal proofs.
'''◊'''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, besides the outdated 1691 from the top table.
{| class="wikitable"
!BB(6) holdouts
!Unproven
!Proven
|-
!By TNF
|3164
|3166
|-
!By Equivalence Classes
|1684
|1686
|}
Note that in the table above, the holdout counts in the unproven columns might be even lower, however, I cannot check every page, post and message looking for potential solved TMs.
<references />
== Specialized tables: ==
Coming soon.

Latest revision as of 17:13, 30 September 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.

Number of holdouts (latest exact counts)
2-state 3-state 4-state 5-state 6-state 7-state
2-symbol 0 0 0 0[1] 1691*[2] 22,801,601[3]
3-symbol 0 6*** 97,701,052[4]
4-symbol 0 434,787,751[5]
5-symbol 75[6]
6-symbol 873,469[7]

*The 1691 holdouts are based on equivalence classes. For the top table, the amount of individual unsolved TMs in TNF is currently 3171. 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 0 0 0 1684*◊ / 3164*◊ 22,801,601
3-symbol 0 6*** 50,835,926[8]
4-symbol 0 <434,787,751**[9]
5-symbol 75 / 68†[6]
6-symbol 873,468[7][10]

**Lúkos[11] and I are 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, we will upload our 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 2025-09-28, however, I have delayed the deadline to 2025-10-05.

Other technicalities:

***This addendum applies to both tables. For BB(3,3), the most commonly accepted value is 6 holdouts[12], however, there are other values that I want to highlight in the table below:

BB(3,3) holdouts Unproven Proven
By TNF 6 10
By Equivalence Classes 4 Not Applied Yet.

†For BB(2,5), the situation is similar to BB(3,3), but the other way around. The most commonly accepted value is 75, the formally proven value, and the 68 value uses informal proofs.

◊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, besides the outdated 1691 from the top table.

BB(6) holdouts Unproven Proven
By TNF 3164 3166
By Equivalence Classes 1684 1686

Note that in the table above, the holdout counts in the unproven columns might be even lower, however, I cannot check every page, post and message looking for potential solved TMs.

  1. ↑ https://arxiv.org/pdf/2509.12337
  2. ↑ https://discord.com/channels/960643023006490684/1239205785913790465/1419290767767240734
  3. ↑ https://discord.com/channels/960643023006490684/1369339127652159509/1422298181693079743
  4. ↑ https://drive.google.com/drive/folders/11ei0G8izILonMHH62e8ev0F8ur8S5Yft
  5. ↑ https://drive.google.com/drive/folders/1bZxl7jg5q9IVvHQNZwItx1kPusAWznZk
  6. ↑ 6.0 6.1 https://discord.com/channels/960643023006490684/1259770421046411285/1411512242498961458
  7. ↑ 7.0 7.1 https://discord.com/channels/960643023006490684/1084047886494470185/1419506101912866937
  8. ↑ https://discord.com/channels/960643023006490684/1084047886494470185/1422325962980196392
  9. ↑ https://discord.com/channels/960643023006490684/1084047886494470185/1419658118505169039
  10. ↑ https://discord.com/channels/960643023006490684/1084047886494470185/1422203693268205699
  11. ↑ https://discord.com/channels/960643023006490684/1084047886494470185/1419663299640823828
  12. ↑ https://discord.com/channels/960643023006490684/1084047886494470185/1421447666889523260

Specialized tables:

Coming soon.

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