User:XnoobSpeakable/Holdouts-temp: Difference between revisions

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(temporary page for keeping track of holdouts)
 
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== Main tables: ==
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.
{| class="wikitable"
|+Number of holdouts (latest exact counts)
!
!2-state
!3-state
!4-state
!5-state
!6-state
!7-state
|-
!2-symbol
|0
|0
|0
|0<ref>https://arxiv.org/pdf/2509.12337</ref>
|1691*<ref>https://discord.com/channels/960643023006490684/1239205785913790465/1419290767767240734</ref>
|23,314,388<ref>https://discord.com/channels/960643023006490684/1369339127652159509/1421418186145792092</ref>
|-
!3-symbol
|0
|6***
|97,701,052<ref>https://drive.google.com/drive/folders/11ei0G8izILonMHH62e8ev0F8ur8S5Yft</ref>
|
|
|
|-
!4-symbol
|0
|434,787,751<ref>https://drive.google.com/drive/folders/1bZxl7jg5q9IVvHQNZwItx1kPusAWznZk</ref>
|
|
|
|
|-
!5-symbol
|75<ref name=":0">https://discord.com/channels/960643023006490684/1259770421046411285/1411512242498961458</ref>
|
|
|
|
|
|-
!6-symbol
|873,469<ref>https://discord.com/channels/960643023006490684/1084047886494470185/1419506101912866937</ref>
|
|
|
|
|
|}
<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.
{| class="wikitable"
{| class="wikitable"
|+Number of holdouts
|+Number of holdouts (in-progress and approximate values)
!
!
!2-state
!2-state
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|0
|0
|0
|0
|2,592
|1685*'''◊''' / 3165*'''◊'''
|28,189,617
|23,314,388
|-
|-
!3-symbol
!3-symbol
|0
|0
|6
|6***
|460,916,384
|84,066,821<ref>https://discord.com/channels/960643023006490684/1084047886494470185/1421959456161267806</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
|1,688,951
|873,469
|
|
|
|
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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.
<references />
== Other: ==
There will be specific tables here for values by TNF, Equivalence Classes, and for proven and unproven results, like the small BB(3,3) table in the section above.

Latest revision as of 16:00, 29 September 2025

Main tables:

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.

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] 23,314,388[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. 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.

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 1685*◊ / 3165*◊ 23,314,388
3-symbol 0 6*** 84,066,821[8]
4-symbol 0 <434,787,751**[9]
5-symbol 75 / 68†[6]
6-symbol 873,469

**Lúkos[10] 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[11], 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.

  1. ↑ https://arxiv.org/pdf/2509.12337
  2. ↑ https://discord.com/channels/960643023006490684/1239205785913790465/1419290767767240734
  3. ↑ https://discord.com/channels/960643023006490684/1369339127652159509/1421418186145792092
  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. ↑ https://discord.com/channels/960643023006490684/1084047886494470185/1419506101912866937
  8. ↑ https://discord.com/channels/960643023006490684/1084047886494470185/1421959456161267806
  9. ↑ https://discord.com/channels/960643023006490684/1084047886494470185/1419658118505169039
  10. ↑ https://discord.com/channels/960643023006490684/1084047886494470185/1419663299640823828
  11. ↑ https://discord.com/channels/960643023006490684/1084047886494470185/1421447666889523260

Other:

There will be specific tables here for values by TNF, Equivalence Classes, and for proven and unproven results, like the small BB(3,3) table in the section above.

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