User:XnoobSpeakable/Holdouts-temp: Difference between revisions

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BB(4,3) exact value
BB(4,3), add citations wherever possible
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|0<ref>https://arxiv.org/pdf/2509.12337</ref>
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|1691*<ref>https://discord.com/channels/960643023006490684/1239205785913790465/1419290767767240734</ref>
|1691*<ref>https://discord.com/channels/960643023006490684/1239205785913790465/1419290767767240734</ref>
|22,721,168<ref>https://discord.com/channels/960643023006490684/1369339127652159509/1423806362072256676</ref>
|22,721,168<ref name=":3">https://drive.google.com/drive/folders/1-_JHOR89vCIH9RzwDCcoX8JHIz2GwRn0?usp=drive_link</ref>
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|1674*'''◊''' / 3150*'''◊'''
|1674*'''◊''' / 3150*'''◊'''<ref name=":4">https://discord.com/channels/960643023006490684/1239205785913790465/1425515232540889170</ref>
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'''††'''The top two halters ([[BB(2,6)]]) 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.
'''††'''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.


Also, a great source for holdouts lists is [https://drive.google.com/drive/folders/1-_JHOR89vCIH9RzwDCcoX8JHIz2GwRn0?usp=drive_link tjligocki's Google Drive folder]
(A great source for holdouts lists is [https://drive.google.com/drive/folders/1-_JHOR89vCIH9RzwDCcoX8JHIz2GwRn0?usp=drive_link tjligocki's Google Drive folder])
<references />
<references />


== Specialized tables: ==
== Specialized tables: ==
Coming soon.
Coming soon.

Revision as of 15:17, 10 October 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.

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] 1691*[2] 22,721,168[3]
3-symbol 0[1] 6** 33,860,069[3]
4-symbol 0[1] 22,396,711[3]
5-symbol 75[4]
6-symbol 870,085[5]

*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[1] 0[1] 0[1] 0[1] 1674*◊ / 3150*◊[6] 22,721,168[3]
3-symbol 0[1] 6** 33,860,069[3]
4-symbol 0[1] 22,396,711[3]
5-symbol 75 / 68†[4]
6-symbol 870,083††[5]

Other technicalities:

**This addendum applies to both tables. For BB(3,3), the most commonly accepted value is 6 holdouts[7], however, there are other values that I want to highlight in the table below:

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

†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 3150[6] 3153[6]
By Equivalence Classes 1674[6] 1676[6]

††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.

(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. ↑ https://discord.com/channels/960643023006490684/1239205785913790465/1419290767767240734
  3. ↑ 3.0 3.1 3.2 3.3 3.4 3.5 https://drive.google.com/drive/folders/1-_JHOR89vCIH9RzwDCcoX8JHIz2GwRn0?usp=drive_link
  4. ↑ 4.0 4.1 https://discord.com/channels/960643023006490684/1259770421046411285/1411512242498961458
  5. ↑ 5.0 5.1 https://discord.com/channels/960643023006490684/1084047886494470185/1424584096818135072
  6. ↑ 6.0 6.1 6.2 6.3 6.4 https://discord.com/channels/960643023006490684/1239205785913790465/1425515232540889170
  7. ↑ https://discord.com/channels/960643023006490684/1084047886494470185/1421447666889523260

Specialized tables:

Coming soon.

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