User:XnoobSpeakable/Holdouts-temp: Difference between revisions
No edit summary |
(I -> We) |
||
| (4 intermediate revisions by the same user not shown) | |||
| Line 67: | Line 67: | ||
|0 | |0 | ||
|0 | |0 | ||
| | |1685*'''◊''' / 3165*'''◊''' | ||
|23,314,388 | |23,314,388 | ||
|- | |- | ||
| Line 73: | Line 73: | ||
|0 | |0 | ||
|6*** | |6*** | ||
| | |84,066,821<ref>https://discord.com/channels/960643023006490684/1084047886494470185/1421959456161267806</ref> | ||
| | | | ||
| | | | ||
| Line 102: | Line 102: | ||
| | | | ||
|} | |} | ||
<nowiki>**</nowiki>I | <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, | 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 | Said work was supposed to be done by 2025-09-28, however, I have delayed the deadline to 2025-10-05. | ||
'''Other technicalities:''' | '''Other technicalities:''' | ||
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.
| 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.
| 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.
- ↑ https://arxiv.org/pdf/2509.12337
- ↑ https://discord.com/channels/960643023006490684/1239205785913790465/1419290767767240734
- ↑ https://discord.com/channels/960643023006490684/1369339127652159509/1421418186145792092
- ↑ https://drive.google.com/drive/folders/11ei0G8izILonMHH62e8ev0F8ur8S5Yft
- ↑ https://drive.google.com/drive/folders/1bZxl7jg5q9IVvHQNZwItx1kPusAWznZk
- ↑ 6.0 6.1 https://discord.com/channels/960643023006490684/1259770421046411285/1411512242498961458
- ↑ https://discord.com/channels/960643023006490684/1084047886494470185/1419506101912866937
- ↑ https://discord.com/channels/960643023006490684/1084047886494470185/1421959456161267806
- ↑ https://discord.com/channels/960643023006490684/1084047886494470185/1419658118505169039
- ↑ https://discord.com/channels/960643023006490684/1084047886494470185/1419663299640823828
- ↑ 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.