TMBR: July 2026: Difference between revisions

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→Holdouts: Updated BB(4,3)
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* A new champion was discovered for Ξ₀(12).
* A new champion was discovered for Ξ₀(12).
* New champions were discovered for Ξ₀_SK(12), Ξ₀_SK(13), Ξ₀_SK(14), Ξ₀_SK(15), Ξ₀_SK(16) and Ξ₀_SK(17).
* New champions were discovered for Ξ₀_SK(12), Ξ₀_SK(13), Ξ₀_SK(14), Ξ₀_SK(15), Ξ₀_SK(16) and Ξ₀_SK(17).
TODO: update
[[Lambda Calculus]]:
[[Lambda Calculus]]:
* [https://discord.com/channels/960643023006490684/1355653587824283678/1528855324881326181 BBλ(40) was solved] on 20 July, showing that BBλ(40) <math>\approx 10\uparrow\uparrow\uparrow 16</math>. BBλ(40) is the first solved domain in any BB variant to reach pentational values.
* [https://discord.com/channels/960643023006490684/1355653587824283678/1528855324881326181 BBλ(40) was solved] on 20 July, showing that BBλ(40) <math>\approx 10\uparrow\uparrow\uparrow 16</math>. BBλ(40) is the first solved domain in any BB variant to reach pentational values.

Revision as of 15:50, 28 July 2026

Prev: June 2026 This Month in Beaver Research Next: August 2026

This edition of TMBR is in progress and has not yet been released. Please add any notes you think may be relevant (including in the form a of a TODO with a link to any relevant Discord discussion).

BB Adjacent

SKI Calculus:

  • A new champion was discovered for Ξ₀(12).
  • New champions were discovered for Ξ₀_SK(12), Ξ₀_SK(13), Ξ₀_SK(14), Ξ₀_SK(15), Ξ₀_SK(16) and Ξ₀_SK(17).

TODO: update Lambda Calculus:

  • BBλ(40) was solved on 20 July, showing that BBλ(40) ≈10↑↑↑16. BBλ(40) is the first solved domain in any BB variant to reach pentational values.

TODO: Post Tag System

Holdouts

  • BB(6):
  • BB(4,3):
    • Andrew Ducharme reduced the number of holdouts from 4,784,443 to 4,747,566, a 0.77% reduction.[3][4]
  • BB(2,7):
    • Terry Ligocki enumerated 140K more subtasks, increasing the number of holdouts to 2,061,161,825. A total of 660K subtasks out of the 1 million subtasks (or 66%) have been enumerated.