TMBR: September 2026

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This Month in Beaver Research

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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

TODO: Cyclic Tag

Holdouts

• BB(6)
  • By September 4, mxdys solved all 16 Counter Class 1 TMs.^[1]
  • On September 4, Discord user fifi_49513 claimed to have proven a TM non-halting. ^[2] This machine was later confirmed non-halting in Rocq on September 5 by mxdys. ^[3]
  • On September 14, an independent computation by Seiji extended the Space Needle trajectory to 100,000,000 terms: no power of 2 was ever encountered, and the most factors of 2 any term had was 25 (first occurring at n = 23,145,881; the previously documented state was >17,000,000 terms with max 24). The full final value (94,125,050 bits) is published with SHA-256 anchors, together with 400 checkpoints cross-verified by two independent implementations, and exact macro step-count laws of the machine (L0–L4; L1 and L3 formally proven). ^[4]
• BB(2,7)
  • Terry Ligocki enumerated 25K more subtasks, increasing the number of holdouts to 2,873,381,794. A total of 920K subtasks out of the 1 million subtasks (or 92%) have been enumerated.

Misc

• On September 5, XnoobSpeakable began an opt-in archival project of the bbchallenge Discord server ^.[5]