TMBR: May 2026
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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
General Recursive Functions: TODO: Further progress
- Some new cryptids were hand-built:
- Size 56, by Shawn on 2 May (simulating 5x+1 problem starting at 7).[1]
- Size 49, by aparker, star and Shawn on 3 May (simulating Brocard's problem).[2]
- The first non-trivial divergent GRF was found (size 15). It halts iff there exists some n ≥ 1 such that n+3 divides .[3] aparker[4] and star[5] proved that there is no such n.
TODO
TODO: Check for other BB-like functions' progress
TODO: Fractran progress
TODO: BBCS
Misc
- mxdys made his inductive decider for history-linear machines compilable into an executable file.[6]
- TODO: BB Bignum Bakeoff
Holdouts
| Domain | Previous Holdout Count | New Holdout Count | Holdout Reduction | % Reduction |
|---|---|---|---|---|
| BB(4,3) | 5,641,006 | 5,127,263 | 513,743 | 9.11% |
| BB(3,4) | 12,049,358 | 11,362,197 | 687,161 | 5.70% |
| BB(2,5) | 66 | 65 | 1 | 1.52% |
| BB(2,6) | 536,112 | 413,513 | 122,599 | 22.87% |
- BB(2,5)
- Andrew Ducharme found a FAR solution for a machine, which previously had an informal nonhalting argument. On June 1st, mxdys provided the Rocq proof, reducing the Rocq-holdout count to 65.
- BB(4,3)
- Andrew Ducharme reduced the number of holdouts from 5,641,006 to 5,127,263, a 9.11% reduction, with mxdys's new inductive decider.[7]
- BB(3,4)
- XnoobSpeakable completed Stage 2 of Phase 3, reducing to number of holdouts from 12,049,358 to 11,362,197, a 5.70% reduction.
- BB(2,6)
- Andrew Ducharme reduced the number of holdouts from 536,112 to 527,232 via Enumerate.py and TM-enum, a 1.66% reduction.[8][9]
- Using the new inductive decider by mxdys and TM-enum, Andrew Ducharme first reduced the number of holdouts from 527,232 to 501,914[10][11], then to 439,120 again using the inductive decider.[12] In total this was a 16.71% reduction.
- Using FAR, Andrew Ducharme further reduced the number of holdouts from 439,120 to 418,127, a 4.78% reduction.
- Using some mxdys deciders, Andrew Ducharme continued reducing the number of holdouts through May 17, from 418,127 to 413,513 (a 1.10% reduction).[13][14][15][16]
- BB(2,7)
- Terry Ligocki enumerated 130K more subtasks, increasing the number of holdouts to 1,087,732,936. A total of 350K subtasks out of the 1 million subtasks (or 35%) have been enumerated.[17]