TMBR: August 2025

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Cryptids

A fast algorithm for Consistent Collatz simulation was re-discovered and popularized. Using it:
- apgroucher simulated Antihydra to $2^{38}$ iterations. This is actually a result from one year ago, but was rediscovered and added to the wiki. https://discord.com/channels/960643023006490684/1026577255754903572/1271528180246773883
- Shawn Ligocki simulated 1RB1RA_0RC1RC_1LD0LF_0LE1LE_1RA0LB_---0LC (bbch) out to one additional Collatz reset, demonstrating that (if they halt, which they probviously should) they will have sigma scores $> 1 0^{1 0^{1 0^{7}}}$ .

BB(6) holdouts:
- XnoobSpeakable found 9 new halting TMs in the high exponential runtime range (~10^100000) by running Enumerate.py out to extremely high parameters. https://discord.com/channels/960643023006490684/1239205785913790465/1401470301467836556
- Andrew Ducharme found a couple surprisingly short running halting TMs in the BB(6) holdouts list with runtime ~10^78. https://discord.com/channels/960643023006490684/1239205785913790465/1407754434523693179
TODO: BB(7) holdout list reduced from 86,129,304 to 68,695,205.
BB(3,3) Rocq certified holdout list down to 12. https://discord.com/channels/960643023006490684/1259770474897080380/1409402854292066335

John Tromp introduced the $B B λ_{1} (n)$ function for Busy Beaver for lambda calculus with an oracle and computed it up to $B B λ_{1} (22)$ .
Instruction-Limited Greedy Busy Beaver gBBi(n) and an Instruction-Limited variant of the Blanking Busy Beaver (BLBi(n)) were introduced. gBBi(n) was computed up to n = 13 and BLBi(n) was computed up to n = 7.

Iijil shared an algorithm for converting an arbitrary n-state m-symbol TM into a 2-state TM with 3(n+1)m symbols. https://gist.github.com/Iijil1/0d611dbf0a9d52984f72cb14e66a4b28
Carl K extended his series of videos showing TM simulation accompanied by classical music out to multisymbol TMs:
- Bigfoot: https://youtu.be/YvOHWbQNMoY
- Brady's Surprise in a Box: https://youtu.be/vIG2CvJShRc
- BB(2,5) champ: https://youtu.be/QpYBzYDdLEY