Only read the abstract, but if as I suspect it is using nested directories as "cells" in the "tape", the proof will require directories to be able to nest arbitrarily deep (which maybe some filesystems already permit; but even if all existing filesystems have some finite limit, this would not be considered an obstacle to the result, since it's certainly possible to construct a filesystem where directory nesting level is limited only by storage size). That's because it needs to be able to simulate a Turing Machine, which could read and write an infinite amount of storage.

Then, there just needs to be a way to force find to stop in some finite amount of time -- that's the halting state. I don't know what mechanism they use for that, but if I were trying to do this, I would lean towards looking for a way to make it error out.

If you upload to arxiv, there are explicit instructions which tell you what latex commands work and which don’t for the abstract. The authors didn’t read those instructions.

Doom Complete

Can Find and Mkdir write to any kind of graphical output? And take any kind of input?

For a TM, you nees the ability to write and read in some kind of list and a finite state automata that is driven by what’s in the list. The bar is very low.