Maybe I'm wrong, but it looks like the authors did not actually have any LLMs write or verify any code for their experiments. Instead, their experiments consist of simulating the simplified Markov chain model itself. They simulated their simple Markov chain and checked if the theorem's predictions matched empirical statistics. This amounts to a test not of their model, but of basic Markov chain theory.

Did I misread or miss something?

This line made me pause:

"We prove that for any non-zero stage success probability, the system reaches the verified state almost surely"

What's the point if its still stochastic?