The program this fits into was not started by us nor was it proposed by a Large Language Model. (…) We took their work as a starting point, using Large Language Models to push their program to completion.

Thats how most people use LLMs? If I was back in my student days working in Navier-Stokes, I guess I would also punch at blow ups. The number of students doing this at the same time, posting open efforts to GitHub then retraining of the models. If there is solutions to the problem, it’s a real possibility that it was not a result of this effort?

Using a large amount of tokens is not a good augment that it’s not likely others have done the same. Good questions is the difference between $10 and $10M in token usage to solve a problem.