[matheist]

Agreed. It's straightforward to check that a token was the argmax, but it seems difficult to check that a token appeared with the probability you wanted it to. You could still do the fine-tuning step I guess, where you train the trajectories to approach n-token completions with the statistics you want, but I can't see how you can replace the "check for a fixed point" step. Maybe "check the result was above this fixed threshold for likelihood".