I definitely agree with those who say that Haruto should just give the finger to the principal.
She set the bounds... pretty broadly... then she walks them all back. Including the one she named explicitly.
If she can do this, she can't be trusted with anything else, including the basic promise to let Haruto skip classes.
(She has her reasons, but she should have thought that out more deeply before setting the terms.)
To begin with, it's already suspicious that her request is for Haruto to do what elite adults couldn't. For a pretty weak reward.
"Do what nobody ever could and I'll reward you with the right to skip classes... but you'll still have to do research work for the school."
Basically, a lose-lose for Haruto. Assuming he succeeds, he'll stand out and he'll still have to attend school anyway. Less formally, but still.
This is not a test, it's actual work. With the reward being more work instead of education.
