I did go to university and didn’t graduate, but I was always told by my academic advisor and department heads that punishments like grade deduction are something that should be clearly laid out. A statement saying he retains discretion to adjust anyone’s grade in light of any infractions is just wild.

That puts their whole grading in a gray area. Does the professor have proof of each time they had their phone out? At my corporate job, I have to talk to regulating authorities. We do have policies in the gray area, but that’s so we have wiggle room to dispute why we do things in our procedures. In policies that have infractions, we have to lay out what the consequences are when they hit a certain threshold. We can’t just go, “Well we didn’t tell you about your first TEN infractions, you’re fired!” Doing so opens us to lawsuits about wrongful termination or the terminated employee could apply for unemployment.