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Apropos of nothing - a random HP thought.
Where does half the fandom get the impression that Harry is cheating by using a book with notes in it?
They are allowed to use their book while brewing and are supposed to have read up on the potion they are preparing in class.
And in written tests, I doubt they are allowed to use their books anyway, so the notes won't be any help to him there.
The only difference I see between Harry and a Ravenclaw (in this instance) is that the Ravenclaw would have made the notes himself - and probably not in the book, but on a spare bit of paper.

no subject
It's not as if there were whole essays written on the margins of the book. More improvements on the potions the like of which could probably be found in more up to date potions texts.
In the chapter where actual understanding of the concepts is required, *no one* in the whole class but Hermione has any idea what to do, so I don't think the actual underlying principles are something that's often mentioned in class.
So all the advantage Harry has in most lessons is an improved recipe. Which he could have come by himself if he actually did the work.
Of course, he is lazy, but that doesn't mean he's cheating.
(And I certainly used the scribbled in answers in my English textbooks to answer the teacher's questions. As long as it wasn't during an exam, I fail to see how that's cheating.
I might regret it now, because it didn't do me much good for actually learning the language, but it's not cheating.)